RU2490661C1 - Method of determining coordinates of short-wave radio-frequency source - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention can be used in determining coordinates of a radio-frequency source, particularly for determining coordinates of a short-wave (SW) radio-frequency source. A known method of determining coordinates of a SW radio-frequency source, which involves receiving radio signals using spaced apart bearing posts, frequency selection, determining bearing lines, weight processing and recording, includes operations where for each obtained bearing, a three-dimensional measurement vector is constructed as a vector of the normal to the surface which passes through the centre of the Earth, the bearing position and the generatrix of the bearing line when cross the surface of the Earth; for each measured bearing, a 3×3 measurement matrix is found through a dyadic product of the measurement vector and its transposed value; all the obtained measurement matrices are summed; an ellipsoid is constructed based on second-order control coefficients given elements of the resultant matrix; orientation of the ellipsoid in space is determined and coordinates of the radio-frequency source are determined as the points of intersection of the principal axis of the ellipsoid and the surface of the Earth.

EFFECT: faster determination of coordinates of a radio-frequency source during long-range radio monitoring.

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Description

The invention relates to radio engineering and can be used to determine the coordinates of the source of radio emissions (IRI), in particular to determine the coordinates of the IRI short-wave (HF) range during radio monitoring.

Modern communication systems make extensive use of the HF frequency range, which ensures reliable communications, minimal dependence on environmental conditions and surface topography, the possibility of contact with any point on the Earth, and high resistance to interference [1]. The HF band is also actively used in over-the-horizon radar systems [2] and passive location systems [3]. The determination of the coordinates of the IR of the HF band is an important task of radio monitoring [4 p. 374], in particular, if it is necessary to make decisions on response measures [5, p. 344, 416, 511] when detecting IRI signals (suppression by using active noise, force and other means, semantic analysis, creation of false goals, etc.). The greatest difficulty is the determination of the coordinates of mobile IRI (aviation, navy, motor vehicles) operating in a limited time mode. In the radio monitoring of signals in the far zone (at extremely large distances), the most effective is the triangulation location of the IRI, for the implementation of which several direction finding (PP) posts are used, located at significant distances from each other.

The speed of determining the coordinates of the IRI is an important parameter in radio monitoring, especially when deciding on measures to respond to a newly detected IRI.

A known method for determining the coordinates of the IRI HF range described in [6, p. 585-586]. The method includes receiving radio signals by several separated in space PP, frequency selection, determination of bearing lines, weight processing and registration of the data obtained, after which the coordinates of all pairwise intersections of bearings in the geosphere are calculated, its weight is determined for each notch taking into account the measurement error of bearings, the distance from each PP to Iran and the angle of convergence of bearings in the serif. The IRI coordinates are estimated by averaging the coordinates of the serifs, taking into account their weight.

But the speed of the process of determining the coordinates of the IRI when using the known method is low. This is explained by the fact that in order to ensure the direction finding accuracy necessary for making a decision on measures to respond to the appearance of IRI, it is necessary to repeatedly measure and select bearings using a complex computational procedure due to the influence of the ionosphere state and a change in the polarization of the monitored signal. With an increase in the distances from each SP to IRI, their differences, and the direction-finding base, this influence increases [7, p. 211], zones of silence and uncertainty appear, in which determining the location of the IRI is problematic.

To compensate for direction-finding errors caused by the influence of the ionosphere, long-term forecasting of the state of the ionosphere is used [8]. But when direction finding in the far zone and significant distances between the SPs, ambiguity appears in the data of long-term forecasting of the state of the ionosphere, and in the case of an unpredictable radio monitoring area of the Iranian location, accounting of forecasting data becomes impossible.

A known method for determining the coordinates of IRI (radar stations - radar), based on a comparison of the received signals of an unknown radar with a known map of the area [9]. The method includes receiving PP radio signals IRI, frequency selection, determination of bearing lines, recording and matching the received data with a map of a known area. For greater reliability of the reproduced information when receiving radar signals, a correction is introduced for the coefficient 1 / (1-cosβ _η ), where β _η is the current azimuth value. The correction evens out the propagation delays of signals reflected from targets and “locals” with the propagation delay of the radar probe signal and brings the source image on the PP viewing indicator closer to the image of an unknown radar, thereby increasing the speed of IRI location.

The method allows not only to determine the coordinates of the radar, but also to monitor unknown targets by the passive method.

The disadvantage of this method is the dependence of the speed of determining the coordinates of the source from the operating mode of the radar. In addition, the disadvantage of this method is also a narrow functional orientation, which does not allow it to be used in determining the coordinates of other types of IRI.

The closest in technical essence to the claimed object is a method for determining the coordinates of the IRI HF range, the essence of which is described in [10] (prototype). The method includes receiving signals at several points in space, frequency selection, determination of bearing lines, weight processing and recording of received data. Bearing lines are determined in the direction-finding antenna plane, and according to the results of weight processing, auxiliary planes orthogonal to the direction-finding antenna plane and passing through each received bearing line are formed. The IRI position lines are determined as the intersection lines of each auxiliary plane with the Earth’s surface, and the IRI coordinates are calculated as the intersection points of the IRI position lines.

The method can significantly improve the speed and accuracy of determining the coordinates of the IRI in the near zone of radio monitoring.

However, when monitoring signals in the far zone of radio monitoring, the speed in determining coordinates in a known manner is not enough, in particular for taking one or another response. This is due to the fact that the known method is based on the representation of a part of the Earth’s surface in the form of a plane on which the Iranian positioning operations are performed. But in the far zone of radio monitoring, the sphericity of the surface will lead to a distortion of the coordinate values and, accordingly, to an increase in the error space [11, p. 259, 260]. Estimating the point of the most probable coordinates of the IRI with an error that is acceptable for decision-making on response measures requires a complex procedure for resolving the spatial polyhedron of errors, repeated repeated direction finding, which slows down the performance of locating the IRI, and is ineffective in cases of moving IRI. The speed of the process of locating the IRI when using the known method is also limited by the flight time of the aircraft on which the PP is located.

The aim of the invention is to increase the speed and accuracy of determining the coordinates of the IRI in the far zone of radio monitoring.

This goal is achieved due to the fact that in the known method for determining the coordinates of the IRI HF range, including the reception of radio signals by several spaced apart in the space PP, frequency selection, determination of bearing lines, weight processing and registration, operations are introduced, during which a three-dimensional is constructed for each bearing received vector of measurement as the vector of the normal to the plane passing through the center of the Earth, the bearing position and forming the line of the bearing at the intersection with the surface of the Earth, for each of this bearing, find a 3 × 3 dimension matrix by the dyadic [12, p. 509] product of the measurement vector by its transposed value, summarize all the obtained measurement matrices, construct an ellipsoid from the coefficients of the second order equation specified by the elements of the total matrix, determine the orientation of the ellipsoid in space and find the coordinates of the IRI to be registered as the coordinates of the point of intersection of the main axis of the ellipsoid with the Earth's surface.

The introduction of new operations can significantly increase the speed when determining the coordinates of the IRI during radio monitoring in the far zone by eliminating the multi-stage estimation of spatial errors and determining the point of the most probable coordinates of the IRI, which makes it possible to ensure timely response measures and reliable registration of IRI.

The combination of distinctive features and properties of the proposed method for determining the coordinates of the IRI HF range from patent sources are not known, therefore it meets the criteria of novelty and inventive step.

Figure 1 shows a functional diagram of a set of means for determining the coordinates of the IRI that implements the proposed method;

figure 2 - spherical coordinate system when direction finding IRI;

figure 3 - diagram of the construction of the measurement vector;

figure 4 - diagram of the construction of the measurement plane;

figure 5 - scheme for determining the coordinates of the IRI.

The complex of means for determining the coordinates of the IRI (Fig. 1), which implements the proposed method, contains N direction-finding posts 1 (SP 1) spaced in space, each of which includes antenna system 2 (AC 2) connected in series, receiver 3 (PR 3) , Bearing calculation module 4 (MVP 4), codec 5, and satellite communications module 6 (MSS 5). The second output of the antenna system 2 is connected to the second input of the bearing calculation module 7, and the output of the codec 5 is connected to the second input of the receiver 3. The complex also contains an information processing post 8 (POI 8), including a control module 9 (MU 9) connected in series, an encoder 10 teams (CC 10), a module 11 receiving and transmitting data (MPPD 11), a decoder 12 signals of direction finding posts (DSPP 12), a digital signal processor 13 (DSP 13) and module 14 mapping and display (MKI 14). The second output of the control module 9 is connected to the second input of the mapping and indication module 14, and the second output of the direction finding signal decoder 12 through the weight processing module 15 (MVO 15) is connected to the second input of the digital signal processor 13 and to the third input of the mapping and indication module 14. The input of the control unit 9 is the input of the information processing post 8.

The method for determining the coordinates of the IR HF range is as follows.

When radio monitoring signals in the far zone, it is necessary to determine the coordinates of the IRI at a distance of hundreds and thousands of kilometers from the BCP (13, p. 223). Under these conditions, the well-known methods for determining the coordinates of Iran from the results of its multi-direction finding, based on the use of weighted averaging of the coordinates of the points of intersection of bearings (serifs), require the implementation of N ^* (N-1) / 2 solutions of spherical triangles, where N is the number of direction finders forming at summing up the spatial polyhedron of possible coordinates. The resolution of the spatial polyhedron does not provide the required speed and accuracy of measurements when determining the IRI and does not allow to determine the point of the most probable coordinates of the IRI, necessary to assess the possibility of taking response measures and their sufficiency.

When performing the proposed method for determining the coordinates of the IRI KV range, N PP (stationary or mobile) with known coordinates is used

{P _i }, i = 1, ..., N.

From each position, a bearing measurement is performed on the IRI

{Θ _i }, i = 1, ..., N

with measurement errors (standard errors)

{σ _i }, i = 1, ..., N.

In the course of processing the measurement results, an estimate of the coordinates of the IRI should be found:

$$\widehat{v}=arg\underset{v}{min}F\left(v\right)\left(\mathrm{one}\right)$$

where Φ (v) is the functional of the generalized quadratic residual of measurements:

$$F\left(v\right)={\displaystyle \sum _{i=\mathrm{one}}^N{\left(\frac{\Delta {\Theta }_i\left(v\right)}{{\sigma }_i}\right)}^2,\left(2\right)}$$

ΔΘ _i (v) = Θ _i -f _i (v),

f _i (v) = azimuth (П _i , v) - bearing from the i-th position of the PP to the point v.

In a three-dimensional Cartesian coordinate system with the origin at the center of the geosphere of unit radius

$$v^{T}v=\mathrm{one}\left(3\right)$$

where T is the symbol of transposition of the vector [13, p. 7], the deviation of the measured bearing value from the true direction to point V in the geosphere can be represented as:

$$\Delta {\Theta }_i\left(v\right)\approx \frac{{\eta }_i^{T}v}{sin{\delta }_i},\left(\mathrm{four}\right)$$

where η _i is the unit normal vector to the large circle of the i-th bearing;

δ _i - the angular distance to the IRI from the i-th position P _i (angular separation of points when viewed from the center of the geosphere).

When substituting expression (4) into the residual functional (2):

$$F\left(v\right)={\displaystyle \sum _{i=\mathrm{one}}^N{\left(\frac{\Delta {\Theta }_i\left(v\right)}{{\sigma }_i}\right)}^2={\displaystyle \sum _{i=\mathrm{one}}^N{\left(\frac{{\eta }_i^{T}v}{{\sigma }_{i}sin{\delta }_i}\right)}^2={\displaystyle \sum _{i=\mathrm{one}}^N\frac{\left(v^T{\eta }_i\right)\left({\eta }_i^{T}v\right)}{{\left({\sigma }_{i}sin{\delta }_i\right)}^2}=v^{T}Av,\left(5\right)}}}$$

Where $$A={\displaystyle \sum _{i-\mathrm{one}}^N\frac{{\eta }_i{\eta }_i^T}{{\left({\sigma }_{i}sin{\delta }_i\right)}^2}}\left(6\right)$$

- information matrix of positioning - symmetric 3 × 3 matrix of covariance of measurement vectors

$$n_i=\frac{{\eta }_{i}v}{{\sigma }_{i}sin{\delta }_i},\left(7\right)$$

minimization of functional (5) with constraint (3) is reduced by the method of Lagrange multipliers to the problem of unconditional minimization of the generalized functional Φ '(v):

$$F\text{'}\text{'}\left(v\right)=v^{T}Av-\lambda v^{T}v,\left(8\right)$$

where λ is the Lagrange multiplier [11, p.335],

and after differentiating (8) and equating the derivative to 0, to the problem of the eigenvalues of matrix A:

$$Av=\lambda v.\left(9\right)$$

Thus, the coordinate estimate (1) is reduced to the eigenvalue problem (9) for the information matrix (6), and the coordinate estimation algorithm is reduced to the following sequence of actions:

- for each received bearing, a three-dimensional vector of measurement n _{i is built} as the normal vector to the plane passing through the center of the Earth [14, p. 87] and forming the bearing line at the intersection with the geosphere;

- for each measured bearing find the matrix A _i measurements of dimension 3 × 3 by dyadic [12, p. 509] product of the measurement vector by its transposed value;

- summarize all the obtained measurement matrix A _i ;

- build an ellipsoid according to the coefficients of the second-order equation specified by the elements of the total matrix;

- determine the orientation of the ellipsoid in space;

- find the coordinates of the IRI to be registered as the coordinates of the point of intersection of the main axis of the ellipsoid with the Earth's surface.

The whole cycle of determining the coordinates of the IRI of the proposed method can be implemented using a complex of means of direction finding IRI, a functional diagram of which is shown in figure 1.

The command for radio monitoring a given area in the far zone from the control module 9 through the command encoder 10, the coded control command contains the PP address (conditional number) and the coordinates of the direction finding area, and the data reception and transmission module 11 is supplied to the satellite communication module 6 of each direction finding station 1 . The command is decoded by codec 5 and arrives at receiver 3, which provides the selection of IRI signals in a wide band of the HF frequency range.

The signal f _c IRI is fed to the antenna system 2 of each post 1

direction finding and further to the information input of the receiver 3. First of all, the receiver 3 determines the electromagnetic availability of the IRI signal for monitoring. The probability of a correct decision on the presence of a signal in the Δf band is determined in accordance with the expression [15, p.42]

P _right = 1-F _{s + w} (h, ΔfT _c ),

where P is _right - the probability of a correct decision on the presence of a signal;

F _{c + w} (h, ΔfT _c ) is the integral function of the conditional probability distribution of the process at the input of the decider of the receiver 3, corresponding to the action of the signal and noise at the input.

Direction 1 posts that do not provide the required value of P _rights from the further monitoring process of this IRI can be excluded.

The extracted and detected IRI signal from the output of the receiver 3 is sent to the bearing calculation module 4 simultaneously with the orientation signal of the antenna system 2. The received bearing value is fed to the codec 5 and then via the information bus to the satellite communication module 6 with the command post 8. In module 6, the bearing signal is transferred to the frequency f _Pn .

The radio signals containing the encoded values of the bearings of the IRI are fed to the module 11 of the command post 8, demodulated (the frequency f _{Pn is removed} ) and fed to the decoder 12 of the PP signals and then to the weight processing module 15.

The root-mean-square error of determining the range for two angles of convergence of the bearings symmetrical with respect to the bisector is determined by the expression [16, p.175]:

, $${\sigma }_D\approx \frac{D\sigma }{\sqrt{2}sin\left(\psi /2\right)}$$

,

where σ is the standard error of the bearing measurement;

D is the range from PP to IRI.

For different D, the value of a possible error can increase.

Module 15 provides, by pairwise processing, the selection (similar to [10]) of bearings to determine the coordinates of the IRI, providing a minimum standard error. The values of these bearings are fed to a digital signal processor 13 for subsequent processing, during which the following are determined: measurement vectors n _i , measurement matrices A _i , information matrix A, an informational location ellipsoid is constructed, the main axis vector of the ellipsoid and the IRI coordinates are found.

Using the representation of the measurement vector n _i in the selected coordinate system

$$n_i=\left(\begin{array}{c}{n}_{ix}\\ n_{iy}\\ n_{iz}\end{array}\right)$$

matrix A _i measurements takes the form:

, $$A_i=n_i{n}_i^T=\left(\begin{array}{c}{n}_{ix}\\ n_{iy}\\ n_{iz}\end{array}\right)\cdot \left(n_{ix}{n}_{iy}{n}_{iz}\right)=\left(\begin{array}{ccc}{n}_{ix}^2& n_{ix}{n}_{iy}& n_{ix}{n}_{iz}\\ n_{ix}{n}_{iy}& n_{iy}^2& n_{iy}{n}_{iz}\\ n_{ix}{n}_{iz}& n_{iy}{n}_{iz}& n_{iz}^2\end{array}\right)$$

,

and the positioning information matrix A is represented as

. $$A=\left(\begin{array}{ccc}{a}_{xx}& a_{xy}& a_{xz}\\ a_{xy}& a_{yy}& a_{yz}\\ a_{xz}& a_{yz}& a_{zz}\end{array}\right)={\displaystyle \sum _{i=\mathrm{one}}^N{A}_i}={\displaystyle \sum _{i=\mathrm{one}}^N{n}_i{n}_i^T}=\left(\begin{array}{ccc}{\displaystyle \sum _{i=\mathrm{one}}^N{n}_{ix}^2}& {\displaystyle \sum _{i=\mathrm{one}}^N{n}_{ix}{n}_{iy}}& {\displaystyle \sum _{i=\mathrm{one}}^N{n}_{ix}{n}_{iz}}\\ {\displaystyle \sum _{i=\mathrm{one}}^N{n}_{ix}{n}_{iy}}& {\displaystyle \sum _{i=\mathrm{one}}^N{n}_{iy}^2}& {\displaystyle \sum _{i=\mathrm{one}}^N{n}_{iy}{n}_{iz}}\\ {\displaystyle \sum _{i=\mathrm{one}}^N{n}_{ix}{n}_{iz}}& {\displaystyle \sum _{i=\mathrm{one}}^N{n}_{iy}{n}_{iz}}& {\displaystyle \sum _{i=\mathrm{one}}^N{n}_{iz}^2}\end{array}\right)$$

.

The construction of the information ellipsoid location is carried out using a digital signal processor 13 as follows. Ellipsoid equation in vector form:

,v ^T Av = 1, where $$v=\left(\begin{array}{c}x\\ y\\ z\end{array}\right)$$

,

or in coordinate form:

$$a_{xx}{x}^2+a_{yy}{y}^2+a_{\mathrm{<figure-callout\; id="2"\; label="z\; z\; z"\; filenames="00000030.png"\; state="\{\{state\}\}">z\; </figure-callout>}z}{z}^{}{}^2+2a_{xy}xy+2a_{xz}xz+2a_{xz}yz=\mathrm{one}\left(\mathrm{one}0\right)$$

By turning [17, p. 91] the coordinate system (SC) using the coordinate transformation matrix

$$V={\left(v_{\mathrm{one}}{v}_2{v}_3\right)}^T,\left(\mathrm{one}\mathrm{one}\right)$$

$$\left(\begin{array}{c}x\text{'}\text{'}\\ y\text{'}\text{'}\\ z\text{'}\text{'}\end{array}\right)=V\left(\begin{array}{c}x\\ y\\ z\end{array}\right)={\left(v_{\mathrm{one}}{v}_2{v}_3\right)}^T\left(\begin{array}{c}x\\ y\\ z\end{array}\right)=\left(\begin{array}{ccc}{v}_{\mathrm{one}x}& v_{\mathrm{one}y}& v_{\mathrm{one}z}\\ v_{2x}& v_{2y}& v_{2z}\\ v_{3x}& v_{3y}& v_{3z}\end{array}\right)\left(\begin{array}{c}x\\ y\\ z\end{array}\right)$$

where v ₁ , v ₂ , v ₃ - the basis of the new SK,

the ellipsoid equation can be reduced to the canonical form:

$$\frac{x{\text{'}\text{'}}^2}{a^2}+\frac{y{\text{'}\text{'}}^2}{b^2}+\frac{z{\text{'}\text{'}}^2}{c^2}=\mathrm{one},\left(\mathrm{one}2\right)$$

where a ≥b≥с> 0 is the semiaxis of the ellipsoid.

In this case, the axes of the new SC coincide with the axes of the ellipsoid, and the vectors v ₁ , v ₂ , v _{3 of the} new basis are eigenvectors of the matrix A, that is, they satisfy equation (9). To find the vector of the principal axis v ₁ corresponding to the axis OX 'of the new SC, we find the smaller of the eigenvalues of the matrix A, which are the roots of the characteristic equation det (A-λI) = 0, where det (·) is the determinant of the identity matrix [17, p .96], I is the identity matrix:

. $$I=\left(\begin{array}{ccc}\mathrm{one}& 0& 0\\ 0& \mathrm{one}& 0\\ 0& 0& \mathrm{one}\end{array}\right)$$

.

The equation for determining λ:

$$\begin{array}{l}det\left(A-\lambda I\right)=det\left(\begin{array}{ccc}{a}_{xx}-\lambda & a_{xy}& a_{xz}\\ a_{xy}& a_{yy}-\lambda & a_{yz}\\ a_{xz}& a_{yz}& a_{zz}-\lambda \end{array}\right)=\left(a_{xx}-\lambda \right)\left(a_{yy}-\lambda \right)\left(a_{zz}-\lambda \right)+\left(\mathrm{one}3\right)\\ +2a_{xy}{a}_{yz}{a}_{xz}-a_{yz}^2\left(a_{xx}-\lambda \right)-a_{xz}^2\left(a_{yy}-\lambda \right)-a_{xy}^2\left(a_{zz}-\lambda \right)=0\end{array}$$

after opening the brackets and grouping the terms, it reduces to the equation cubic with respect to λ

$${\mathrm{<figure-callout\; id="3"\; label="\lambda "\; filenames="00000030.png,00000031.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}^3+\mathrm{<figure-callout\; id="2"\; label="\rho \; \lambda "\; filenames="00000030.png"\; state="\{\{state\}\}">\rho \; </figure-callout>}{\lambda }^{}{}^2+q\lambda +r=0\left(\mathrm{one}\mathrm{four}\right)$$

where ρ = - a _xx - a _yy - a _zz ;

; $$q=a_{xx}{a}_{yy}+a_{xx}{a}_{zz}+a_{yy}{a}_{zz}-a_{xy}^2-a_{xz}^2-a_{\mathrm{<figure-callout\; id="2"\; label="y\; z"\; filenames="00000030.png"\; state="\{\{state\}\}">y\; </figure-callout>}z}^2$$

;

$$r=a_{xx}{a}_{\mathrm{<figure-callout\; id="2"\; label="y\; z"\; filenames="00000030.png"\; state="\{\{state\}\}">y\; </figure-callout>}z}^2+a_{yy}{a}_{\mathrm{<figure-callout\; id="2"\; label="x\; z"\; filenames="00000030.png"\; state="\{\{state\}\}">x\; </figure-callout>}z}^2+a_{zz}{a}_{xy}^2-a_{xx}{a}_{yy}{a}_{zz}-2a_{xy}{a}_{xz}{a}_{yz}$$

The solution of equation (14) gives the roots λ ₁ , λ ₂ , λ ₃ corresponding to the semiaxes of the ellipsoid (12):

, $${\lambda }_2=\frac{1}{b^2}$$

, $${\lambda }_3=\frac{1}{c^2}$$

. $${\lambda }_{\mathrm{one}}=\frac{\mathrm{one}}{a^2}$$

, $${\mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="00000030.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}_2=\frac{\mathrm{one}}{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="00000030.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}$$

, $${\mathrm{<figure-callout\; id="3"\; label="\lambda "\; filenames="00000030.png,00000031.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}_3=\frac{\mathrm{one}}{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="00000030.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}$$

.

The result of the substitution of λ ₁ in equation (9) gives the coordinates of the guide vector v _{1 of the} main axis of the ellipsoid:

$$v_{\mathrm{one}}=\left(\begin{array}{c}{v}_{\mathrm{one}x}\\ v_{\mathrm{one}y}\\ v_{\mathrm{one}z}\end{array}\right)=\left(\begin{array}{c}{a}_{xy}{a}_{yz}-\left(a_{yy}-{\lambda }_{\mathrm{one}}\right)a_{xz}\\ \left(a_{xx}-{\lambda }_{\mathrm{one}}\right)a_{yz}-a_{xy}{a}_{xz}\\ \left(a_{xx}-{\lambda }_{\mathrm{one}}\right)\left(a_{xx}-{\lambda }_{\mathrm{one}}\right)-a_{xy}^2\end{array}\right)\left(\mathrm{one}5\right)$$

Hence the coordinates of the IRI:

, широта $$\beta =\left(\frac{v_{1z}}{\sqrt{v_{1x}^2+v_{1y}^2+v_{1z}^2}}\right)$$

.longitude $$\alpha =arctg\left(\frac{v_{\mathrm{one}z}}{v_{\mathrm{one}x}}\right)$$

latitude $$\beta =\left(\frac{v_{\mathrm{one}z}}{\sqrt{v_{\mathrm{one}x}^2+v_{\mathrm{one}\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000030.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+v_{\mathrm{one}z}^2}}\right)$$

.

The output signal of the digital signal processor 13 is supplied to the module 14 mapping and display, simultaneously registering the command and used to determine the coordinates of the bearings (PP). The result is a point of the most probable coordinates of the IRI, and an increase in speed and accuracy makes it possible to take timely measures of an effective response when an IRI is detected during radio monitoring.

Graphically, the transformations during the use of the proposed method are illustrated in FIGS. 2-5. Figure 2 leads SC [14, p.87], adapted to the proposed measurement cycle. Figure 3 shows graphically the construction of the measurement vector n, figure 4 - the construction of the measurement plane PI, figure 5 - determination of the coordinates of the IRI. Figure 2-5 adopted the following notation: SP - North Pole; E is the equator; NM is the initial meridian; e is a vector; α is the longitude; β is the latitude; M is the meridian passing through the point e, (P); P - position of the direction finder; LP - bearing line; Θ - bearing value; IE is an informational ellipsoid.

Management of direction finding posts 1 can be organized similarly, for example, to a set of tools according to patent RU No. 2391619 [18] using the hardware described, for example, in the book [19, p.17, 183].

The digital signal processor 13 can be performed, for example, on the basis of processors Texas Instruments TMS 320 C 6416/6713 and FPGA [20].

Thus, the proposed method can significantly increase the speed of determining the coordinates of the IRI in the far zone of radio monitoring. Computer modeling has shown the effectiveness and sufficiency of technical solutions. In the course of experimental studies, the possibility of increasing the speed of determining the coordinates of the IRI in the far zone of radio monitoring by 3-6 times was shown, while the accuracy of positioning can be increased by 15-25%.

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Claims (1)

A method for determining the coordinates of a shortwave radio emission source, including receiving radio signals by several direction-finding posts in space, frequency selection, determining bearing lines, weight processing and registration, characterized in that for each received bearing a three-dimensional measurement vector is constructed as a normal vector to the plane passing through the center of the Earth, the bearing position and forming the bearing line at the intersection with the Earth’s surface, find for each measured bearing measure 3 × 3 dimension by dyadic product of the measurement vector by its transposed value, summarize all the obtained measurement matrices, construct an ellipsoid using the coefficients of the second-order equation specified by the elements of the total matrix, determine the ellipsoid's orientation in space and find the coordinates of the radiation source to be registered as the coordinates of the intersection point the main axis of the ellipsoid with the surface of the earth.

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