RU2325666C2 - Differential-range technique of locating radio-frequency radiation source - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: determination of the azimuth and position angle of the radio-frequency radiation source in wide-base location systems. The surface of position of the radio-frequency radiation source is a plane, which has a positioning line of the source, in the form of intersection of two hyperbolic surfaces of position of the corresponding differential-time measurements. The technique for locating the radio-frequency radiation source is based on receiving its signal using three antennae, measurement of two time differences for receiving the signal from the source using the antennae, which form measuring bases, subsequent processing of measuring results with the aim of calculating the value of the bearing angle of the radio-frequency radiation source, coordinate points, through which the observation line of the radio-frequency radiation source passes, as well as the position angle of the radio-frequency radiation source.

EFFECT: measurement of the bearing angle and position angle of the radio-frequency radiation source with high accuracy due to elimination of systematic errors during direction finding.

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Description

The invention relates to the field of radio engineering and can be used in direction finding complexes to determine the angular coordinates of a radio emission source (IRI).

Modern systems for determining the direction to the IRI are built using well-known methods of direction finding: amplitude (maximum method, minimum method, comparison method, etc.), phase, frequency and time.

Known methods and devices for direction finding [1-5, 10-20, etc.].

For example, a number of direction finding methods are known, based on the fact that the phase relations between signals received at spatially separated points can be converted into the amplitude dependence of the sum of received signals on the location of the IRI.

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

This direction finding method can be considered as a degenerate case of the differential-ranging method, when due to the mechanical movement of the antenna system its position is selected so that the distance differences from the IRI to the symmetrical points of the antenna are equal to zero (and therefore the phase differences of the signals arriving at these points were equal to zero). In-phase addition of signals arriving along different paths provides maximum energy at the receiving point.

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

There is also a method of direction finding based on measuring the difference in the time of reception of signals from the IRI by two spaced antennas [for example, 6]. When the position of the IRI deviates from the perpendicular to the center of the base, a difference in the signal path Δr = r ₁ -r ₂ occurs (r ₁ and r ₂ are the distances from the IRI to the first and second antennas, respectively). The relative delay of the τ signals due to the constancy of the speed and linearity of propagation of radio waves is proportional to the path difference

τ = Δr / s.

The azimuth value α IRI is calculated by the formula

α≈arccos (Δr / d),

where d is the distance between the antennas,

wherein

where r = min (r ₁ , r ₂ ).

In the general case, systems using the principle considered are differential-ranging, however, at large distances from the center of the IRI, when the distance to the IRI is significantly larger than the base, the hyperbolic position lines characteristic of the differential-ranging method in the far zone practically coincide with their asymptotes emanating in the form of rays from the center of the base. In this case, difference-ranging systems can be considered goniometric.

Direction finding can also be done on the basis of measuring the Doppler frequency offset Δf _d [see, for example, 7]. Insofar as

Δf _d = -ν _r / λ,

where λ is the wavelength of the IRI signal;

ν _r is the radial speed of the IRI relative to the receiving antenna,

then, by measuring Δf _d on an extremely small interval, you can get a variant of the frequency method called the Doppler differential, which allows you to determine the value of the angular location parameter α:

α = 2arccos (ν _r / ν),

where ν is the IRI velocity in the coordinate system, the beginning of which coincides with the location of the receiving antenna.

Such an approach to measuring the angle is based on the assumption that for small measuring bases (“small” compared to the distance to the positioned object) the hyperbolic position surface asymptotically tends to conical, the shape of which is in turn uniquely described by the vertex point and the angle at the base.

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

r >> d,

where r is the distance to Iran;

d is the length of the measuring base.

The fulfillment of this condition allows us to make an assumption about the plane of the propagation front of the electromagnetic wave.

It is known that the accuracy of determining the IRI bearing depends on the ratio of the size of the measuring base to the distance to the IRI (the dependence is characterized by an expression that takes into account the lower Cramer-Rao boundary [6]). However, a significant increase in the size of the measuring base leads to an increase in the systematic error of direction finding due to the sphericity of the front of the electromagnetic wave. The magnitude of the direction finding error at range values r <10d can reach ten or more percent of the value of the angular coordinate of the IRI. To reduce the direction finding error, direction finding devices are used (for example, [20]), in which the systematic direction finding error is minimized by taking into account the sphericity of the wave front.

Of the known methods of direction finding closest to the proposed method is [20], which involves the following operations:

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

- receive an IRI signal to all three antennas;

- measure the time difference Δt _AC and Δt _{BC of the} reception of the IRI signal by antennas placed in pairs of points {A, C} and {B, C}, respectively;

- calculate the value of the azimuth of the IRI using the expression

where x ₃ = (b ² -c ² ) / a;

- calculate the coordinates {x _f , y _f } of the point F belonging to the line of the bearing IRI, using the expressions:

Where

- display the results.

The disadvantage of this method of direction finding is that only one angular coordinate of the IRI is determined - azimuth, while for the unambiguous determination of the line of the bearing of the IRI it is also necessary to determine the elevation angle β (see Fig. 1)

This method is selected as a prototype.

The aim of the invention is to develop a method that allows you to calculate the angle β - the elevation angle of the IRI.

This goal is achieved by the fact that in the method of direction finding of the IRI, based on the reception of its signal by three antennas that form two pairs of measuring bases, measuring the differences in the times of arrival of the IRI signal to the antennas and calculating using the expressions (above) used in the prototype:

- values of differences of ranges from IRI to pairs of points {A, C} and {B, C} of antenna placement;

- values of the angle γ of the azimuth of the IRI;

- coordinates {x _f , y _f } of the point F belonging to the line of the bearing IRI,

additionally calculate the elevation angle β IRI using the expression

Where

and display the results.

The proposed method involves the following operations:

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

- receive an IRI signal to all three antennas;

- measure the time difference between the reception of the IRI signal by the antennas forming the measuring bases [A, C} and {B, C];

- calculate the value of the angle γ of the azimuth of the IRI;

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

- calculate the value of the angle β of the IRI;

- display the results.

A device that implements this method of direction finding, similar to the device described in [20], and consists of three functionally interconnected elements (figure 2):

- an antenna system containing three antennas 1, 2 and 3;

- a measurement system containing blocks 4 and 5, designed to measure differences in the time of reception of the IRI signal by antenna pairs {1; 3} and {2; 3};

- a processing and display system comprising a computing unit 6 and a unit 7, which implements a visualization of the results.

The difference from the device described in [20] is that in the computing unit 6, the elevation angle β is also calculated.

The principle of operation of the device that implements the proposed method is as follows: antennas 1, 2 and 3 are located at three points in the three-dimensional space A, B, C having coordinates <x _A , y _A , z _A >, <x _B , y _B , z _B > and <x _C , y _C , z _C >, respectively.

For convenience and clarity of the further discussion, let us assume that the IRI location point coincides with some point D having unknown coordinates <x, y, z>. Denote the difference of the distances from it to points A and B by Δr _AB , and the difference of the distances to points A and C by Δr _AC .

, а плоскость хОу совпадала с плоскостью АВС (фиг.3). Тогда координаты точек А, В и С в системе Oxyz соответственно равныWe introduce the coordinate system Oxyz defined in such a way that its origin coincides with the middle of the segment AB, the axis Ox is collinear to the vector

, and the xOy plane coincided with the ABC plane (Fig. 3). Then the coordinates of points A, B, and C in the Oxyz system are respectively equal

x _A = -a; at _A = 0; z _A = 0;

x _B = a; y _B = 0; z _B = 0;

x _C = x ₃ ; y _C = y ₃ ; z is _C = 0;

Where

In this coordinate system, in accordance with [20], the equation of the surface of the position of the point D has the form of the canonical equation of a two-sheeted hyperboloid of revolution (see figure 4)

Where

Similarly, introducing the coordinate system O'x'y'z ', the origin of which coincides with the middle of the segment AC, the axis O'x' is collinear to the half-line AC, and the x'O'y 'plane coincides with the Oxyz plane, we can obtain 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'x'y'z'.

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

Since the planes xOy and x'O'y 'coincide, then equation (2) in the coordinate system Oxyz can be obtained by changing the variables in accordance with the known expressions [8]:

x '= (x-x ₀ ) cosα + (y- ₀ ) sinα,

y '= - (x-x ₀ ) sinα + (y-y ₀ ) cosα,

where x ₀ , y ₀ are the coordinates of the point O'x 'in the coordinate system Oxyz;

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

As a result of this transformation, equation (2) takes the form

a ₂ x ² + b ₂ y ² + s ₂ xy + d ₂ x + e ₂ y + f ₂ = z ² ,

where a ₂ = (a + x ₃ ) ² / Δr ² _AC - 1;

b ₂ = y ² ₃ / Δr ² _AC - 1;

c ₂ = 2y ₃ (a + x ₃ ) / Δr ² _AC ;

d ₂ = x ₃ -a-2 (a + x ₃ ) (2b ² -a (a + x ₃ )) / Δr ² _AC ;

e ₂ = y ₃ -2y ₃ (2b ² -a (a + x ₃ )) / Δr ² _AC ;

f ₂ = (2b ² -a (a + x ₃ )) ² / Δr ² _AC - ((ax ₃ ) ² + y ² ₃ + 4b ² -Δr ² _AC ) / 4;

If we consider the difference in the differences of the distances from the point D to the pairs of points {A, B} and {A, C}, then it is obvious that

that is, the difference in the differences of the distances from the point D to the pairs of points {A, B} and {A, C} is equal to the difference in the distances from the point D to the pair of points {C, B}. It follows that the point D also belongs to the third surface described by the equation

a ₃ x ² + b ₃ y ² + c ₃ xy + d ₃ x + e ₃ y + f ₃ = z ² ,

where a ₃ = (a-x ₃ ) ² / Δr ² _BC - 1;

b ₃ = y ₃ ² / Δr ² _BC - 1;

c ₃ = -2y ₃ (ax ₃ ) / Δr ² _BC ;

d ₃ = x ₃ + a + 2 (a-x ₃ ) (2c ² -a (a-x ₃ )) / Δr ² _BC ;

e ₃ = y ₃ -2y ₃ (2c ² -a (ax ₃ )) / Δr ² _BC ;

f ₃ = (2s ² -a (a-x ₃ )) ² / Δr ² _BC - ((a + x ₃ ) ² + y ² ₃ + 4c ² -Δr ² _BC ) / 4.

Thus, the location of point D in the Oxyz coordinate system is determined by the 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 (3) connects the unknown values of the coordinates of the point D with the known coordinates of the points A, B, C and the values of the distance differences Δr _AB , Δr _AC and Δr _BC . However, due to the presence of a functional relationship between the equations in the system, this system has an infinite number of solutions. The set of solutions will include the coordinate vectors of all the intersection points of the position surfaces of the point D described by the equations included in system (3).

Let us determine the form of the spatial line containing all points whose coordinates are the roots of the system of equations (3). To do this, we consider the section of the surfaces of the position of the point D by the plane described by the equation z = z _S = const (see Fig. 6).

For an arbitrary value of z _S, we can write

where f ' _i = f _i -z ² _S ; i = 1 ... 3.

The equations in system (4) are hyperbole equations. Thus, to solve the system of equations (4) means to find the coordinates of the intersection points of three hyperbolas described by the equations included in the system.

In order to find solutions of system (4), we bring it to the form

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 1Δ _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 / K; n ₃ = (- Δ _cf + f ₁ Δ _bc ) / K;

K = a ₁ Δ _bc + Δ _ac ;

From the first equation of system (5) it follows that

y = - (l ₁ x + n ₁ ) / (x + m ₁ ),

therefore, the system of equations (5) can be represented as

where B ₁ = l ² ₁ + 2l ₂ m ₁ -l ₁ m ₂ + n ₂ ;

C ₁ = 2l ₁ n ₁ + l ₂ m ₁ ² -m ₂ n ₁ -l ₁ m ₁ m ₂ + 2m ₁ n ₂ ;

D ₁ = n ² ₁ -m ₁ m ₂ n ₁ + m ² ₁ n ₂ ;

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 of system (6) are two values of the variable x, defined by well-known expressions:

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

If we introduce the notation

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 ),

then the quotient of the difference y ₂ and y ₁ and the difference of the roots of the quadratic equation x ₂ and x ₁ is determined by the expression

and the sum of these quantities is expressed by the expressions:

Where

The obtained result can be interpreted as follows: since the value of relation (7) does not depend on the value of the variable z, therefore, taking into account (8), all points whose coordinates are solutions of the system of equations (3) lie in one plane perpendicular to the xOy plane intersecting the axis Ox at an angle

and passing through point F with coordinates

The obtained result means that two values of the differences of ranges from two pairs of reference points to the desired location of the IRI determine the direction (azimuth angle γ) to the radio source located at an arbitrary height h above the plane ABC (see figure 1).

Thus, the value of the angle γ of the azimuth of the IRI is calculated using the expression

The coordinates {x _f , y _f } of the point F belonging to the IR bearing line are calculated using the expressions:

Where

The three calculated values (γ, x _f , y _f ) correspond to the plane Ω passing through the point F at an angle γ to the axis Ox and perpendicular to the plane ABC. Since the point D belongs simultaneously to the plane Ω and the position surface described by equation (1), therefore, it belongs to the intersection line of these surfaces (see Fig. 7).

(см. фиг.8), то уравнение поверхности положения, описываемой уравнением (1), в данной системе координат имеет видIf we introduce the coordinate system Ex''y''z '', whose origin coincides with the intersection point of the plane Ω with the axis Ox, ∠xEx '' = ∠γ,

(see Fig. 8), then the equation of the position surface described by equation (1) in this coordinate system has the form

Where

Since the plane Ω coincides with the plane x``Ez '', the hyperbola equation, which is the intersection line of the plane Ω and the position surface described by equation (9), is obtained by equating y '' = 0 and has the form (see Fig. 9)

Transforming equation (10), we obtain

Where

m = a ₁ ² l ² + b ² 2x ₀ ² cos ² γ-l ² x ₀ ² ;

x '' ₀ = -b ₁ ² x ₀ cosγ / l ² .

Since the hyperbola described by the canonical equation of the form

asymptotically tends to the line (asymptote) [8] described by the equation

therefore, for the elevation angle of the IRI, we can take the angle of inclination of the asymptote of the hyperbola in the x``Ez '' plane (see Fig. 10), the value of which is calculated by the formula

The calculated values of γ, β from the output of the analysis unit go to the display unit, which is intended to visualize the results of the proposed direction finding method.

Thus, the proposed method of direction finding, in comparison with the prototype, provides the ability to determine the elevation angle of the IRI.

LITERATURE

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Claims (1)

The method of direction finding of a source of radio emission (IRI), based on the reception of its signal by three antennas, measuring the difference in the time of reception of the signal by the antennas forming two measuring bases, calculating the difference values of the distances from the IRI to the antennas forming the measuring bases, calculating the value of the azimuth angle of the IRI, calculating the values the coordinates of the point belonging to the line of position of the IRI, and displaying the results, characterized in that they calculate the value of the elevation angle of the IRI using the expression

Where

α ₁ = Δr _AB / 2,

γ is the value of the azimuth angle of the IRI, Δr _AB is the difference between the distances from the location of the IRI to points A and B of the location of the corresponding antennas.

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