RU2539649C2 - Method for high-speed determination of azimuth and elevation bearings of radio-frequency source and initial phase of signal thereof - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: invention relates to radio engineering, particularly to single-signal radio direction-finding of a radio-frequency source. The method includes dividing an arbitrary nonlinear antenna system into logic parts on elements (dipoles) of the antenna system. The antenna system is divided into n parts, but not less than three parts (three elements of the antenna system). Measured complex amplitudes of signals obtained from the output of each element are transmitted to a unit for calculating natural logarithms and then to a computer, into which analytical expressions of the natural logarithm of a function have been input, said function describing a complex envelope of output signals of elements of the antenna system, the real and imaginary parts of which are compared with real and imaginary parts of the natural logarithm of the measured complex amplitudes of signals obtained from the output of each element of the antenna system. A system of algebraic equations is obtained, from which analytical expressions are determined for calculating the azimuth bearing θ, elevation bearing β and the initial phase of the signal φ₀ according to defined matrix trigonometrical formulae. The bearing β is determined after finding the bearing θ and the initial phase φ₀. Dispersion D of the found parameter values is further calculated to find confidence intervals of the determined parameters.

EFFECT: high speed and accuracy of determining azimuth and elevation components of bearings and initial phase of a signal of a radio-frequency source.

Description

Technical field

The invention relates to radio engineering, in particular to a single-signal direction finding of a radio emission source (IRI).

State of the art

Direction finding IRI takes place in the process of monitoring the electronic environment. In this case, it is necessary to determine the azimuthal, elevation bearings of the IRI and the signal amplitude. The direction finder registers radiation by recording signals on the elements of the antenna system (AC) - vibrators. Performing various actions on signals from vibrators, determine the radiation parameters. The problem is which actions on the signals will turn out to be more effective (accurate and fast).

The known method [1], according to which the azimuthal and elevation bearings are determined by searching for the maxima of the squared absolute value of the angular spectrum obtained using the two-dimensional Fourier transform of the convolution of complex signals obtained from the m-th element of AC, m = 1; 2; ...; M, M - the number of elements of the speaker, and the complex signal received from the reference element of the speaker. In this case, a two-dimensional grid is introduced in the azimuth θ and in elevation angle β.

The disadvantage of this method [1] is the high computational complexity due to the need to calculate the two-dimensional Fourier transform, and the need for a sufficiently large number of elements in the AS to obtain acceptable results. But according to the initial phase of the signal φ _{0, no} grid was introduced, since the cumbersome solution to the problem became even more cumbersome, and it was believed that the initial phase had little effect on obtaining the true result.

The author's method of determining bearings IRI [2] adopted as a prototype. In the prototype, it was proposed to use one grid, obtain the product of the cosine functions of the angles of the bearings using less cumbersome methods, and then determine the angles of the bearings from the system of two equations, still not taking into account the initial phase. For this, the nonlinear AS is logically divided into two parts so that the reference lines of the azimuthal bearings of each of the parts are not parallel to each other (coordinate systems associated with each of the parts are deployed relative to each other). In each of the parts, a support element is selected (an element with respect to which phase incursions are measured on the remaining elements of the AC part). The same elements of the speaker can enter both selected parts at the same time. In any way, for example, by searching for the maxima of the squared modulus of the one-dimensional angular spectrum obtained by the one-dimensional Fourier transform, we calculate the product of the cosines of the azimuthal and elevation bearings for each IRI in coordinate systems associated with the first and second logical parts of the AS (in the analytical expression of the complex amplitude of the signal on the m-th element of the AS, azimuthal and elevation bearings are included as the product of their cosines), and the calculations are based on phase incursions on the element AU minute relative to the corresponding reference oscillators. The azimuthal bearings of all IRIs, measured in coordinate systems associated with various logical parts of the AS, differ by the angle γ between the corresponding reference lines of the bearings. The calculation of the azimuthal and elevation bearings of the k-th IRI is carried out according to the formulas

, $${\theta }_k=arctg\left\{\frac{P_2-P{}_{\mathrm{one}}cos\gamma }{P_{\mathrm{one}}\sin \gamma }\right\}$$

,

$${\beta }_k=\arccos \left\{\frac{P_{\mathrm{one}}}{\cos {\theta }_k}\right\}$$

where P ₁ - the magnitude of the product of the cosines of the azimuthal and elevation bearings of the k-th Iran, k = 1; 2; ...; K, where K is the number of IRI obtained in the coordinate system associated with the first logical part of the AS; P ₂ - the value of a similar product obtained in the coordinate system associated with the second logical part of the AS.

The prototype has the following disadvantages.

1. The calculations do not take into account the initial phase of the signal φ ₀ , which affects the phase shift, from which bearings are determined. Therefore, the values of bearings are distorted. In most practical cases, the phase of the signal φ _{0 is} not equal to zero.

2. High computational complexity, due to the need to calculate the one-dimensional Fourier transform, and, as a consequence, the large time costs.

3. A nonlinear AS is logically divided into only two parts and so that the reference lines of the azimuthal bearings of each of the parts are not parallel to each other (coordinate systems associated with each of the parts would be deployed relative to each other). However, this is not enough to exclude the influence of the initial phase φ ₀ on finding the bearings closest to the true values.

Disclosure of invention

Achievable technical result - a significant increase in the speed and accuracy of determining the azimuthal and elevation components of bearings and the initial phase of the signal when receiving a radio signal of one IRI using non-linear (including ring) speakers consisting of weakly directed elements (vibrators). Improving the accuracy and speed of determining bearings is achieved through the use of features of nonlinear ASs, which eliminate the influence on the values of bearings of the unaccounted initial phase of the signal φ ₀ and reduce the algorithm for determining signal parameters to direct calculation using elementary formulas (in the present invention, all cumbersome computational operations are eliminated).

In the proposed method, the signals are considered as deterministic, subject to additive interference, the parameter estimates of which are to be determined.

To achieve a technical result, a method is proposed for determining the azimuthal and elevation bearings of a radio emission source and the initial phase φ _{0 of} its signal, which includes dividing an arbitrary nonlinear antenna system (AC) into logical parts by elements (vibrators) of the AC, reconstructing the vector of complex signal amplitudes obtained from the output of each element of the AU, with its subsequent separation corresponding to the logical separation of the AU, trigonometric formulas of bearings, which determine the angles of bearings. In this case, the division is carried out into n parts, but not less than three parts — three AC elements at different angles to the direction of the zero reference angle γ of the AC elements. The measured complex amplitudes of the signals obtained from the output of each element of the AC are fed to the natural logarithm calculation unit, then to the calculator, where the analytical expressions of the natural logarithm of the function describing the complex envelope of the output signals of the AC elements, the real and imaginary parts of which are equal to the real and imaginary parts of the natural logarithm of the measured complex amplitudes of the signals received from the output of each element of the speaker. A system of algebraic equations is obtained from which analytical expressions for calculating the azimuthal bearing θ, elevation bearing β, and the initial phase of the signal φ _{0 are} determined according to matrix trigonometric formulas

; $$\cos \beta =\frac{p_1-{\stackrel{⌢}{\varphi }}_0}{\cos \theta }$$

, $$\left(\begin{array}{c}tg\theta (P_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0)\\ {\stackrel{⌢}{\varphi }}_0\end{array}\right)={(A^{T}A)}^{-\mathrm{one}}{A}^{T}Y$$

; $$\cos \beta =\frac{p_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0}{\cos \theta }$$

,

where γ _m is the angle between the m-th element of the AC and the reference direction at m = 1 ... n;

γ ₁ = 0 (angle of the 1st element of the AC) - the origin of the angles γ _m ;

; $$p_m=\frac{P_m\lambda }{2\pi R}$$

при m=1, …, n; $$P_1=2\pi \frac{R}{\lambda }\cos \theta \cos \beta +{\varphi }_0$$

; $$P_m=2\pi \frac{R}{\lambda }\cos (\theta -{\gamma }_m)\cos \beta +{\varphi }_0$$

; $$p_m=\frac{P_m\lambda }{2\pi R}$$

when m = 1, ..., n; $$P_{\mathrm{one}}=2\pi \frac{R}{\lambda }\cos \theta \cos \beta +{\varphi }_0$$

;

, где λ - длина волны сигналов ИРИ, R - радиус круговой АС; $${\stackrel{⌢}{\varphi }}_0=\frac{{\varphi }_0\lambda }{2\pi R}$$

where λ is the wavelength of the IRI signals, R is the radius of the circular speaker;

;matrix $$A=\left(\begin{array}{c}\sin {\gamma }_2\mathrm{one}-\cos {\gamma }_2\\ \sin {\gamma }_3\mathrm{one}-\cos {\gamma }_3\\ \cdots \\ \sin {\gamma }_n\mathrm{one}-\cos {\gamma }_n\end{array}\right)$$

;

;column vector $$Y=\left(\begin{array}{c}{p}_2-p_{\mathrm{one}}\cos {\gamma }_2\\ p_3-p_{\mathrm{one}}\cos {\gamma }_3\\ \cdots \\ p_n-p_{\mathrm{one}}\cos {\gamma }_n\end{array}\right)$$

;

after finding the values of the bearing θ and the initial phase φ ₀ determine bearing β.

To exclude the influence of the initial phase φ ₀ on the results of determining the angles of bearings, it is necessary to divide the AS into the number of parts of at least three (in principle, the more parts of the separation of the AS, the more accurate the results will be).

, где f(x) - функция, определяющая значение искомого параметра; x_i - i-я переменная, входящая в f(x_i), i=1, 2, …, k, k - число переменных; с использованием аналитических выражений частных производных $$\frac{\partial f(x)}{\partial x_i}$$

и заранее известных величин дисперсий D(x_i) переменных x_i. В данном случае в качестве f(x) выступают формулы для cosβ, tgθ, φ₀, а в качестве x_i выступают все другие переменные, входящие в формулу, а именно: $$\cos \beta =\frac{P_1-{\varphi }_0}{\cos \theta }$$

; тогда f(x)=cosβ, P₁≡x₁; φ₀≡x₂; cosθ≡x₃. и $$D(\cos \beta )={\displaystyle \sum _{i=1}^3{(\frac{\partial \cos \beta }{\partial x_i})}^{2}D(x_i)}$$

.To find the confidence intervals of the determined parameters, the variances D of the azimuthal and elevation bearings and the initial phase of the signal of the radio emission source are additionally calculated according to the general formula $$D(f(x))={\displaystyle \sum _{i=\mathrm{one}}^k{[\frac{\partial f(x)}{\partial x_i}]}^{2}D(x_i)}$$

where f (x) is the function that determines the value of the desired parameter; x _i is the ith variable in f (x _i ), i = 1, 2, ..., k, k is the number of variables; using analytic expressions of partial derivatives $$\frac{\partial f(x)}{\partial x_i}$$

and the previously known variances D (x _i ) of the variables x _i . In this case, the formulas for cosβ, tgθ, φ ₀ act as f (x), and all other variables in the formula act as x _i , namely: $$\cos \beta =\frac{P_{\mathrm{one}}-{\varphi }_0}{\cos \theta }$$

; then f (x) = cosβ, P ₁ ≡x ₁ ; φ ₀ ≡x ₂ ; cosθ≡x ₃ . and $$D(\cos \beta )={\displaystyle \sum _{i=\mathrm{one}}^3{(\frac{\partial \cos \beta }{\partial x_i})}^{2}D(x_i)}$$

.

Dispersions are calculated to determine the confidence interval (possible spread of values) at a given confidence probability. But for practice, it is not the dispersion itself that is needed, but the square root of it - the standard deviation (standard deviation σ). What is obtained from the solution of the basic system of equations is the most probable value for given initial data. With other data, they will receive another solution that falls into the confidence interval. If ± σ is added to the solution, then with a probability of 0.68, when the data changes (due to interference), the solutions will be in this interval. The primary operations on the signals are the moments of the first order, the spread of values is a few percent. Correlation coefficients — second-order moments — have scatter values of hundreds of percent.

The implementation of the invention

The proposed method is shown on the example of a circular speaker.

1. In a circular speaker, each vibrator element is offset by a certain angle from the other, i.e. circular speakers can be automatically divided into a number of areas equal to the number of vibrators. The vector of complex amplitudes of the signals y = [y ₁ y ₂ ... y _M ] ^T obtained from the output of each AC element is restored. The vector y is restored once for the entire AS (that is, they make one physical measurement).

2. We write a nonlinear system of equations, the right side of which is an analytical expression of the complex amplitude of the signal at the m-th element of the speaker, the complex envelope of the outputs of the elements of a circular speaker

$$y_m(\theta ,\beta ,t)=u\exp \left\{j\left[2\pi f_{0}t+{\varphi }_0+(2\pi /\lambda )R\cos (\theta -{\gamma }_m)\cos \beta \right]\right\};(\mathrm{one})$$

where m = 1, ..., n;

,j is the imaginary unit $$j=\sqrt{-\mathrm{one}}$$

,

θ - azimuth bearing

β - elevation bearing

γ _m is the angle between the m-th element of the AC and the reference direction,

f ₀ - the frequency of the signals emitted by direction finding IRI,

u is the signal amplitude,

φ ₀ - the initial phase of the signal,

t is the time, in this case it can be set equal to zero,

λ is the wavelength of the IRI signals,

R is the radius of the antenna system.

3. Logarithm of expression (1), we obtain

$$\ln \left|y_m\right|+j\arg y_m=\ln u+j(2\pi \frac{R}{\lambda }\cos (\theta -{\gamma }_m)\cos \beta +{\varphi }_0).(2)$$

We denote argy _m = P _m and equate the real and imaginary parts, respectively: u = | y _m |; Thus, we determine the amplitude u. Next, we denote:

или: $$P_m=2\pi \frac{R}{\lambda }\cos (\theta -{\gamma }_m)\cos \beta +{\varphi }_0$$

or:

, m=1, …, n; $$p_m=\cos (\theta -{\gamma }_m)\cos \beta +{\stackrel{⌢}{\varphi }}_0$$

, m = 1, ..., n;

; $${\stackrel{⌢}{\varphi }}_0=\frac{{\varphi }_0\lambda }{2\pi R}$$

; γ₁=0 - начало отсчета углов γ_m.Where $$p_m=\frac{P_m\lambda }{2\pi R}$$

; $${\stackrel{⌢}{\varphi }}_0=\frac{{\varphi }_0\lambda }{2\pi R}$$

; γ ₁ = 0 is the origin of the angles γ _m .

:4. We compose a system of equations for bearings θ, β and the initial phase of the signal $${\stackrel{⌢}{\varphi }}_0$$

:

$$\begin{array}{l}\cos \theta \cos \beta +{\stackrel{⌢}{\varphi }}_0=p_{\mathrm{one}}\\ \cos (\theta -{\gamma }_2)\cos \beta +{\stackrel{⌢}{\varphi }}_0=p_2\\ \mathrm{.........................}\\ \cos (\theta -{\gamma }_n)\cos \beta +{\stackrel{⌢}{\varphi }}_0=p_n.\end{array}$$

вправо, делим все уравнения на первое. ПолучимThis system can be solved by different methods. We give the following. We carry $${\stackrel{⌢}{\varphi }}_0$$

to the right, divide all the equations into the first. We get

$$\begin{array}{l}\sin {\gamma }_{2}tg\theta (p_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0)+(\mathrm{one}-\cos {\gamma }_2){\stackrel{⌢}{\varphi }}_0=p_2-p_{\mathrm{one}}\cos {\gamma }_2\\ \sin {\gamma }_{3}tg\theta (p_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0)+(\mathrm{one}-\cos {\gamma }_3){\stackrel{⌢}{\varphi }}_0=p_3-p_{\mathrm{one}}\cos {\gamma }_3\\ \mathrm{...........................................}\\ \sin {\gamma }_{n}tg\theta (p_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0)+(\mathrm{one}-\cos {\gamma }_n){\stackrel{⌢}{\varphi }}_0=p_n-p_{\mathrm{one}}\cos {\gamma }_n\end{array}$$

, гдеor in matrix form: $$A\overrightarrow{\theta }=Y$$

where

; $$\overrightarrow{\theta }=\left(\begin{array}{c}tg\theta (P_1-{\stackrel{⌢}{\varphi }}_0)\\ {\stackrel{⌢}{\varphi }}_0\end{array}\right)$$

; $$Y=\left(\begin{array}{c}{p}_2-p_1\cos {\gamma }_2\\ p_3-p_1\cos {\gamma }_3\\ \cdots \\ p_n-p_1\cos {\gamma }_n\end{array}\right)$$

. $$A=\left(\begin{array}{c}\sin {\gamma }_2\mathrm{one}-\cos {\gamma }_2\\ \sin {\gamma }_3\mathrm{one}-\cos {\gamma }_3\\ \cdots \\ \sin {\gamma }_n\mathrm{one}-\cos {\gamma }_n\end{array}\right)$$

; $$\overrightarrow{\theta }=\left(\begin{array}{c}tg\theta (P_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0)\\ {\stackrel{⌢}{\varphi }}_0\end{array}\right)$$

; $$Y=\left(\begin{array}{c}{p}_2-p_{\mathrm{one}}\cos {\gamma }_2\\ p_3-p_{\mathrm{one}}\cos {\gamma }_3\\ \cdots \\ p_n-p_{\mathrm{one}}\cos {\gamma }_n\end{array}\right)$$

.

Hence the decision

. $$\left(\begin{array}{c}tg\theta (P_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0)\\ {\stackrel{⌢}{\varphi }}_0\end{array}\right)={(A^{T}A)}^{-\mathrm{one}}{A}^{T}Y;\cos \beta =\frac{p_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0}{\cos \theta }.(3)$$

.

и φ₀=a₂. Тогда $$tg\theta =\frac{a_1}{P_1-{\stackrel{⌢}{\varphi }}_0}$$

и φ₀=a₂; $$\cos \beta =\frac{P_1-{\stackrel{⌢}{\varphi }}_0}{\cos \theta }$$

.Formula (3) is the matrix formula for tgθ and φ ₀ . The computer is given matrices and formula (3), and the computer gives 2 numbers: values $$tg\theta (P_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0)=a_{\mathrm{one}}$$

and φ ₀ = a ₂ . Then $$tg\theta =\frac{a_{\mathrm{one}}}{P_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0}$$

and φ ₀ = a ₂ ; $$\cos \beta =\frac{P_{\mathrm{one}}-{\stackrel{⌢}{\varphi }}_0}{\cos \theta }$$

.

But you can do something else, namely: write down the functional of the least squares method and minimize it:

$$F={\displaystyle \sum _{i=2}^n{(\sin {\gamma }_{i}tg\theta (P_{\mathrm{one}}-{\varphi }_0)+(\mathrm{one}-\cos {\gamma }_i){\varphi }_0-P_i+P_{\mathrm{one}}\cos {\gamma }_i)}^2}$$

;Then the value of tgθ is found from the condition $$\frac{\partial F}{\partial tg\theta }=0$$

;

; $$\cos \beta =\frac{P_1-{\varphi }_0}{\cos \theta }$$

.φ ₀ - from the condition $$\frac{\partial F}{\partial {\varphi }_0}=0$$

; $$\cos \beta =\frac{P_{\mathrm{one}}-{\varphi }_0}{\cos \theta }$$

.

You can choose either of these two approaches. At the end, after finding the bearing θ and the initial phase φ ₀ determine bearing β.

Due to the simplicity of the calculations, the accuracy of the determination of bearings is significantly increased. In addition, the accuracy of the determination of bearings increases, because the quantity φ ₀ , which is included in the phase incursion, is taken into account, which determines the values of bearings.

It should be noted that the operations taking place in formulas (2) and (3) are not of great computational complexity and, accordingly, require little time. If we compare the proposed method with the prototype method, then in this case, instead of the one-dimensional Fourier transform, we calculate the logarithm of a function that describes the complex amplitude of the signal on the mth element and analytically obtain formulas for directly calculating the desired quantities, which also seriously reduces computational complexity and reduces processing time signal and reduces the error in the determination of bearings.

The proposed method can be used in conjunction with any direction finding method to reduce the computational (and, accordingly, time) costs for determining the values of azimuthal and elevation bearings of the IRI, since the calculation of the product of the cosines of the azimuthal and elevation bearings is much less complicated than the calculation of the mentioned bearings separately.

Implementation of the invention:

1. For a functioning speaker (before measurements), the natural logarithm (2) of the function describing the complex envelope of the outputs of the elements of the speaker (1) is calculated once analytically.

2. The measured complex amplitudes of the signals from each element of the AC are fed to the natural logarithm calculation unit, where their natural logarithm is determined, then they are sent to the calculator,

3. The analytical expressions of the natural logarithm of the complex envelope of the outputs of the AC elements (2) are introduced into the direction finder calculator, where the real and imaginary parts of the obtained expressions are equal to the real and imaginary parts of the natural logarithm y _m, respectively.

4. We arrive at a system of algebraic equations from which analytical expressions are determined for calculating the azimuth bearing θ, elevation bearing β, and the initial phase of the signal φ ₀ .

5. According to formulas (3), the azimuth bearing θ, the initial phase of the signal β, and then the elevation bearing φ ₀ are calculated.

6. If necessary, calculate the variance of the obtained values of the azimuth bearing θ, the initial phase of the signal φ ₀ and elevation bearing β.

Compare the results of the obtained values of the azimuth bearing θ and elevation bearing β, according to the prototype and the proposed method, using three elements of the AS (the first three equations). According to the proposed method, the bearing θ is equal to

(по прототипу: $$tg\theta =\frac{p_2-p_1\cos {\gamma }_2}{p_1\sin {\gamma }_2}$$

). $$tg\theta =\frac{p_2-p_3+p_{\mathrm{one}}(\cos {\gamma }_3-\cos {\gamma }_2)}{p_{\mathrm{one}}(\sin {\gamma }_2-\sin {\gamma }_3)}$$

(prototype: $$tg\theta =\frac{p_2-p_{\mathrm{one}}\cos {\gamma }_2}{p_{\mathrm{one}}\sin {\gamma }_2}$$

)

The difference is obvious. From formula (3) it follows that the elevation bearing β will also have a different meaning.

Consider a numerical example.

On a circular speaker with a radius of 50 m at a frequency of 1 MHz with a signal to noise ratio of 10, a signal is recorded. The following phases were recorded on the first three vibrator elements: P ₁ = 35 degrees, P ₂ = P ₃ = 45.98 degrees. The angle between the elements of the AC γ _m equal to 30 degrees. Substitute the source data in the formula

. $$P_m=2\pi \frac{R}{\lambda }\cos (\theta -{\gamma }_m)\cos \beta +{\varphi }_0$$

.

For the first vibrator we get:

. $$35=\frac{2\times 180\times \mathrm{fifty}\times {1.10}^6}{{3.10}^8}\cos \theta \cos \beta +\varphi =60\cos \theta \cos \beta +{\varphi }_0$$

.

Similarly, for the second - 45.98 = 60cos (θ-30) cosβ + φ ₀ ;

for the third, 45.98 = 60cos (θ-60) cosβ + φ ₀ .

According to formulas (3), it was obtained: θ = 45 degrees, β = 45 degrees, φ ₀ = 5 degrees. The standard deviation (standard deviation σ) θ is equal to 0.006 degrees, standard deviation σ for β is equal to 0.009 degrees.

и $${\beta }_k=\arccos \left\{\frac{P_1}{\cos {\theta }_k}\right\}$$

получено: θ=41,8 град, β=38,5 град. С увеличением значения φ₀ ошибка резко возрастает.According to the prototype formulas $${\theta }_k=arctg\left\{\frac{P_2-P_{\mathrm{one}}\cos \gamma }{P_{\mathrm{one}}\sin \gamma }\right\}$$

and $${\beta }_k=\arccos \left\{\frac{P_{\mathrm{one}}}{\cos {\theta }_k}\right\}$$

obtained: θ = 41.8 degrees, β = 38.5 degrees. As the value of φ ₀ increases, the error increases sharply.

The model calculation of the bearing was carried out on a computer with a processor with a clock frequency of 2 GHz. The counting time is about 0.001 s. And with a manual calculation, it will take about 1 min, since in each measurement only P _m changes.

Information sources

1. Patent RU 2151406, published on 06/20/2000, IPC G01S 5/04, G01S 5/14, H04B 17/00.

2. Patent RU 2380720, published 01/27/2010, IPC G01S 5/04.

3. Greshilov A.A. Mathematical decision-making methods: Textbook for universities. - M.: Publishing House of MSTU. N.E. Bauman, 2006 .-- 584 p.

Claims (1)

A method for determining the azimuthal and elevation bearings of a radio emission source (IRI) and the initial phase φ _{0 of} its signal, which includes dividing an arbitrary nonlinear antenna system (AS) into logical parts by elements (vibrators) of the AS, restoring the vector of complex amplitudes of the signals received from the output of each the element of the AS, with its subsequent separation corresponding to the logical separation of the AS, trigonometric formulas of bearings, by which the angles of bearings are determined, characterized in that the separation is performed by n cha if, but not less than in three parts — three AC elements at different angles to the direction of the zero reference angle γ, the measured complex amplitudes of the signals obtained from the output of each AC element go to the calculation unit of the natural logarithms, then to the computer, which is entered in advance analytical expressions of the natural logarithm of a function that describes the complex envelope of the output signals of the AC elements, the real and imaginary parts of which are equal to the real and imaginary parts of the natural logarithm of the measured complex amplitudes of the signals obtained from the output of each speaker element, a system of algebraic equations is obtained from which determine the analytical expression for the calculation of azimuth bearing of θ, the bearing approach elevation β, the initial phase φ ₀ signal matrix according trigonometric formulas

where γ _m is the angle between the m-th element of the AC and the reference direction at m = 1 ... n;
γ ₁ = 0 (angle of the 1st element AC) - the origin of the angles γ _m ;

$${\stackrel{⌢}{\phi }}_0=\frac{{\phi }_0\lambda }{2\pi R}$$

where λ is the wavelength of the IRI signals, R is the radius of the circular speaker;
matrix $$A=\left(\begin{array}{c}\sin {\gamma }_2\mathrm{one}-\cos {\gamma }_2\\ \sin {\gamma }_3\mathrm{one}-\cos {\gamma }_3\\ \cdots \\ \sin {\gamma }_n\mathrm{one}-\cos {\gamma }_n\end{array}\right)$$

;
column vector $$Y=\left(\begin{array}{c}{p}_2-p_{\mathrm{one}}\cos {\gamma }_2\\ p_3-p_{\mathrm{one}}\cos {\gamma }_3\\ \cdots \\ p_n-p_{\mathrm{one}}\cos {\gamma }_n\end{array}\right)$$

;
after finding the values of the bearing θ and the initial phase φ ₀ determine bearing β.