# Differential-ranging method of direction finding emitters and realizing it device

The invention is used in electronics to determine the azimuth of the source of radio emission (IRI) in sirokopasovnih dynamical systems. Technical result achieved - ensuring the possibility of determining the azimuth of the IRI for any size of the measurement bases of the direction finder and options relative position of Iran and antenna direction finder. The method of finding the IRI is based on the reception of its signal by the three antennas, the measurement of the two differences of the times of reception of the signal IRI antennas forming an orthogonal base, post-processing of results of measurements in order to calculate the values of the azimuth angle of the IRI and the coordinates of a point through which passes the line of sight of the IRI. The results display in a readable form. A device that implements the method contains three antennas are placed at the vertices of an isosceles right triangle, two meter difference between the times of reception of the signal blocks subtraction, summarize, analyze, and display. Offered the option readable form display the results. 2 C. p. F.-ly, 9 Il. This proposal relates to the field of radio engineering and can be used in direction-finding systems for determination is received using known methods of direction finding: amplitude (method of maximum method minimum method comparison and others), phase, frequency and time.Known methods and devices of direction finding [1-5, 10-19 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 IRI.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 viewed as a degenerate case of difference-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 was the giving signals, come on different trajectories, 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 signalsr = r

_{1}-r

_{2}(r

_{1}and r

_{2}the distance from Iran to the first and second antennas respectively). The relative delaysignals, due to the constancy of the speed and linearity of propagation of radio waves is proportional to the difference of course:The azimuth valueThe IRI is calculated by the formulawhere d is the distance between the antennas, withwhere r=min(r

_{1},r

_{2}).In the General case, a system that uses considered are differential-ranging, however, with large deletions IRI from the center of the base, when the distance to Iran to asobu, 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.The direction finding is also possible to produce based on measurements of the Doppler shift frequencyf

_{}[see, for example, 7]. Sincewherethe wavelength of the signal IRI, v

_{r}- radial velocity IRI relative to the receiving antenna,

then, measuringf

_{}at extremely small interval, you can get variant frequency method, called differential Doppler, which allows to determine the value of the angular setting of the positioning:

where v is the 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 asymptotically tends to a conical form to the listed methods is the possibility of finding IRI only in the far zone i.e., if the condition

r>>d (1)

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. The dependence of the error of the bearing shown in Fig.1.Known way of finding the closest to the present invention is a method [6] , based on the measurement of the phase difference signal IRI taken three antennas, forming two pairs of orthogonal measurement bases (see Fig.2), and calculating the value of the angleazimuth on Iran using expression

where(the wavelength of the signal IRI). This method is chosen as a prototype.The aim of the invention is to improve the accuracy of direction finding and expanding the functionality of direction finder (removing the restrictions described by the expression (1)) by taking into account the sphericity of the front of propagation of electromagnetic waves.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 equal orthogonal measurement bases (see Fig.3), provide measurements of differences in arrival times of the signal Iran's antenna, calculate:

the angleazimuth IRI using expression

wheret

_{AC},t

_{BC}- the difference between the time of signal reception IRI antennas forming the pairs A, C and b, respectively,

coordinates (x

_{f},

_{f}points F owned by a bearing line on Iran, using expressions

the/916.gif">r

_{BC}=t

_{BC}c - difference of the distance from Iran to pairs of points a, C and b, respectively,

display the result.The proposed method involves the following operations:

- have three antennas at the vertices of an isosceles right triangleABC;

- accept signal IRI on all three antennas

- measure the time differences of signal IRI antennas forming an orthogonal basis;

- calculates the sum and difference of the difference of times of signal reception IRI;

- calculate the value of the ratio of the sum of the differences between the times of reception of Iran to the difference of difference of times of signal reception IRI;

- calculate the value of the function arctan(x), the argument of which is the result of the previous operation;

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

- show the obtained results.In Fig.4 shows a variant of the device that implements 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, which are intended to measure razvlecheniya blocks 6-8 and block 9, performing a visualization of the results.The principle of the proposed device consists in the following. Antenna 1, 2 and 3 have three points in three-dimensional space a, b, C having coordinates (x

_{A}, y

_{A}, z

_{A}), (x

_{In}, y

_{In}, z

_{B}) and (x

_{With}, y

_{C}, z

_{C}respectively.For convenience and clarity, the further discussion will assume that the location of Iran coincides with some point D with coordinates x, y, z. We denote the difference of the distances from it to points a and b throughr

_{AB}and the difference of the distances from points a and C throughr

_{AC}.Now we introduce a coordinate system z 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 (Fig.5). Then the coordinates of the points a, b and C in the system z respectively

x

_{And}=-a; y

_{A}=0; z

_{A}=0;

x

_{In}=a; y

_{B}=0; z

_{B}=0;

x

_{C}=0; y

_{C}=a; z

_{C}=0,

where a = |AB|/2,

and therefore, you can write

Erected in the square right and left side of equation (2), we obtain

where

Thus, from the above reasoning it follows that the point D belongs to the surface described by equation (4) (see Fig.6).Note, however, that when squaring equation (2) has occurred, the loss of the sign of the difference rangesr

_{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 u z', the beginning of which coincides with the midpoint of the segment AC, the axis O x' collinear the half-line speakers and the plane x O y' coincides with the plane zO', you can get that point D belongs to the surface described by the equation

where

x', y', z' coordinates of the point D in the coordinate system O h u z';

b = |AC|/2.Since point D belongs simultaneously to two surfaces, therefore, it belongs to the line of intersection of these surfaces.Because the plane HOU and x O y' are the same, then ur is ojeniyi [8]:

x= (x-x

_{0})cos+(y-y

_{0})sin,

y= -(x-x

_{0})sin+(y-y

_{0})cos,

where x

_{0},

_{0}- coordinates of the point O x' coordinate system Oxyz;

- the angle between the coordinate axes ox and O x' (see Fig.7).As a result of this transformation the equation (7) takes the form

x

^{2}and

_{2}+

^{2}b

_{2}+HUS

_{2}+d

_{2}+UE

_{2}+f

_{2}=z

^{2}, (9)

where

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

that is, the difference of the difference of the distances from point D to pairs of points a, b and a, C is equal to the difference of the distances from point D to point pairs With C From which it follows that the point D also belongs to the third surface described by the equation

x

^{2}a

_{3}+

^{2}b

_{3}+xyc

_{3}+xd

_{3}+UE

_{3}+f

_{3}=z

^{2}, (11)

where

d

_{3}=a;

e

_{3}=a;

a/59/594465.gif">

where

The system of equations (12) 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 ofr

_{AB},r

_{AC}andr

_{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 (12) equations.Find the equation of the spatial line containing all points whose coordinates are the roots of the equation system (12). 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 write

where f'

_{1}=f

_{1}-z

^{2}

_{s}; f'

_{2}=f

_{2}-z

^{2}

_{s}; f'

_{3}=f

_{3}-z

^{2}

_{s}. (15)

Included in the system (14) equations are the equations of hyperbole. Thus, to solve the system of equations (14) means to find the coordinates of the intersection points of the dem it to mind

where d

_{15}=(a

_{1}(b

_{2}d

_{3}-b

_{3}d

_{2})-b

_{1}(a

_{2}d

_{3}-a

_{3}d

_{2}))/G;

e

_{15}=(a

_{1}(b

_{2}e

_{3}-b

_{3}e

_{2})-b

_{1}(a

_{2}e

_{3}-a

_{3}e

_{2}))/G;

f

_{15}=(a

_{1}(b

_{2}f

_{3}-b

_{3}f

_{2})-b

_{1}(a

_{2}f

_{3}-a

_{3}f

_{2})+f

_{1}(a

_{2}b

_{3}-a

_{3}b

_{2}))/G; d

_{26}=-a

_{1}(c

_{2}d

_{3}-c

_{3}d

_{2})/G;

e

_{26}=-a

_{1}(c

_{2}e

_{3}-c

_{3}e

_{2})/G;

f

_{26}=(-a

_{1}(c

_{2}f

_{3}-c

_{3}f

_{2})-f

_{1}(a

_{2}c

_{3}-a

_{3}c

_{2}))/G;

d

_{36}=b

_{1}(c

_{2}d

_{3}-c

_{3}d

_{2})/G;

e

_{36}=b

_{1}(c

_{2}e

_{3}-c

_{3}e

_{2})/G;

f

_{36}=(b

_{1}(c

_{2}f

_{3}-c

_{3}f

_{2})+f

_{1}(b

_{2}c

_{3}-b

_{3}c

_{2}))/G;

G=a

_{1}(b

_{2}c

_{3}-b

_{3}c

_{2})-b

_{1}(a

_{2}c

_{3}-a

_{3}c

_{2}).From the first equation of system (16) it follows that

Therefore, the system of equations (16) can be represented in the form

where a

_{1}=d

_{26};

B

_{1}=d

^{2}

_{15}+2d

_{26}e

_{15}-d

_{15}e

_{26}+f

_{26};

C

_{1}=2d>D

_{1}=f

^{2}

_{15}-f

_{15}e

_{15}e

_{26}+2e

^{2}

_{15}f

_{26};

B

_{2}=e

_{15}+d

_{36};

C

_{2}=d

_{36}e

_{15}-d

_{15}e

_{36}+f

_{36};

D

_{2}=e

_{15}f

_{36}-e

_{36}f

_{15},

or equivalent

The solutions of the quadratic equation system (18) are two values of the variable x, defined by the well-known expressions:

where a, b, C - coefficients quadrature equations for this particular case equal:

If you enter symbols

and

indicates the individual difference variables in

_{1}and I

_{2}and the difference of the roots of the quadratic equation, x

_{1}and x

_{2}is determined by the expression

and the amount of variable y

_{1}, y

_{2}and the roots of the quadratic equation, x

_{1}, x

_{2}are determined by the expressions

The result can be interpreted as follows: because the value of the relationship (19) does not depend on the variable z, zletovosko, perpendicular to the plane HOU, crossing the ox axis at an angle

and passing through the point with coordinates

Sincer

_{BC}=r

_{AC}-r

_{AB}then equation (21) can be represented in the form

The result means that the ratio of the sum and difference of difference of distances from two pairs of reference points to the desired location points IRI determines the direction (angle) a source of radiation located at an arbitrary height h above the plane ABC (see Fig.8).If the measured distancesr

_{AC}andr

_{BC}to use the measure of the difference of times of signal IRI, coming to points a, b and C, equation (22) can be rewritten in the form

wheret

_{AC},t

_{BC}- the difference between the times of reception of IRI in the points a and C and b and C, respectively,

C is the speed of propagation of the radio signal.In the composition of the claimed device comprises the antenna 1, 2 and 3, the measure of radioedit with the first inputs of the measure of the difference between times 4 and 5, on the second input of which is supplied the output signal from the antenna 3. The meter output is the difference of the times 4 is connected to the first input of the subtraction unit 6 and unit summation 7, and the output of the meter to the difference of times 5 is connected to the second input of the subtraction unit 6 and unit summation 7. The inputs of the analysis block receives signals from the outputs of the measure of the difference between times 4 and 5, the subtraction unit 6 and unit summation 7. The output of the analysis block is connected to the input of the display unit.Antenna 1, 2 and 3 are placed at the vertices of an isosceles right triangleABC 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(

_{0}t+

_{0}),

u

_{2}(t) = U(t+t

_{21})cos[

_{0}(t+t

_{21})+

_{0}],

u

_{3}(t) = U(t+t

_{31})cos[

_{0}(t+t

_{31})+

_{0}],

respectively.The signals from the outputs of the antennas 1 and 3 are received at first and second inputs of the meter difference of 4 times, respectively, similarly, the signals from you is agnosti times 4 and 5 perform the operation of measuring the difference of timet

_{13}andt

_{23}a signal IRI on a pair of antennas (1, 3) and (2, 3). This

t

_{ij}= t

_{i}-t

_{j},

where t

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

t

_{nm}- the time difference of signal arrival Iran's 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 oft

_{13}andt

_{23}come on blocks subtracting 6 and summation 7. The subtraction unit performs the operation of calculating the values of t

_{}difference of difference of times of signal reception, Iran; unit summation performs the operation of calculating the values of t

_{}the amount of the difference of times of signal reception Iran:

t

_{}=t

_{13}+t

_{23},

t

_{}=t

_{13}-t

_{23}.

The calculated values of t

_{}and t

_{t13andt23from the outputs of the sensors of the differences of the times of 4 and 5. The unit of analysis 8 is a specialized computing device, performing the following computation:- calculated value of the ratio of- calculate the value ofelevation IRI using expression=ASAP(w),where the argument is the result of the previous computation;- calculate values of xf,fthe coordinates of a point belonging to the line position on Iran.The calculated values of, xf,ffrom the output of the analysis block enter display unit, which is designed to visualize the results of the proposed method of direction finding.Display option finding results presented in figure 9.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 for any size of the measurement bases of the direction finder and options relative position of Iran and antenna direction finder.In addition, the proposed method PIM functionality of the direction finder expanded.Sources of information1. Shebshaevich B. C. introduction to theory of space navigation. - M.: Owls. radio, 1971. - 296 S.2. The dulevich C. E., Korostelev, A. A., Miller S. A. and other Theoretical bases of radar./Edited Century. Dulevich. - M.: Owls. radio, 1964. - 732 S.3. Theoretical bases of radar. Textbook for high schools./Ed. by J. D. Shirman. - M.: Owls. radio, 1970. - 560 C.4. Finkelstein, M. I. fundamentals of radar. - M.: Owls. radio, 1973. - 496 S.5. Belotserkovsky, B. fundamentals of radar and radar devices. - M.: Owls. radio, 1975. - 336 S.6. Klymenko N. N., Klimenko S. C. current state of theory and practice of radiointerference.//Arabina electronics, 1990. N 1. - N-3-14.7. The international space radio detection system in distress. /Ed. by C. C. of Websevices. - 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, N 4, Pp. 828-835.10. RDF system that uses a circular antenna array. U.S. patent 4633257.11. Direction finder: A. C. the USSR 1555695 MKI5G 01 S 3/46. Dikarev Century. And., Provotorov, F., Sherstobitov centuries12. the FDS and apparatus for direction finding and frequency identification. Patent 4443801 USA.15. Single location system. Patent 4819053 USA.16. The method of determining the location of the transmitter by measuring the difference of the delay times. Patent GDR 274102.17. Method hyperbolic determine where and device for its implementation. Patent GDR 229866.18. The finder. The Japan Patent 57-51910.19. Direction finding the source of the radio emission using an adaptive antenna array. U.S. patent 4862180. Claims1. The method of finding the source of the radio emission (IRI) based on the reception of its signal three antennas, forming two pairs of equal orthogonal measurement bases, characterized in that the measured difference of times of signal reception IRI antennas forming an orthogonal measurement bases; calculates the sum and difference of the difference of times of signal reception IRI; calculate the value of the ratio of the sum of the differences between the times of reception of Iran to the difference of difference of times of signal reception IRI; calculate the value of the function arctan (w), as an argument which is the result of the previous operation; calculate a coordinate value of a point belonging to the line position on Iran; display the received result the frame of a rectangular triangle two meter difference between the times of reception of the signal blocks subtraction, summarize, analyze, and display, characterized in that the antenna 1 and 3, 3 and 2 form an orthogonal measurement bases, the output signal of the antenna 1 receives at the first input of measuring the difference between the times of 4, the output signal of the antenna 2 receives at the first input of measuring the difference between the times of 5, the output signal from the antenna 3 is supplied to the second inputs of measuring the difference between times 4 and 5, the meter output is the difference of the times 4 is connected to the first input of the subtraction unit 6 and unit summation 7, and the meter output is the difference of times 5 is connected to the second input of the subtraction unit 6 and unit summation 7, the inputs of the analysis block 8 receives signals from the outputs of the measure of the difference between times 4 and 5, the subtraction unit 6 and unit summation 7, the output of the analysis block is connected to the input of the display unit. }

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