RU2518007C1 - Ionospheric signal direction-finding method - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: new minimum base antenna system is formed. The maximum value of the two-dimensional beam pattern $$U\left({\alpha }_s^{\text{'}},{\beta }_s^{\text{'}}\right)$$

of the minimum base antenna system is used to estimate, in conditions of receiving two beams, a stable single-beam value of the azimuth $${\alpha }_s^{\text{'}}$$

and elevation angle $${\text{β}}_{\text{s}}^{\text{'}}\text{,}$$

that solution is further refined by a two-beam solution

within a limited four-dimensional area $${\alpha }_1^{\text{'}}={\alpha }_s^{\text{'}}\pm 10\mathrm{deg}rees,$$

$${\alpha }_2^{\text{'}}={\alpha }_s^{\text{'}}\pm 10\mathrm{deg}rees,$$

$${\beta }_1^{\text{'}}={\beta }_s^{\text{'}}\pm 10\mathrm{deg}rees,$$

$${\beta }_2^{\text{'}}={\beta }_s^{\text{'}}\pm 10\mathrm{deg}rees.$$

The two-dimensional beam pattern $$U\left({\alpha }_s^{\text{'}},{\beta }_s^{\text{'}}\right)$$

is formed using a certain computation expression. The region for determining the stable single-beam solution $${\alpha }_s^{\text{'}}$$

$${\beta }_s^{\text{'}}$$

is the azimuth interval 0-360 degrees and the elevation angle interval 0-90 degrees. Stability of estimates of the azimuth and elevation angle and a wide frequency range are provided by using a phase difference of two adjacent dipoles ψn+1-Ψn when forming the two-dimensional beam pattern of the antenna system.

EFFECT: shorter time for determining angular parameters of a two-beam ionospheric signal.

10 dwg

Description

The invention relates to radio engineering, and in particular to the field of direction finding, and can be used for direction finding (azimuth measurement) and measuring elevation angles of ionospheric signals under the conditions of reception of one or two interfering rays in a wide frequency range. When receiving ionospheric signals, as a rule, several rays are reflected at the receiving point, reflected from different layers of the ionosphere, with azimuths located in the main lobe of the radiation pattern (~ 5 ÷ 10 degrees). Due to the interference of the rays, the total main lobe of the radiation pattern of the antenna system, consisting of the sum of the radiation patterns of the individual rays, varies significantly. As a result, false bearings arise, which differ from true bearings by tens of degrees. The presence of false bearings significantly reduces the reliability of the received information about the azimuth and elevation angle of the ionospheric signal.

. В условиях приема двух близких по азимуту лучей фазовые способы пеленгации являются неустойчивыми. При разности фаз между лучами ~180° они дают отклонения пеленга на десятки градусов (ложные пеленги), что значительно снижает достоверность оценок азимутов и углов места ионосферных сигналов.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. 2263327, published October 27, 2005; Patent RU No. 2365931, published August 27, 2009; RU patent 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 to determine the angular parameters of the signal. 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 $${\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n<\frac{\mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="00000105.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}{2}$$

. Under conditions of receiving two rays close in azimuth, the phase direction finding methods are unstable. With a phase difference between the rays of ~ 180 °, they give bearing deviations of tens of degrees (false bearings), which significantly reduces the reliability of estimates 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. 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):

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

Where:

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

, $${\widehat{E}}_n$$

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

,

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

- 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

$$U^2\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right)=\frac{{\overline{E_n\cos \left({\psi }_n-\overline{K}\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right){\overline{R}}_n\right)}}^2+{\overline{E_n\sin \left({\psi }_n-\overline{K}\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right){\overline{R}}_n\right)}}^2}{{\overline{E}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="00000105.png"\; state="\{\{state\}\}">n</figure-callout>}}^2},\left(2\right)$$

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

The disadvantage of the direction finding methods for the maximum radiation pattern of the antenna system associated with the spatial Fourier transform is the instability of the solution in the presence of two 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. 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 requirements for the accuracy of bearing measurement in the low-frequency part of the range (3 ÷ 4 MHz) determine the base of the antenna system R≥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.

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.

Known methods of 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 interfering rays, false bearings may occur, which significantly reduces the reliability of estimates of azimuths and elevation angles of ionospheric signals.

The closest (prototype) to the proposed method of direction finding when receiving both one beam and two rays of 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 It includes the following sequence of actions.

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, 3) amplify through a multi-channel receiver. Analog signals at the output of a 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 between the rays according to the expressions.

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

Where

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

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

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

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

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

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

- коэффициент корреляции между лучами, $$\widehat{A}\mathrm{one}$$

- 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, запоминая значения параметров $${\alpha }_1^{\text{'}}$$

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

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

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

, $${\widehat{U}}_1$$

, $${\widehat{U}}_2$$

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

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

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

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

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

, $${\widehat{U}}_{\mathrm{one}}$$

, $${\widehat{U}}_2$$

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

. The azimuth and elevation of each beam 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.The disadvantage of this method is the high complexity, the duration of the calculations 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.

The block diagram of this method of direction finding (prototype) is presented in figure 1. According to this method of direction finding, the sequence of actions is as follows.

, расположенных на поверхности земли равномерно по окружности радиуса R $$(R\ge \frac{2\pi }{3\left|{\overline{k}}_1\left({\alpha }_{01},{\beta }_{01}\right)-{\overline{k}}_2\left({\alpha }_{02},{\beta }_{02}\right)\right|})$$

(блок 1). Круговые антенные системы характеризуются максимальным частотным диапазоном. Количество вибраторов определяется количеством параметров ионосферного сигнала и требуемым отношением сигнал/шум. Радиус антенной системы определяется размером интерференционной структуры поля на поверхности земли.1. Receive signals using a circular antenna system consisting of N-vibrators $$(N\ge \text{A.}N\mathrm{one}+\frac{\mathrm{one}}{(\mathrm{one}-{|\; |\; |\tilde{A}\mathrm{one}|\; |\; |}^2},N\mathrm{one}=8)$$

located on the surface of the earth evenly around a circle of radius R $$(R\ge \frac{2\mathrm{<figure-callout\; id="3"\; label="\pi "\; filenames="00000105.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{3|\; |\; |{\overline{k}}_{\mathrm{one}}\left({\mathrm{<figure-callout\; id="01"\; label="\alpha "\; filenames="00000104.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{01},{\beta }_{01}\right)-{\overline{k}}_2\left({\mathrm{<figure-callout\; id="02"\; label="\alpha "\; filenames="00000104.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{02},{\beta }_{02}\right)|\; |\; |})$$

(block 1). Circular antenna systems are characterized by a maximum frequency range. The number of vibrators is determined by the number of parameters of the ionospheric signal and the required signal-to-noise ratio. The radius of the antenna system is determined by the size of the interference structure of the field on the earth's surface.

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

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

и запоминают ее значения и значений переменных $${\widehat{U}}_1$$

, $${\widehat{U}}_2$$

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

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

and remember its values and variable values $${\widehat{U}}_{\mathrm{one}}$$

, $${\widehat{U}}_2$$

(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 $${\widehat{U}}_1={\widehat{U}}_{01}$$

, $${\widehat{U}}_2={\widehat{U}}_{02}$$

(блок 7).7. 0 determine the maximum value of the four-dimensional radiation pattern and fix the parameters $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}={\mathrm{<figure-callout\; id="01"\; label="\alpha "\; filenames="00000104.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{01}$$

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

, $${\alpha }_2^{\text{'}\text{'}}={\mathrm{<figure-callout\; id="02"\; label="\alpha "\; filenames="00000104.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{02}$$

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

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

, $${\widehat{U}}_2={\widehat{U}}_{02}$$

(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 (technical result) is to reduce the time for calculating the angular parameters of a two-beam ionospheric signal in the prototype "Method of direction finding taking into account the correlation between the rays."

антенной системы с минимальной базой оценивают устойчивое (отсутствие ложных пеленгов) однолучевое, в условиях приема двух лучей, значение азимута $${\alpha }_y^{\text{'}}$$

и угла места $${\beta }_y^{\text{'}}$$

. Далее это решение уточняют двулучевым решением по выражениям (3) в пределах ограниченной четырехмерной площадки $${\alpha }_1^{\text{'}}={\alpha }_y^{\text{'}}\pm 10градусов$$

, $${\alpha }_2^{\text{'}}={\alpha }_y^{\text{'}}\pm 10градусов$$

, $${\beta }_1^{\text{'}}={\beta }_y^{\text{'}}\pm 10градусов$$

, $${\beta }_2^{\text{'}}={\beta }_y^{\text{'}}\pm 10градусов$$

. Двумерную диаграмму направленности $$U\left({\alpha }_y^{\text{'}},{\beta }_y^{\text{'}}\right)$$

формируют по оригинальному выражению (4), отличному от известного выражения для диаграммы направленности (2)The technical result is achieved by the fact that algorithmically form an additional antenna system with a minimum base. By the maximum value of the two-dimensional radiation pattern $$U\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)$$

antenna systems with a minimum base estimate stable (absence of false bearings) single-beam, in terms of receiving two rays, the azimuth value $${\alpha }_y^{\text{'}\text{'}}$$

and elevation $${\beta }_y^{\text{'}\text{'}}$$

. Further, this solution is specified by a two-beam solution according to expressions (3) within a limited four-dimensional area $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}={\alpha }_y^{\text{'}\text{'}}\pm 10gR\mathrm{but}d\mathrm{at}\mathrm{from}\mathrm{about}\mathrm{at}$$

, $${\alpha }_2^{\text{'}\text{'}}={\alpha }_y^{\text{'}\text{'}}\pm 10gR\mathrm{but}d\mathrm{at}\mathrm{from}\mathrm{about}\mathrm{at}$$

, $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}={\beta }_y^{\text{'}\text{'}}\pm 10gR\mathrm{but}d\mathrm{at}\mathrm{from}\mathrm{about}\mathrm{at}$$

, $${\beta }_2^{\text{'}\text{'}}={\beta }_y^{\text{'}\text{'}}\pm 10gR\mathrm{but}d\mathrm{at}\mathrm{from}\mathrm{about}\mathrm{at}$$

. Two-dimensional radiation pattern $$U\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)$$

form according to the original expression (4), different from the known expression for the radiation pattern (2)

, $$U^2\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)=\frac{2\overline{E_{n+\mathrm{one}}{E}_n\cos \left[{\psi }_{n+\mathrm{one}}-{\psi }_n+\overline{K}\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)\left({\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n\right)\right]}}{\overline{E_{n+\mathrm{one}}^2}+\overline{{\mathrm{<figure-callout\; id="2"\; label="E\; n"\; filenames="00000105.png"\; state="\{\{state\}\}">E\; </figure-callout>}}_n^{}}}\left(\mathrm{four}\right)$$

,

Where:

E _n , Ψ _n - amplitude and phase, measured on an n-vibrator,

R _n - radius vector that determines the location of the vibrator,

- волновой вектор ионосферного сигнала в условиях двулучевого приема, $$\overline{K}\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)$$

- wave vector of the ionospheric signal in the conditions of two-beam reception,

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

- оценочные азимут и угол места ионосферного сигнала устойчивые в условиях двух лучевого приема. $${\alpha }_y^{\text{'}\text{'}}$$

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

- estimated azimuth and elevation angle of the ionospheric signal are stable under two beam reception conditions.

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

является интервал азимутов 0÷360 градусов и интервал углов места 0÷90 градусов. Устойчивость оценок азимута и угла места и широкий частотный диапазон обеспечиваются использованием при формировании двумерной диаграммы направленности (4) разности фаз двух соседних вибраторов ψ_n+1-ψ_n.The scope of a sustainable single-beam solution $${\alpha }_y^{\text{'}\text{'}}$$

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

is the azimuth interval 0 ÷ 360 degrees and the interval of elevation angles 0 ÷ 90 degrees. The stability of the azimuth and elevation estimates and the wide frequency range are ensured by using the phase difference of two adjacent vibrators ψ _{n + 1} -ψ _n when forming a two-dimensional radiation pattern (4).

The reduction of the calculation time is ensured by the fact that the most laborious calculation of the four-dimensional radiation pattern according to expression (3) is performed on a limited site, and not on the entire angular range of azimuths and elevation angles.

The rationale for a stable single-beam direction finding method in the conditions of double-beam reception is the following.

в комплексной форме в видеRecord the signal on the n-vibrator $${\widehat{E}}_n$$

in complex form as

$${\widehat{E}}_n=\widehat{U}{e}^{-i\overline{K}\left({\alpha }_{0y},{\beta }_{0y}\right){\overline{R}}_n}\left(5\right)$$

- комплексная амплитуда,Where $$\widehat{U}$$

- complex amplitude

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

- wave vector of the ionospheric signal,

α _0y , β _0y - stable values of azimuth and elevation angle of the ionospheric signal in the conditions of two beam reception,

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

- location of the n-vibrator.

, тогдаIn expression (5), we change the index “and” by one and exclude $$\widehat{U}$$

then

$${\widehat{E}}_{n+\mathrm{one}}={\widehat{E}}_n{e}^{-i\overline{K}\left({\alpha }_{0y},{\beta }_{0y}\right)\left({\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n\right)}\left(6\right)$$

Based on expression (6), we compose the likelihood functional

$$\Delta \left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)={{\displaystyle \sum _{n=\mathrm{one}}^N|\; |\; |{\widehat{E}}_{n+\mathrm{one}}-{\widehat{E}}_n{e}^{i\overline{K}\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)\left({\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n\right)}|\; |\; |}}^2\left(7\right)$$

When squaring (7) we get:

$$\Delta \left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)=\overline{E_{n+\mathrm{one}}^2}+\overline{{\mathrm{<figure-callout\; id="2"\; label="E\; n"\; filenames="00000105.png"\; state="\{\{state\}\}">E\; </figure-callout>}}_n^{}}-2\overline{E_{n+\mathrm{one}}{E}_n\cos \left[{\psi }_{n+\mathrm{one}}-{\psi }_n+\overline{K}\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)\left({\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n\right)\right]}\left(8\right)$$

The bar above means summation over N-vibrators (at index n).

When normalizing (8) to the sum of the first two terms, we obtain:

$${\Delta }_{\mathrm{one}}\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)=\mathrm{one}-\frac{2\overline{E_{n+\mathrm{one}}{E}_n\cos \left[{\psi }_{n+\mathrm{one}}-{\psi }_n+\overline{K}\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)\left({\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n\right)\right]}}{\overline{E_{n+\mathrm{one}}^2}+\overline{{\mathrm{<figure-callout\; id="2"\; label="E\; n"\; filenames="00000105.png"\; state="\{\{state\}\}">E\; </figure-callout>}}_n^{}}}\left(9\right)$$

The second term in (9) determines the square of the normalized radiation pattern (4).

$$U^2\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)=\frac{2\overline{E_{n+\mathrm{one}}{E}_n\cos \left[{\psi }_{n+\mathrm{one}}-{\psi }_n+\overline{K}\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)\left({\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n\right)\right]}}{\overline{E_{n+\mathrm{one}}^2}+\overline{{\mathrm{<figure-callout\; id="2"\; label="E\; n"\; filenames="00000105.png"\; state="\{\{state\}\}">E\; </figure-callout>}}_n^{}}}$$

подобрать так, чтобы аргумент косинуса в (4) был близок нулю, тогда $$U\left({\alpha }_y^{\text{'}},{\beta }_y^{\text{'}}\right)$$

будет близко к максимуму, к единице.If the wave vector $$\overline{K}\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)$$

choose so that the cosine argument in (4) is close to zero, then $$U\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)$$

will be close to maximum, to unity.

определяет в диаграмме направленности (4) новую базу антенной системы (фиг.4), и диаграмма направленности будет более широкой. Это способствует увеличению устойчивости решения в области высоких частот ~20÷30 МГц.Of fundamental importance for the stability of the solution is the presence of a difference in the measured phases on adjacent vibrators ψ _{n + 1} -ψ _n in expression (4). It significantly reduces the dependence of azimuth and elevation on the phase difference of individual rays of the ionospheric signal. In addition, the difference of radius vectors $${\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n$$

determines in the radiation pattern (4) the new base of the antenna system (figure 4), and the radiation pattern will be wider. This contributes to an increase in the stability of the solution in the high frequency region ~ 20–30 MHz.

The essence of the method 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 of direction finding is implemented. Compared with the prototype, four action blocks are added related to the assessment of stable azimuth and elevation values.

Figure 3 presents the location of the vibrators of the antenna system on the surface of the earth. The diameter of the circle is 130 m, the number of vibrators is 16.

Figure 4 shows the location of the vibrators of the new antenna system with a minimum base. The diameter of the circle in this case is 50.72 m., The number of vibrators remains equal to 16. The phase distribution on the vibrators of the new antenna system is ψ _{n + 1} -ψ _n .

Using model calculations, we compare solutions (2) and (4). We will call solution (2) the Fourier method, and solution (4) the single-beam maximum likelihood method.

Figure 5 shows the azimuthal radiation pattern calculated according to (4) (solid line) under the condition of a two-beam field with azimuths of 78 ° and 73 ° and a phase difference between the rays of 180 °. The main lobe of the radiation pattern is larger in amplitude than the side lobes. Bearing (azimuth) is determined correctly. When calculating the radiation pattern according to the expression (2) (dashed line in FIG. 5), the main lobe of the radiation pattern is suppressed as a result of interference of two rays. The side lobe (α ~ 160 °) significantly exceeds the main lobe in amplitude. As a result, the bearing will be ~ 160 °.

Figure 6 shows the elevation radiation pattern obtained by the Fourier method (by expression (2)) and the maximum likelihood method (by expression (4)). The operating frequency is 10 MHz (λ = 30 m). As a result of the interference of two rays, the main lobe of the radiation pattern determined by the Fourier method is suppressed. Under these conditions, the elevation angle will be zero, which is incorrect. The radiation pattern determined by the maximum likelihood method allows you to determine the elevation angle β = 15 °. The model value of the elevation angles of the two rays is 10 ° and 30 °, the azimuth is 76 °, and the phase difference is 180 °.

Figure 7 shows the changes in azimuths depending on the phase difference between the rays. Dots indicate the azimuths obtained by the Fourier method (expression (2)). In the region Δφ ~ 180 °, the azimuths strongly deviate from the true values. The line shows the azimuth obtained by the maximum likelihood method (expression (4)). It is equal to 76 °. This is the average azimuth of two rays, and it is practically independent of the phase difference. When the amplitude ratio changes, this azimuth changes from 78 ° to 73 °.

On Fig shows the changes in elevation depending on the phase difference of the two rays. The elevation angle determined by the Fourier method (points, expression (2)) in the region of 180 ° of the phase difference has strong deviations. The elevation angle determined by the maximum likelihood method (expression (4)) almost does not change when the phase difference between the rays changes. Thus, the new processing algorithm can significantly reduce the dependence of the solution of the problem of estimating azimuths and elevation angles on the phase difference in the case of two-beam reception.

Figure 9 shows the frequency dependence of azimuths. In the model calculations, two beams with azimuths of 76 and 78 degrees are specified. Added noise component. The calculation of stable azimuth values was carried out in accordance with the expression (4) (Line with a triangular marker (row 3)). The azimuths of the first and second rays were calculated in accordance with expression (3) (Line with dots and solid line). As can be seen from the figure, the stable azimuths are within the azimuths of the first and second rays. False azimuths are not observed in the entire frequency range of 2–30 MHz. The calculation time in accordance with the prototype is about three hours on a Pentium type computer. The calculation time in accordance with the proposed method is 0.5 s.

Figure 10 shows the frequency range of changes in stable elevation angles (line with triangular markers, row 3). The signal model contains two beams with elevation angles of 30 ° and 10 °. The frequency dependences of the estimated elevation angles determined by the proposed method are represented by a solid line (row 1, a beam with an elevation angle of 10 degrees) and a line with point markers (row 2, a ray with an elevation angle of 30 degrees). In these calculations, stable elevation angles are located in a region bounded by elevation angles of the first and second rays. Significant deviations in elevation angles are not noted.

The proposed method of direction finding (Figure 2) is as follows.

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 at the output 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 and phases of the signals from each vibrator (in each channel), for example using a temporary Fourier transform (block 4).

, их местоположение определяется радиус вектором $${\overline{R}}_{n+1}-{\overline{R}}_n$$

, а пространственные фазы значениями ψ_n+1-ψ_n (блок 5).5. Create an algorithmically new antenna system with a minimum base, the vibrators of which are located in a circle with a radius $$|\; |\; |{\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n|\; |\; |$$

, their location is determined by the radius of the vector $${\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n$$

, and the spatial phases with the values ψ _{n + 1} -ψ _n (block 5).

6. Set a point in the space of estimated azimuths (0 ÷ 360 °) and elevation angles (0 ÷ 90 °) and calculate according to (4) at the point the value of the two-dimensional radiation pattern from the data sample and the estimated wave vector of the beam and store the values, (block 6 )

7. Repeat steps (6) with other values of the parameters from the domain of their determination (0 ÷ 360 ° in azimuth and 0 ÷ 90 ° in elevation) and create a surface in two-dimensional space of azimuths and elevation angles (two-dimensional radiation pattern) (block 7) .

8. Determine the maximum value of the two-dimensional radiation pattern and fix the parameters (block 8).

и переменные $${\alpha }_1^{\text{'}}$$

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

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

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

и значение четырехмерной диаграммы направленности по выборке данных и оценочным волновым векторам двух лучей (блок 9).9. Set a point on a limited four-dimensional platform of estimated azimuths and elevations and calculate according to (3) at $$\hat{U}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right)$$

and variables $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}$$

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

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

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

and the value of the four-dimensional radiation pattern from the data sample and the estimated wave vectors of the two rays (block 9).

10. Repeat actions (9) with other values of the parameters and from the domain of their determination (limited four-dimensional area) and create a part of the surface in the four-dimensional space of azimuths and elevation angles (four-dimensional radiation pattern near the maximum) (block 10).

, $${\hat{U}}_{02}$$

(блок 11).11. Determine the maximum value of the four-dimensional radiation pattern and fix the parameters α ₀₁ , α ₀₂ , β ₀₁ , β ₀₂ , $${\hat{U}}_{01}$$

, $${\hat{U}}_{02}$$

(block 11).

и оставляют решения, удовлетворяющие данному условию (блок 12).12. Determine the rank of the field (single-beam or double-beam) by condition $$\frac{U_{01}}{{\mathrm{<figure-callout\; id="02"\; label="U"\; filenames="00000104.png"\; state="\{\{state\}\}">U</figure-callout>}}_{02}}\ge 3$$

and leave decisions that satisfy this condition (block 12).

The calculation of azimuths and elevations according to the proposed method is reduced by five orders of magnitude compared with the calculation time for the prototype. According to the results of model calculations, the technical result of the proposed method of direction finding is quite achieved.

Taking into account all the above, it can be argued that the goal is to reduce the calculation time of azimuths and elevation angles of the ionospheric signal under two-beam reception due to a preliminary assessment of stable azimuth and elevation angles is fully achieved while maintaining high accuracy estimates of azimuths and elevation angles of the first and second rays.

Claims (1)

A method for detecting ionospheric signals, including receiving an ionospheric signal 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, conversion of analog signals at the output of a multi-channel receiver in each 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 signal in each channel, four-dimensional radiation pattern $$\hat{U}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right)$$

in two azimuths $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}$$

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

and two corners of the place $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}$$

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

scanning by four-dimensional radiation pattern $$\hat{U}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right)$$

two azimuths and two elevation angles in the field of their definition $$({\alpha }_{\mathrm{one}}^{\text{'}\text{'}}=0-{360}^{\circ },{\beta }_{\mathrm{one}}^{\text{'}\text{'}}=0-{90}^{\circ },{\alpha }_2^{\text{'}\text{'}}=0-{360}^{\circ },{\beta }_2^{\text{'}\text{'}}=0-{90}^{\circ })$$

, estimation of two azimuths, two elevation angles and two amplitudes U ₀₁ , U _{02 of the} received ionospheric signal from the maximum value of the four-dimensional radiation pattern $$\hat{U}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right)$$

when scanning, evaluation of the field rank by condition $$\frac{U_{01}}{U_{02}}\ge 3$$

and selection of solutions that satisfy this condition, characterized in that they additionally algorithmically form a new antenna system with a minimum base $$|\; |\; |{\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n|\; |\; |$$

, on the basis of this antenna system form a two-dimensional radiation pattern $$\hat{U}\left({\alpha }_y^{\text{'}\text{'}},{\beta }_y^{\text{'}\text{'}}\right)$$

in the domain of determination (α _y = 0-360 °, β _y = 0-90 °), stable under the conditions of interference of two rays of the ionospheric signal, the azimuth α _0y and _elevation angle β _{0y of the} beam, the values of which are weakly dependent, are estimated from the maximum of the two-dimensional radiation pattern from the phase difference between the two rays of the ionospheric signal, from the obtained values of the azimuth α _0y and elevation angle β _0y determine the four-dimensional area of the estimated azimuths $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}={\alpha }_{0y}^{\text{'}\text{'}}\pm {10}^{\circ }$$

, $${\alpha }_2^{\text{'}\text{'}}={\alpha }_{0y}^{\text{'}\text{'}}\pm {10}^{\circ }$$

and estimated elevation angles $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}={\beta }_{0y}^{\text{'}\text{'}}\pm {10}^{\circ }$$

, $${\beta }_2^{\text{'}\text{'}}={\beta }_y^{\text{'}\text{'}}\pm {10}^{\circ }$$

within which the azimuths are estimated $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}={\alpha }_{01}$$

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

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

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

two rays of the ionospheric signal along the maximum of the four-dimensional radiation pattern $$\hat{U}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right).$$

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