RU2363010C2 - Method of determining coordinates of radio-frequency radiation source and device to this end - Google Patents

Abstract

FIELD: instrument making.

SUBSTANCE: proposed invention aims at determining coordinates of radio-frequency radiation source (RRS) in space. On compliance with this invention, two-cavity hyperboloids of revolution are used as RRS location surfaces that correspond to two measurements of time difference, and a sphere with parametres defined in processing power flux density values at locations of two receiving aerials. The method is based on reception of RRS signal by three aerials, measurement of two differences in time of reception of aforesaid signals by aerials that form measurement bases, measurement of two RRS signal power flux density values. Then, measurement results are processed to calculate RRS azimuth and elevation angle, coordinates of the point the RRS location line passes through and range from RRS to aforesaid point. In compliance with this invention, the proposed device comprises three aerials, two signal reception time difference metres, two power flux density metres, computer and display.

EFFECT: determination of RRS three coordinates.

2 cl, 7 dwg

Description

This proposal relates to the field of radio engineering and can be used in passive radio complexes to determine the coordinates of sources of isotropic and quasi-isotropic radio emission.

The coordinates of the object is an ordered set of linear and (or) angular numerical quantities that determine the position of the object on the surface or in space in the corresponding coordinate system [1].

Therefore, devices for determining coordinates are divided into two groups:

1) positioning system (WMD) - a device for determining the three coordinates of an object;

2) direction finders - devices for determining one or two angular coordinates of an object.

In modern passive coordinate determination systems, the difference-ranging (RDM) principle is widely used.

So known [2] RDM method for determining the three linear coordinates of a source of radio emission (IRI), involving the following:

;- place four antennas at spaced points A _i , i = 1, 2, 3, 4 so that the volume

;

- simultaneously receive an IRI signal to all antennas;

- measure three independent time differences Δt _j1 = t _j -t ₁ , j = 2, 3, 4 of signal reception by pairs of antennas forming measuring antenna bases (where t _j is the signal reception time at point A _j );

- make up a system of nonlinear equations relating the sought coordinates 〈x, y, z〉 IRI with the coordinates 〈x _i , y _i , z _i приема receiving points A _i , i = 1, 2, 3, 4 and the measured range differences Δr _j1 = Δt _j1 / s (where c is the propagation velocity of electromagnetic waves):

- introduce an additional variable r ₁ and transform the system of nonlinear equations (1) to the form of a system of linear equations:

Where

, j=2, 3, 4;

, j = 2, 3, 4;

- substitute the solutions of the system of linear equations (2) of the form x (r ₁ ), y (r ₁ ), z (r ₁ ) in equation (3) and solve the quadratic equation with respect to the unknown value of r ₁ ;

- find two sets of roots of the system of equations (2) for two values of r ₁ ;

- choose one of the two sets of roots corresponding to the desired coordinates of the IRI.

The disadvantages of this method are the need for a priori information about the location of the object to perform the last operation (ambiguity of the solution) and the need to use 4 antennas to determine the three coordinates of the IRI.

Known [3] RDM direction finding method, 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 the antennas forming the measuring bases {A, C} and {B, C};

- calculate the difference values of the distances from the IRI to pairs of antennas using the expressions:

Dr _AU = Δt · _AS v _EMW, dr _VS = Δt · _Sun v _EMB, dr _AB = Δr -Δr _{AS Sun,}

where ν _EMB is the propagation velocity of the electromagnetic wave,

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

;where x ₃ = (b ² -c ² ) / a;

;

a = | AB | / 2; b = | AC | / 2; c = | BC | / 2;

- 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 is that only one angular coordinate of the IRI is determined - the azimuth γ (see Fig. 1), while for the unambiguous determination of the coordinates of the IRI it is also necessary to determine the elevation angle β and the distance to the IRI.

This method is selected as a prototype.

The aim of the invention is the ability to determine the three coordinates of the IRI.

This goal is achieved by the fact that in the method of direction finding (determining the angular coordinates) of the IRI, based on the reception of its signal by three antennas forming two measuring bases, measuring the differences in the signal reception times of the IRI by the antennas forming the measuring bases, calculating the azimuth value of the IRI, as well as the coordinates of the point belonging to the IRI bearing line, additionally calculate the elevation angle of the IRI, measure the power flux density of the IRI signal at the points of placement of the two antennas, calculate the distance to the IRI from the point, coordinates which is also calculated, the distance to the IRI from the point belonging to the line of the IRI bearing is calculated, and the calculated coordinates of the IRI are displayed in a convenient form.

The proposed method involves the following operations:

- have three antennas at the vertices of the triangle Δ ABC, while antennas 1, 2 and 3 are located at points A, B and C, respectively;

- 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 the antennas forming the measuring bases {A, C} and {B, C},

- measure the power flux density of the signal P ₁ and P ₂ at the locations of the antennas 1 and 2;

- calculate the difference values of the distances from the IRI to pairs of antennas using the expressions:

Δr _AC = Δt _AC · ν _EMB , Δr _BC = Δt _BC · ν _EMV , Δr _AB = Δr _AC -Δr _BC ,

where ν _EMW is the propagation velocity of the electromagnetic wave,

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

where x ₃ = (b ² -c ² ] / a;

;

;

a = | AB | / 2;

b = | AC | / 2;

c = | BC | / 2;

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

;Where

;

- calculate the value of the elevation angle β IRI using the expression

β = arctan (l / a ₁ ),

,Where

,

;a ₁ = Δr _AB / 2;

;

- calculate the value of the distance L to the IRI from point J and the coordinates of point J using the expressions:

,

,

x _J = 2aP ₂ / (P ₁ -P ₂ ) -a,

for _J = 0, z _J = 0,

- calculate the value of the distance L 'to the IRI from point F using the expression

where Δx = x _J -x _F ;

- display the results.

A device that implements this method 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 pairs of antennas {1; 3} and {2; 3}, and blocks 6 and 7, designed to measure the density of the power flux of the received signals at the locations of the antennas 1 and 2;

- a processing and display system comprising a computing unit 8 and a unit 9, which implements a visualization of the results.

The principle of operation of a 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, with coordinates 〈x _A , for _A , z _A 〉, 〈x _B , for _B , z _B 〉 and 〈x _C , for _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〉.

Any radio emission in the time domain can be represented as a stream of infinitely short pulses [4]. Let us imagine the radiation of PX in the form of a sequence of pulses specified by the function

,

,

;

;

t _i is the instant of occurrence of the i-th impulse;

U _i is the amplitude of the i-th pulse.

Then the IRI radiation can be characterized by the power P ₀ and the time t _{0 of the} radiation of the i-th pulse.

The location of the IRI relative to reference points (OT) is characterized by a range of r. The power flux density P _P created by the ith radiation pulse in the OT, and the time t _{P of the} arrival of the i-th radiation pulse in the OT contain information about the range r. The density of the radiation power flux in the RT and the radiated power are related to the range value by the multiplicative relation

P _P = P ₀ · k ₁ {r),

and the arrival time in the RT and the emission time of the i-th pulse are additive

t _P = t ₀ + k ₂ (r),

where k ₁ (r), k ₂ (r) are range functions.

When propagating in an isotropic medium for point IRI

k ₁ (r) = 1 / (4πr ² ), k ₂ (r) = r / c,

where c is the propagation velocity of electromagnetic radiation.

By measuring the values of P _P and t _P in OT, with the known values of P ₀ and t ₀ , the range value r can be determined using the formulas:

,

,

r = c (t _P -t ₀ ),

where f is the coefficient of proportionality, taking into account the shape of the radiation pattern of the transmitting antenna.

Range measurement methods based on this approach are called amplitude and temporal, respectively. They are widely used in radar and radio navigation. However, in other practical cases, in particular with passive determination of the coordinates of the IRI, the values of P ₀ , Φ and t _{0 are} unknown.

In the presence of two RTs, unknown values of P ₀ and t ₀ can be excluded from consideration. If the IRI is isotropic or quasi-isotropic (the IRI radiates in all directions with the same intensity in the same plane, which is typical for the VHF IRI using vertical whip antennas), the value of Ф is also excluded from consideration.

From the system of equations

where P _P1 and P _P2 are the values of the radiation power flux density in two spatially separated FROM O ₁ and O ₂ ,

can be proportioned

.

.

By choosing a coordinate system (SK) in such a way that the following conditions are met:

,

,

,

,

where R is the distance between the OT (figure 3),

can write

,

,

whence it follows that

P x ² + y ² _{P1 P1} + z P ² P ² P _P1 -x + 2xRP _{P2 P2 P2} R ² -R -y ² -z ² P P _{P2 P2} = 0.

This equation can be rewritten as

x ² [P _P1 -P _P2 ) + y ² (P _P1- P _P2 ) + z ² (P _P1- P _P2 ) + 2xRP _P2 -R ² RP ₂ = 0.

Insofar as

,

,

then you can write

.

.

Dividing all the terms by (P _P1 -P _P2 ), we can finally obtain that

.

.

и радиусом, равным

.The resulting equation is the canonical equation of a sphere centered at a point with coordinates

and a radius equal to

.

Thus, for the case of the presence of two reception points and in the presence of information on the values of the signal power flux density at these points, the a priori uncertainty of the spatial position of the IRI is reduced to belonging to the position surface in the form of a sphere with parameters determined from the above expressions.

Similarly, from the system of equations

where t _P1 and t _P2 - the values of the moments of time of reception of radiation in two spatially separated FROM O ₁ and O ₂ ,

can make an equation

t _П1 -t _П2 = k ₂ (r ₁ ) -k ₂ (r ₂ ).

Given the fact that

k ₂ (r _i ) = r _i / c, i = 1, 2.

can write

t _P1 -t _P2 = (r ₁ -r ₂ ) / c.

Selecting the SC so that the conditions are met (figure 4)

,

,

,

,

available

.

.

Squaring the right and left sides of the equation, we get

,

,

and consequently,

If you open the brackets on the left side and simplify, then equation (4) can be represented as the equation of a two-sheeted hyperboloid of revolution

,

,

.where a ₁ = Δr / 2;

.

Thus, for the case of two points of reception and when there is information about the values of the time of reception of the signal at these points, the a priori uncertainty of the spatial position of the IRI is reduced to belonging to the position surface in the form of a two-sheeted hyperboloid of revolution with parameters determined from the above expressions.

We denote the difference between the distances from the IRI point to antennas 1 and 3 through Δr _AC , to antennas 2 and 3 through Δr _BC , to antennas 1 and 2 through Δr _AB , the power flux density of the signal at the input of antenna 1 is through P ₁ , at the input antennas 2 through P ₂ .

Based on the processing of the two values of the distance differences Δr _AB and Δr _{AC, the} azimuth γ, the elevation angle β of the IRI and the coordinates {x _F , y _F ) of the point F are calculated, through which the line of position of the IRI (Fig. 5) passes using the expressions [3]:

;where x ₃ = (b ² -c ² ) / a;

;

a = | AB | / 2; b = | AC | / 2; c = | BC | / 2;

;

;

;

;

.a ₁ = Δr _AB / 2;

.

Based on the processing of two values of the power flux density P ₁ and P ₂ calculate the value of the distance L to the IRI from point J and the coordinates of point J (figure 5) using the expressions:

,

,

x _J = 2aP ₂ / {P ₁ -P ₂ ) -a,

for _J = 0, z _J = 0.

Since the bearing line passes through point F, for practical convenience it is advisable to determine the distance to the IRI not from point J, but from point F.

The IRI bearing line passing through point F and defined by the angles γ and β is the IRI position line. The sphere defined by the center at point J and radius L is the surface of the IRI position. Therefore, the IRI is located at the intersection of the bearing line with this sphere.

Since the IRI belongs to the bearing line, therefore, it also belongs to the plane Ω, perpendicular to the xOy plane and passing through the point F at an angle γ to the Ox axis (since this plane contains the bearing line). The line of intersection of the plane Ω and the sphere corresponding to the range L is a circle of radius | NS | (Fig.6).

The coordinate of point M along the x axis can be calculated using the expression

x _M = x _F -y _F ctg (γ).

Hence

| JN | = | JM | ctg (γ) = (x _J -x _M ) ctg (γ).

Therefore, we can calculate

.

.

Since L '= | FD |, then taking into account Fig.7 you can write

.

.

Eventually

,

,

where Δx = x _J -x _F.

Thus, at the final stage, the value of the distance L 'to the IRI from point F is calculated using the expression

.

.

and display the results.

The composition of the claimed device includes (figure 2):

1 - antenna;

2 - antenna;

3 - antenna;

4 - time difference meter;

5 - time difference meter;

6 - power density meter;

7 - meter power flux density;

8 - computing unit;

9 - display unit.

The outputs of the antennas 1 and 2 are connected to the first inputs of the time difference meters 4 and 5, respectively, to the second inputs of which a signal is output from the output of the antenna 3. The outputs of the antennas 1 and 2 are also connected to the inputs of the power density meters 6 and 7, respectively. The outputs of the time difference meters 4 and 5 are connected to the first and second inputs of the computing unit 8, respectively. The outputs of the power flux density meters 6 and 7 are connected to the third and fourth inputs of the computing unit 8, respectively. The output of the computing unit 8 is connected to the input of the display unit 9.

Antennas 1, 2 and 3 are located at the vertices of the triangle ΔABC, respectively.

The signals from the outputs of antennas 1 and 3 are fed to the first and second inputs of the time difference meter 4, respectively, similarly the signals from the outputs of antennas 2 and 3 are fed to the first and second inputs of the time difference meter 5, respectively. The time difference meters 4 and 5 perform the operation of measuring the time differences Δt _AC and Δt _{BC of the} arrival of the IRI signal to the pairs of antennas {1,3} and {2,3}.

The time difference meters 4 and 5 implement one of the known [eg, 5] methods for measuring the time difference.

From the outputs of the time difference meters 4 and 5, the measured values Δt _AC and Δt _BC are supplied to the first and second inputs of the computing unit 8, respectively.

The signals from the outputs of antennas 1 and 2 also go to the inputs of the power flux density meters 6 and 7, respectively. Power flux density meters 6 and 7 perform an operation of measuring power flux density P ₁ and P _{2 of} the IRI signal at the inputs of antennas 1 and 2, respectively.

Power flux density meters 6 and 7 implement one of the known methods for measuring power flux density. The prior art power flux density meters PO-1, M3-10, P3-9, P3-13, P3-18, etc.

From the outputs of the power flux density meters 6 and 7, the measured values of P ₁ and P ₂ are supplied to the third and fourth inputs of the computing unit 8, respectively.

Computing unit 8 is a specialized computing device in which the following operations are sequentially performed:

- the values of the differences of the ranges Δr _AC , Δr _BC and Δr _{AB are} calculated using the expressions:

Δr _AC = Δt _AC · ν _EMB , Δr _BC = Δt _BC · ν _EMV , Δr _AB = Δr _AC -Δr _BC .

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

- the values of x _F are calculated, the _F coordinates of the point F belonging to the IRI position line, using the expressions:

,Where

,

- the value of the elevation angle β IRI is calculated using the expression

,

,

- the value of the distance L to the Iran from the point J and the coordinates of the point J are calculated using the expressions:

,

,

x _J = 2aP ₂ / (P ₁ -P ₂ ) -a,

- calculates the value of the distance L 'to the IRI from point F using the expression

,

,

where Δx = x _J -x _F.

The a priori known values required for the calculations are:

- ν _EMW - propagation velocity of the electromagnetic wave;

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

- x ₃ , at ₃ - the coordinates of antenna 3 in the coordinate system Oxyz are stored in the memory of computing unit 8.

The calculated values of γ, β, x _F , for _F , L 'from the output of the computing unit 8 go to the display unit 9, which is intended to visualize the results of the proposed method.

Thus, the proposed method and device for its implementation, in comparison with the prototype, provide the ability to determine the three coordinates of the IRI by determining the distance to the IRI.

BIBLIOGRAPHY

1. Shebshaevich B.C. Introduction to the theory of space navigation. - M .: Owls. Radio, 1971. - 296 p.

2. Dulevich V.E., Korostelev A.A., Melnik Yu.A. et al. Theoretical Foundations of Radar / Ed. V.E.Dulevich. - M .: Owls. Radio, 1964 .-- 732 p.

3. Saibel A.G. Difference-range measuring method of direction finding of a source of radio emission and device realizing it. RF patent No. 2258242 dated 05/31/2005.

4. Sedyakin N.M. Elements of the theory of random pulsed flows. - M .: Owls. Radio, 1965 .-- 263 p.

5. Wuu Chenn, Pearson Allan E. On time deley estimation involving received signals // IEE Trans. Acount, Speech and Signal Process., 1984, 32, N 4, C.828-835.

Claims (2)

1. A method for determining the coordinates of a radio emission source (IRI), based on the reception of IRI signals to three antennas, characterized in that they have three antennas at the vertices of the triangle ΔABC, measure the time difference Δt _AC and Δt _{BC of the} reception of the IRI signal by the antennas forming the measuring base {A , C} and {B, C}, calculate the values of Δr _AC , Δr _BC and Δr _{AB of the} differences of the distances from the IRI to the pairs of antennas, calculate the value of the azimuth of the IRI using the expression
γ = arctan (a (Δr _AC + Δr _BC ) -x ₃ (Δr _AC -Δr _BC )) / (for ₃ (Δr _BC -Δr _AC )), where x ₃ = (b ² -c ² ) / a; y ₃ = √4b ² - (a + x ₃ ) ² ; a = | AB | / 2; b = | AC | / 2; c = | BC | / 2, calculate the coordinates {x _F , y _F ) of the point F belonging to the IRI bearing line using the expressions:
x _F = (2aΔr _AC - (a + x ₃ ) Δr _AB ) (a ² + Δr _AC (Δr _AC -Δr _AB ) -g ² ) Δr _AB / K,
y _F = -y ₃ (4a ² -Δr ² _AB ) (a ² -g ² + Δr _AC (Δr _AC -Δr _AB )) / K,
K = 4a ² (for ₃ ² + Δr _AC (Δr _AB -Δr _AC )) - Δr ² _AB (a ² + g ² ) + 2ax ₃ (2-Δr ² _AB );
g = √ x ₃ ² + y ₃ ² ,
calculate the elevation angle β of the IRI using the expression β = arctan (l / a ₁ ), where l = √ (b ₁ ² cos ² γ-a ₁ ² sin ² γ); and ₁ = Δr _AB / 2; b ₁ = √ Δa ² -Δr ² _AB / 2, measure the power flux density P ₁ and P _{2 of} the IRI signal at points A and B, respectively, calculate the value of the distance L to the IRI from point J, which is the center of a sphere with radius L, which is the surface of the IRI position, the coordinates of the point J are also calculated using the expressions:
L = 2a√P ₁ P ₂ / | P ₁ -P ₂ |, x _J = 2aP ₂ / (P ₁ -P ₂ ) -a, y _J = 0, z _J = 0, calculate the value of the distance L 'to the IRI from point F using the expression L '= (Δx · cos (γ) -y _F · sin (γ) · cos (β) + √ L ² - (Δx · sin (γ) -y _F -cos (γ)) ² - (Δx-cos (γ) -y _F · sin (γ)) ² · sin ² (β), where Δx = x _J -x _F , and the results are displayed. 2. A device for determining the coordinates of a radio emission source (IRI), comprising three receiving antennas, two meters for measuring the difference in signal reception times, a computing unit and an indication unit, the outputs of the first and second antennas being connected respectively to the first inputs of the first and second meters for measuring the difference in signal reception times IRI, the second inputs of which are connected to the output of the third antenna, and the outputs are connected respectively to the first and second inputs of the computing unit, the output of which is connected to the input of the display unit, distinguishing the fact that two IRI signal power flux density meters have been introduced, designed to measure the IRI signal power flux density at the locations of the first and second antennas, the inputs of the first and second IRI signal power flux density meters are connected to the outputs of the first and second antennas, respectively, and the outputs connected respectively to the third and fourth inputs of the computing unit for calculating the azimuth γ, elevation angle β of the IRI, the coordinates of the point F belonging to the line of the bearing of the IRI, the range L to the IRI of t of the point J, the coordinates of the point J, the distance L 'to the IRI from the point F, while the point J is the center of the sphere with radius L, which is the surface of the position of the IRI.

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