# Method and device for difference-range finding direction finding of radio emission source

FIELD: finding of azimuth of radio emission source (RES) in wide-base direction finding systems.

SUBSTANCE: angle of azimuth of RES is measured with high degree of precision due to elimination of methodical errors in direction finding caused by linearization of model electromagnet wave propagation wave front. As surface of RES location the plane is used which has RES line of location which has to be crossing of two hyperbolic surfaces of location corresponding to difference-time measurement. Method of RES direction finding is based upon receiving its signal by three aerials disposed randomly, measuring of two time differences of RES signal receiving by aerials which form measuring bases and subsequent processing of results of measurement to calculate values of RES angles of azimuth and coordinates of point through which the RES axis of sight passes. The data received are represented in suitable form. Device for realization of the method has three aerials disposed at vertexes of random triangle, two units for measuring time difference of signal receiving, computing unit and indication unit. Output of common aerial of measuring bases is connected with second inputs of time difference meters which receive signals from outputs of the rest aerials. Measured values of time differences enter inputs of computing unit which calculates values of RES angle of azimuth and coordinates of point through which the RES axis of sight passes. Data received from output of computing analyzing unit enter indication unit intended for those data representation.

EFFECT: widened operational capabilities of direction finder.

2 cl, 7 dwg

This proposal relates to the field of radio engineering and can be used in direction-finding systems for determining the azimuth of a source of radio emission (IRI).

Modern systems determine the direction of Iran's built using well-known methods of direction finding: amplitude (method of maximum, the minimum, the method of comparison and others), phase, frequency and time.

Known methods and devices of direction finding [1-5, 10-20 and others].

For example, there are a number of ways of finding, based on the fact that the phase relation between the signals received at spatially separated points can be converted to amplitude dependence of the sum of the signals received from location Iran.

The most obvious and widely used is the amplitude method of direction finding, which uses an antenna system having a directional pattern with a pronounced maximum. Due to the mechanical change in the position (orientation) of the antenna is scanning space, the result of which is determined by the position of the antenna at which the output signal of the antenna has a maximum amplitude and a direction coinciding with the maximum of the radiation pattern of antenna is the direction of Iran.

This method of direction finding can be considered as viroj the i.i.d. case differential-ranging way, when due to mechanical movement of the antenna system is chosen in such a position so that the difference of the distance from Iran to symmetric points of the antenna are equal to zero (and, therefore, the phase difference of the signals coming into these points were equal to zero). In-phase addition of signals arriving via different paths, provides the maximum energy at the point of reception.

The main disadvantage of this method is the need for mechanical movement of the antenna system or, at least, of its individual elements (e.g., feed).

There is also known a method of direction finding based on measuring the time differences of the signals from Iran two spaced antennas [e.g. 6]. When the position deviation of the IRI from the perpendicular to the center of the base there is a difference of turn signals Δr=r_{1}-r_{2}(r_{1}and r_{2}the distance from Iran to the first and second antennas respectively). The relative delay τ signals, due to the constancy of the speed and linearity of propagation of radio waves is proportional to the difference of course

The azimuth value α IRI is calculated by the formula

where d is the distance between the antennas

thus

where r=min(r_{1},r_{2}).

In General, systems which, uses considered are differential-ranging, however, with large deletions IRI from the center of the base, when the distance to the IRI significantly exceeds the size of the database, the hyperbolic line of position, typical differential-distance measuring method, in the far zone coincide with their asymptotes, coming in the form of rays from a center of the base. In this case, the differential-ranging system acceptable to assume angular.

Direction finding, it is also possible to produce based on measurements of the Doppler shift frequency Δf_{d}[see, for example, 7]. Because

where λ - wavelength signal IRI,

ν_{r}- radial velocity AT relatively the receiving antenna,

then, measuring Δf_{d}at extremely small interval, you can get variant frequency method, called differential Doppler, which allows to determine the value of the angular parameter positioning α:

where ν - speed of IRI in the coordinate system whose origin coincides with the point of location of the receiving antenna.

This approach to the measurement of the angle based on the assumption that at low measuring bases ("small" compared to the distance to the detected object) hyperbolic surface position Asim is eticheski seeks to conical, the form which in turn is uniquely described by the vertex point and the angle at the base.

The main disadvantages of these methods is the possibility of finding IRI only in the far zone, i.e. when the condition

r≫d

where r is the distance to the IRI,

d is the length of the measuring base.

This condition allows to make an assumption about the plane of the front of propagation of electromagnetic waves.

It is known that the accuracy of determining the bearing IRI depends on the relative sizes of the measuring base to the magnitude of the distance to the IRI (the dependence is characterized by the expression, taking into account the lower bound the Cramer-RAO [6]). However, increasing the size of the measuring base leads to increase in the bias direction finding, due to the sphericity of the front of an electromagnetic wave. The magnitude of the error direction finding, when values of the range r<10d can be up to ten and more percent from the values of the angular coordinates of the IRI. To reduce the error of direction finding using the direction-finding device (e.g., [20]), in which the bias direction finding is minimized by taking into account the sphericity of the wave front.

Known way of finding the closest to the present invention is a method [20], which assumes the implementation of the trail is proposed operations:

- have three antennas at the vertices of the triangle ΔABC;

- accept signal IRI on all three antennas;

- measure the difference between the times Δt_{AC}and Δt_{BC}signal IRI antennas, placed in pairs of points {a,C} and {b,C}, respectively;

- compute the value γ azimuth IRI using expression

- calculate the coordinate value of the point F, which belongs to the line position on Iran, using the expressions:

- display the results.

When this triangle ΔABC, the tops of which have three antennas must be rectangular isosceles, which is not always convenient and/or possible in practice when placing antennas on the ground.

This method is chosen as a prototype.

The aim of the invention is to expand the functionality of the radio signal by eliminating restrictions on the form of a triangle, the vertices of which have antennas.

This objective is achieved in that in the method of finding the IRI based on the reception of its signal three antennas, forming two pairs of random measurement bases (see figure 1), provide measurements of differences in arrival times of the signal Iran's antenna, calculate:

- values of the differences of the distance from Iran to couples that the EC {a,C} and {b,C} placement of antennas:

Δr_{AC}=Δt_{AC}·ν_{EMW}that Δr_{Sun}=Δt_{Sun}·ν_{EMW},

where ν_{EMW}- the speed of propagation of electromagnetic waves;

- the value of the angle γ azimuth IRI using expression

where x_{C}=(b^{2}-with^{2})/a,

coordinates {x_{f},y_{f}} point F owned by a bearing line on Iran, using the expressions:

whereΔr_{AB}=Δr_{AC}-Δr_{BC}.

The proposed method involves the following operations:

- have three antennas at the vertices of the triangle ΔABC;

- accept signal IRI on all three antennas;

- measure the time differences of signal IRI antennas forming the measurement bases {a,C} and {b,C};

- calculate values of differences of ranges Δr_{AB}that Δr_{AC}that Δr_{BC};

- calculate the value of angle γ azimuth IRI;

- calculate the coordinate value of the point belonging to the line position on Iran;

- display the results.

Figure 2 shows a case where the device realize the future the proposed method.

The device consists of three functionally related elements:

- antenna system with three antennas 1, 2 and 3;

- measurement system containing blocks 4 and 5 are intended for measurement of the difference of times of signal reception IRI pairs of antennas {1;3} and {2;3};

- handling system and a display containing the computing unit 6 and unit 7 that render results.

The principle of the proposed device is as follows:

antenna 1, 2 and 3 have three points in three-dimensional space a, b, C having coordinatesandrespectively.

For convenience and clarity, the further discussion will assume that the location of Iran coincides with some point D with unknown coordinatesWe denote the difference of the distances from it to points a and b through Δr_{AB}and the difference of the distances from points a and C through Δr_{AC}.

Now we introduce a coordinate system Oxyz set so that its origin coincides with the midpoint of the segment AB, the ox axis was collinear vectorand the plane HOU coincides with the plane ABC (figure 3). Then the coordinates of the points a, b and C in the system Oxyz respectively

x_{A}=-a; y_{A}=0; z_{A}=0;

x_{}
=a; y_{B}=0; z_{B}=0;

x_{C}=x_{3}; y_{C}=y_{3}; z_{C}=0;

where

x_{C}=(b^{2}-c^{2})/a,

and, therefore, can be written

Erected in the square right and left side of equation (1), we obtain

and, therefore,

If you expand the brackets in the left part and make simplifications, equation (2) takes the form of the canonical equations to two hyperboloid of rotation

where

Thus, from the above reasoning it follows that the point D belongs to the surface described by equation (3) (see figure 4).

Note, however, that when squaring equation (1) has occurred, the loss of the sign of the difference ranges Δr_{AB}so really the point D can belong to only one branch of the hyperboloid in accordance with system conditions

Similarly, typing in consideration of the coordinate system O-x'y'z', the beginning of which coincides with the midpoint of the segment AC, the axis O x' collinear the half-line speakers and PLoS is ity h O y' coincides with the plane Oxyz, you can get point D belongs to the surface described by the equation

where

x',y',z' coordinates of the point D in the coordinate system O'x'y'z'.

Since point D belongs simultaneously to two surfaces, therefore, it belongs to the line of intersection of these surfaces.

Because the plane HOU and h O y' are the same, then equation (4) in the coordinate system Oxyz can be obtained by replacing the variables in accordance with known expressions [8]:

x'=(x-x_{0})cosα+(y-y_{0})sinα,

y'=-(x-x_{0})sinα+(y-y_{0})cosα,

where x_{0}, y_{0}- coordinates of the point O x' in the coordinate system Oxyz;

α - the angle between the coordinate axes ox and O x' (see figure 5).

As a result of this transformation the equation (4) takes the form

a_{2}x^{2}+b_{2}y^{2}+C_{2}Hu+d_{2}x+e_{2}y+f_{2}=z^{2},

where

If we consider the difference of the difference of the distances from point D to point pairs {a, b} and {a, C}, it is obvious that

the EU is ü difference of the difference of the distances from point D to point pairs {A, In} and {a, C} is equal to the difference of the distances from the point D to the pair of points {S, In}. From which it follows that the point D also belongs to the third surface described by the equation

and_{3}x^{2}+b_{3}y^{2}+C_{3}Hu+d_{3}x+e_{3}y+f_{3}=z^{2},

where

Thus, the location of the point D in the coordinate system Oxyz is defined by a system of equations

where a_{1}=(2a/Δr_{AB})^{2}-1; b_{1}=-1; f_{1}=(Δr_{AB}/2)^{2}-a^{2}.

The system of equations (5) relates the unknown values of the coordinates of the point D with known coordinates of points a, b, C, and values of the differences of the distances of Δr_{AB}that Δr_{AC}and Δr_{BC}. However, due to the presence of functional relationships between the associated system of equations, this system has infinitely many solutions. In the composition of the set of solutions will include the vectors of coordinates of all intersection points of the surface position of point D, described within the system (5) equations.

Find the equation of the spatial line containing all points whose coordinates are the roots of the system uravnenii is (5).
For this purpose let us consider a section of the surface position of point D plane described by the equation z=z_{S}=const.

For arbitrary values of z_{S}you can record

where

Included in the system (6) equations are the equations of hyperbole. Thus, to solve the system of equations (6) means to find the coordinates of the points of intersection of the three hyperbole, described within a system of equations.

With the aim of finding solutions of system (6) will bring it to mind.

where l_{1}=(a_{1}Δ_{bd}+Δ_{ad})/K;

m_{1}=(a_{1}Δ_{be}+Δ_{ae})/K;

n_{1}=(a_{1}Δ_{bf}+Δ_{af}+f_{1}Δ_{ab})/K;

l_{2}=-a_{1}Δ_{cd}/K;

m_{2}=-a_{1}+Δ_{ce}/K;

n_{2}=(a_{1}Δ_{cf}+f_{1}Δ_{ac})/K;

l_{3}=-Δ_{cd}/K;

m_{3}=-Δ_{ce}/To;

n_{3}=(-Δ_{cf}+f_{1}Δ_{bc})/K;

K=a_{1}Δ_{bc}+Δ_{ac};

From the first equation of system (7) it follows that

y=-(l_{1}x+n_{1})/(x+m_{1}),

therefore, the system of equations (7) can be represented in the form

where

img src="https://img.russianpatents.com/818/8182199-s.jpg" height="6" width="45" >

B_{2}=m_{1}+l_{3};

C_{2}=l_{3}m_{1}-l_{1}m_{3}+n_{3};

D_{2}=m_{1}n_{3}-m_{3}n_{1}.

The solutions of the quadratic equation system (8) are two values of the variable x, defined by the well-known expressions:

where a,b,c are the coefficients of a quadratic equation, for this particular case is equal to:

a=1;

If you type designation

y_{1}=-(l_{1}x_{1}+n_{1})/(x_{1}+m_{1}and y_{2}=-(l_{1}x_{2}+n_{1})/(x_{2}+m_{1}),

the quotient of the difference y_{2}and y_{1}and the difference of the square roots of the equation x_{2}and x_{1}is determined by the expression

and the sum of these values by the expression:

where

The result can be interpreted as follows: because the value of the relation (9) does not depend on the variable z, hence, taking into account (10), all points whose coordinates are solutions of the system of equations (5), lie in the same plane, perpendicular to the plane HOU, crossing the ox axis at an angle

and passing through the point with position is natami

The result means that the values of the difference of distances from two pairs of reference points to the desired location points IRI determine the direction (angle γ) a source of radiation located at an arbitrary height h above the plane ABC (see Fig.6).

In the composition of the inventive device consists of:

1) antenna;

2) antenna;

3) antenna;

4) measuring the time differences;

5) measuring the time differences;

6) computing unit;

7) the display unit.

The outputs of the antennas 1 and 2 are connected with the first inputs of the measure of the difference between times 4 and 5, the second input of which is supplied the output signal from the antenna 3. The outputs of the measure of the difference between times 4 and 5 are connected to first and second inputs of the computing unit 6, respectively. The output of the computing unit 6 is connected to the input of the display unit.

Antenna 1, 2 and 3 are placed at the vertices of the triangle ΔABC, respectively.

The signal of the Islamic Republic of Iran, adopted by the antennas 1, 2 and 3, at their outputs is

u_{1}(t)=U(t)cos(ω_{0}t+ϕ_{0}),

u_{2}(t)=U(t+Δt_{21})cos[ω_{0}(t+Δt_{21})+ϕ_{0}],

u_{3}(t)=U(t+Δt_{31})cos[ω_{0}(t+Δt_{31})+ϕ_{0}],

respectively.

The signals from the outputs of the antennas 1 and 3 are received at first and second inputs of the meter difference Bremen respectively,
similarly, the signals from the outputs of the antennas 2 and 3 are received at first and second inputs of the meter difference of 5 times, respectively. The measure of the difference between times 4 and 5 perform the operation of measuring the difference of time Δt_{13}and Δt_{23}a signal IRI on a pair of antennas {1,3} and {2,3}. Thus

Δt_{ij}=t_{i}-t_{j},

where t_{k}- the arrival time of the signal IRI at the k-th antenna

Δt_{nm}- the time difference of signal arrival IRI n-th and m-th antenna.

The measure of the difference between times 4 and 5 implement one of the well known [e.g., 9] means of measuring the time differences.

From the outputs of the sensors of the differences of the times of 4 and 5 measured values Δt_{13}and Δt_{23}come respectively into the first and second inputs of the computing unit 6. Computing unit 6 is a specialized computing device, which sequentially perform the following operations:

- values are calculated difference ranges Δr_{13}that Δr_{23}and Δr_{12}using expressions

Δr_{13}=Δt_{13}·ν_{EMW}that Δr_{23}=Δt_{23}·ν_{EMW}that Δr_{12}=Δr_{13}-Δr_{23}.

- calculated value γ elevation IRI using expression

- calculated values of x_{f},y_{f/sub>
the coordinates of point F, which belongs to the line position on Iran, using the expressions:}

Necessary for the calculations a priori known values:

- ν_{EMW}- the velocity of propagation of electromagnetic waves;

- a - half of the distance between the antennas 1 and 2;

- x_{3},y_{3}coordinates of the antenna 3 in the coordinate system Oxyz is stored in a memory of the computing unit 6.

The calculated values γ,x_{f},y_{f}from the output of the computing unit 6 receives the display unit 7, which is designed to visualize the results of the proposed method of direction finding.

From the outputs of the sensors of the differences of the times of 4 and 5 measured values Δt_{13}and Δt_{23}come respectively into the first and second inputs of the computing unit 6. Computing unit 6 is a specialized computing device, which sequentially perform the following operations:

- values are calculated difference ranges Δr_{13}that Δr_{23}and Δr_{12}using expressions

Δr_{13}=Δt_{13}·ν_{EMW}that Δr_{23}=Δt_{23}·ν_{EMW}that Δr_{12}=Δr_{13}-Δr_{23}.

- calculated value γ azimuth IRI using expression

- calculated values of x_{f},y_{f}the coordinates of point F, which belongs to the line position on Iran, using the expressions:

Necessary for the calculations a priori known values:

- ν_{EMW}- the velocity of propagation of electromagnetic waves;

- a - half of the distance between the antennas 1 and 2;

- x_{3},y_{3}coordinates of the antenna 3 in the coordinate system Oxyz is stored in a memory of the computing unit 6.

The calculated values γ,x_{f},y_{f}from the output of the computing unit 6 receives the display unit 7, which is designed to visualize the results of the proposed method of direction finding.

Option display the results of the finding presented in Fig.7.

Thus, the proposed method of direction finding and device for its implementation, in comparison with the prototype, provide the possibility of determining the azimuth of the IRI under arbitrary variations of the mutual location of the antennas of the radio signal. Thus, the functionality of the direction finder expanded.

References

1. Shebshaevich B.C. introduction to theory of space navigation. -M.:Sov.radio, 1971. - 296 S.

2. The dulevich V.E., Korostelev, A., Miller Y.A. and other Theoretical bases of radar/edited Vaitulevich. - M.: Owls. radio, 1964. - 732 S.

3. Theoretical foundations of RA is ilocale. Textbook for high schools/Under the editorship Aderman. - M.: Owls. radio, 1970. - 560 C.

4. Finkelstein M.I. fundamentals of radar. - M.: Owls. radio, 1973. - 496 S.

5. Belotserkovsky G.B. fundamentals of radar and radar devices. - M.: Owls. radio, 1975. - 336 S.

6. Klimenko, N., Klimenko S.V. current state of theory and practice of radiointerference//Foreign Radioelectronics, 1990, N1. - P.3-14.

7. The international space radio detection system in distress, Ed. Wasserchemie. - M.: Radio and communication, 1987. - 376 S.

8. Korn G., Korn M. Handbook of mathematics for scientists and engineers. - M.: Nauka, 1984. - 832 S.

9. Wuu Chenn, Pearson Allan E. On time deley estimation involving received signals//IEEE Trans. Acount., Speech, and Signal Process., 1984, 32, N4, C.828-835.

10. RDF system that uses a circular antenna array. Pat. 4633257, USA.

11. Direction finder: A.S. 1555695 the USSR, MKI^{5}G 01 S 3/46 /Dikarev VI, Provotorov GF, Sherstobitov CENTURIES

12. Active radiointerference system Pat. 57-51632, Japan.

13. The interferometer. Pat. 290308, Germany.

14. Method and apparatus for direction finding and frequency identification. Pat. 4443801, USA.

15. Single location system. Pat. 4819053, USA.

16. The method of determining the location of the transmitter by measuring the difference of the delay times. Pat. 274102, Germany.

17. Method hyperbolic positioning and device for its implementation. Pat. 229866, Germany.

18. The finder. Pat. 57-51910, Japan.

19. Direction finding of the source of electromagnetic radiation using an adaptive antenna array. Pat. 4862180, USA.

20. Sibel A.G. Differential-ranging method of direction finding emitters and realizing it device. RF patent № 2204145 from 10.05.2003.

1. The method of finding the source of the radio emission, based on the reception of its signal by the three antennas; measuring the time differences of signal emitters antennas, forming two measuring base; calculating values of the difference of distance from the emitters to the antennas forming the measuring base; calculating the value of the azimuth of the source of radio emission; calculating coordinate values of a point belonging to the line position of the emitters; displaying the obtained results, wherein the feature of the antenna in an arbitrary manner.

2. A device for determining the bearing of a source of radio emission, containing three antennas, two meter difference between the times of reception of the signal computing unit and a display unit, and the outputs of the antennas 1 and 2 are connected with the first inputs of the measure of the difference between times 4 and 5, the second input of which is supplied the output signal from the antenna 3, characterized in that the antenna is placed in an arbitrary manner, the outputs of the probes to the difference of times is 4 and 5 are connected to first and second inputs of the computing unit 6, the output of which is connected to the input of the display unit 7.

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