RU2534224C1 - Method of measuring coordinates of elements earth's surface in on-board four-channel doppler radar set - Google Patents

Method of measuring coordinates of elements earth's surface in on-board four-channel doppler radar set Download PDF

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RU2534224C1
RU2534224C1 RU2013119344/07A RU2013119344A RU2534224C1 RU 2534224 C1 RU2534224 C1 RU 2534224C1 RU 2013119344/07 A RU2013119344/07 A RU 2013119344/07A RU 2013119344 A RU2013119344 A RU 2013119344A RU 2534224 C1 RU2534224 C1 RU 2534224C1
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Владимир Константинович Клочко
Чунг Тхык Нгуен
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Федеральное государственное бюджетное образовательное учреждение высшего профессионального образования "Рязанский государственный радиотехнический университет"
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Abstract

FIELD: radio engineering, communication.
SUBSTANCE: disclosed method includes forming, on a given synthesis time interval, a radar image of a portion of the earth's surface in the form of a set of complex amplitudes of reflection signals in range resolution elements at Doppler frequencies simultaneously in four measurement channels, the method being characterised by that for every four amplitudes of corresponding image elements obtained at the same frequency, angular coordinates of the corresponding surface element are measured using a monopulse method and said angular coordinates are converted into Cartesian coordinates of the antenna system.
EFFECT: measuring coordinates of elements of the earth's surface while forming a three-dimensional image of the surface in the visibility range of the radar set.

Description

The invention relates to radar, and in particular to airborne radar systems for monitoring the earth's surface (radio vision [1]) based on a four-channel Doppler radar station (radar) with a four-element antenna array, traditionally used in practice [2].

The measurement of the coordinates of the elements of the earth’s surface is necessary for the formation of a three-dimensional image of a portion of the earth’s surface in the radar’s field of view, determined by the antenna radiation pattern (BOTTOM). The presence of such an image makes it possible to increase the safety of low-altitude flights over complex terrain, as well as to increase the likelihood of recognition of spatially extended objects located on the earth's surface.

There is a method of measuring the angular coordinates of single airborne objects in the visibility range of a monopulse radar with a total and two difference channels, based on direction finding of objects using the monopulse method [2, p. 95-105]. In this case, a direction-finding characteristic (bearing) is formed, which linearly depends on the deviation of the object in angular coordinates relative to the equal-signal direction, and the range is measured by the delay time of the reflected signal. However, this method does not work when observing a plot of the earth's surface, consisting of many elements (objects) of reflection.

A known method of obtaining a three-dimensional image of the surface according to the onboard pulse-Doppler radar low-altitude flight [3]. However, the accuracy of determining the angular coordinates of reflection elements in this method is low due to the spatial extent of the resolution elements of the Doppler frequency.

There is also known a method of forming a three-dimensional image of a surface with high-altitude objects according to the data of the on-board pulse-Doppler radar [4], in which, together with the selection of the path signal by the Doppler frequency, it is proposed to use the single-pulse method of measuring angular coordinates. However, it does not indicate how exactly the monopulse method should be implemented in combination with Doppler filtering, in particular, the number of filtering channels is not determined.

The closest in technical essence are the method of measuring the angular coordinates of several objects (air, ground and sea) in multichannel Doppler radars [5], as well as a method of increasing the resolution of the radar in angle in the anterolateral view [6]. With respect to measuring the coordinates of the elements of the earth's surface, the method [5] is as follows.

1. At a given antenna position corresponding to the anterolateral view of the airborne radar, the sequence of complex path signals S ˙ ( t )

Figure 00000001
adopted at a given synthesis time period simultaneously in Q measuring channels as S ˙ q ( t )
Figure 00000002
, q = 1, 2, ..., Q, are selected in the ith range resolution elements by the delay in the arrival time of the reflected signal. As a result of S ˙ q ( t )
Figure 00000003
allocate ie components S ˙ q ( i , t )
Figure 00000004
, i = 1, 2, ..., m, by the number of range elements m.

2. In each i-th element of range with a value of R i the time sequence S ˙ q ( i , t )

Figure 00000004
subjected to fast Fourier transform and thereby select the signal at the Doppler frequency f j in each q-th channel. As a result of S ˙ q ( i , t )
Figure 00000005
distinguish je components S ˙ q ( i , j )
Figure 00000006
, j = 1, 2 ..., n, in qx channels, q = 1, 2, ..., Q, where n is the number of Doppler frequencies. These operations are performed simultaneously (in parallel) in Q channels.

3. The resulting matrix of elements S ˙ q ( i , j )

Figure 00000007
they are complex two-dimensional (in the coordinates of the range — Doppler frequency) radar images of a portion of the earth’s surface along the bottom of the bottom that differ in q phases (in terms of the delay time of the reflected signal when receiving spatially spaced antenna elements in qx).

4. Since the Doppler frequency f j corresponds to a circle line L j in space on which a reflecting surface element with unknown angular coordinates φ and θ can be located, they first decide on the presence of such an element: signal amplitude U q ( i , j ) = | | | S ˙ q ( i , j ) | | |

Figure 00000008
must exceed the detection threshold in all qx channels, and then find the estimates of the angular coordinates of the reflection element.

5. The angular coordinates φ and θ are estimated by the method of solving a system of linear equations for unknown complex amplitudes of the reflected signal distributed along kx line sampling elements L j , k = 1, 2, ..., N, where N is the number of sampling elements, NQ operations of multiplication measurements S ˙ q ( i , j )

Figure 00000007
, q = 1, 2, ..., Q, to pre-calculated complex weights w ˙ q k
Figure 00000009
, q = 1, 2, ..., Q, k = 1, 2, ..., N, and add up the multiplication results. The number of equations depends on the number of measuring channels Q, which should be greater than the number of sampling elements N.

6. The kth sampling element, the amplitude of which exceeds the detection threshold and has a maximum value, is taken as a reflection element. The angular coordinates of the selected sampling element represent estimates of the angular coordinates φ ij and θ ij of the reflecting surface element in the i-th range element with the value of R i at the j-th Doppler frequency. As a result, spatial coordinates (range and angular coordinates) of the i, jth point (element) of the surface are found in the antenna coordinate system.

7. The operations of items 5 and 6 are performed independently (in parallel) for all values of i, j (i = 1, 2, ..., m, j = 1, 2, ..., n) and get a set of points with known spatial coordinates, and it is a three-dimensional image of a controlled area of the earth’s surface in the radar visibility range.

The method [6] is similar to the method [5], but differs from [5] in that it is proposed for observing only the earth's surface.

The prototype method [5] has the following disadvantages.

1. It is designed for use in multichannel radars, for example, radars with a phased antenna array, in which the number of Q channels is large and exceeds the number of sampling elements N in the method of estimating angular coordinates, i.e. makes dozens. For a four-channel total-difference radar (Q = 4), this method is not applicable for the accuracy of measuring angular coordinates, since for solving a system of equations it is necessary that the number of measurements (the number of equations) be greater than the number of unknown amplitudes distributed over the discretization elements. The method has the same drawback [6].

2. The estimates of the angular coordinates are taken on the line L j of the Doppler frequency f j , the equation of which depends on f j . Therefore, the accuracy of the estimates depends on the path of instability of the radar carrier and the approximate nature of the analytical dependence of L j and f j .

3. The use of multi-element antenna arrays is less economical than traditional four-element antennas.

The technical result is aimed at measuring the coordinates of the elements of the earth's surface when forming a three-dimensional image of the surface in the radar visibility zone with the elimination of these disadvantages.

The technical result of the proposed technical solution is achieved by the fact that the method of measuring the coordinates of the elements of the earth’s surface in the airborne four-channel Doppler radar consists in the formation of a radar image of the earth’s surface in the form of a set of complex amplitudes S ˙ q ( i , j )

Figure 00000007
reflection signals in ix range resolution elements (i = 1, 2, ..., m, where m is the number of range elements) at j-Doppler frequencies (j = 1, 2, ..., n, where n is the number of Doppler frequencies) in four measuring channels (q = 1, 2, 3, 4), determining those j-th frequencies at which the amplitude U q ( i , j ) = | | | S ˙ q ( i , j ) | | |
Figure 00000008
signal S ˙ q ( i , j )
Figure 00000007
exceeds the detection threshold, and subsequent processing of the set of measurements S ˙ q ( i , j )
Figure 00000007
characterized in that for each i, jth four of the measurements obtained S ˙ q = S ˙ q ( i , j )
Figure 00000010
, q = 1, 2, 3, 4, the complex total is calculated S ˙ Σ
Figure 00000011
and complex difference signals S ˙ ϕ
Figure 00000012
, S ˙ θ
Figure 00000013
according to the formulas

S ˙ Σ = S ˙ one + S ˙ 2 + S ˙ 3 + S ˙ four

Figure 00000014
, S ˙ ϕ = S ˙ 2 + S ˙ 3 - S ˙ one - S ˙ four
Figure 00000015
, S ˙ θ = S ˙ 3 + S ˙ four - S ˙ one - S ˙ 2
Figure 00000016
,

then extract the real part of the total signal Re { S ˙ Σ }

Figure 00000017
imaginary parts of difference signals Im { S ˙ ϕ }
Figure 00000018
, Im { S ˙ θ }
Figure 00000019
and make up the relationship Im { S ˙ ϕ } / Re { S ˙ Σ } = tan ( μ ϕ )
Figure 00000020
, Im { S ˙ θ } / Re { S ˙ Σ } = tan ( μ θ )
Figure 00000021
,

meaningful direction-finding characteristics with a known coefficient µ, on the linear part of which the estimates of the angular coordinates φ and θ are calculated by the formulas:

ϕ i j = ( one / μ ) Im { S ˙ ϕ } / Re { S ˙ Σ }

Figure 00000022
, θ i j = ( one / μ ) Im { S ˙ θ } / Re { S ˙ Σ }
Figure 00000023
,

these operations are performed independently (in parallel) for all values of i, j and thereby determine the angular coordinates φ ij , θ ij of all i, j elements of the surface in the radar visibility range, which together with the range measurements R i give a three-dimensional image of the earth’s surface in in the form of a set of points with coordinates x ij = φ ij R i , y ij = θ ij R, z i = R i in a rectangular antenna system.

The method is as follows.

1. At a given antenna position corresponding to the anterolateral view of the airborne radar, the sequence of complex path signals S ˙ ( t )

Figure 00000001
, the adoption of a given period of time synthesis at the same time in Q measuring channels, as S ˙ q ( t )
Figure 00000002
, q = 1, 2, ..., Q, are selected in ix range resolution elements by the delay in the arrival time of the reflected signal. As a result of S ˙ q ( t )
Figure 00000002
emit components S ˙ q ( i , t )
Figure 00000004
, i = 1, 2, ..., m, by the number of range elements m.

2. In each i-th element of range with a value of R i the time sequence S ˙ q ( i , t )

Figure 00000004
subjected to fast Fourier transform and thereby select the signal at the Doppler frequency f j in each q-th channel. As a result of S ˙ q ( i , t )
Figure 00000004
distinguish j components S ˙ q ( i , j )
Figure 00000006
, j = 1, 2 ..., n, in qx channels, q = 1, 2, ..., Q, where n is the number of Doppler frequencies. These operations are performed simultaneously (in parallel) in Q channels.

3. The resulting matrix of elements S ˙ q ( i , j )

Figure 00000006
they are complex two-dimensional (in the coordinates of the range — Doppler frequency) radar images of a portion of the earth’s surface along the bottom of the bottom that differ in q phases (in terms of the delay time of the reflected signal when receiving spatially spaced antenna elements in qx).

4. Since the Doppler frequency f j corresponds to a circle line L j in space on which a reflecting surface element with unknown angular coordinates φ and θ can be located, they first decide on the presence of such an element: signal amplitude U q ( i , j ) = | | | S ˙ q ( i , j ) | | |

Figure 00000024
must exceed the detection threshold in all qx channels (as well as the threshold of the signal-to-noise ratio for receiving a signal along the main lobe of the bottom), and then estimates of the angular coordinates of the reflection element are found.

5. The estimation of the angular coordinates φ and θ is carried out by a single-pulse method in the antenna coordinate system. Namely, for each i, jth four measurements S ˙ q = S ˙ q ( i , j )

Figure 00000025
, q = 1, 2, 3, 4, calculate the complex total S ˙ Σ
Figure 00000026
and complex difference signals S ˙ ϕ
Figure 00000012
and S ˙ θ
Figure 00000013
according to the formulas

S ˙ Σ = S ˙ one + S ˙ 2 + S ˙ 3 + S ˙ four

Figure 00000014
, S ˙ ϕ = S ˙ 2 + S ˙ 3 - S ˙ one - S ˙ four
Figure 00000015
, S ˙ θ = S ˙ 3 + S ˙ four - S ˙ one - S ˙ 2
Figure 00000016
.

6. Allocate the real part of the total signal Re { S ˙ Σ }

Figure 00000017
and imaginary parts of difference signals Im { S ˙ ϕ }
Figure 00000018
, Im { S ˙ θ }
Figure 00000019
. Make up relationship

Im { S ˙ ϕ } / Re { S ˙ Σ } = tan ( μ ϕ )

Figure 00000020
, Im { S ˙ θ } / Re { S ˙ Σ } = tan ( μ θ )
Figure 00000021
, μ = 4πd / λ,

meaningful direction-finding characteristics, where 2d is the distance between the centers of the receiving elements of the antenna, λ is the wavelength.

On the linear part of the direction-finding characteristics (for a narrow circular bottom pattern), the estimates of the angular coordinates φ and θ are calculated by the formulas

ϕ i j = ( one / μ ) Im { S ˙ ϕ } / Re { S ˙ Σ }

Figure 00000022
, θ i j = ( one / μ ) Im { S ˙ θ } / Re { S ˙ Σ }
Figure 00000023
.

7. The operations of paragraphs 5 and 6 are performed independently (in parallel) for all values of i, j. This determines the angular coordinates φ ij , θ ij of all j, jx surface elements in the radar visibility range, which, together with the R i range measurements, give a three-dimensional image of the earth's surface as a set of points in a rectangular antenna system with coordinates x ij = φ ij R i , y ij = θ ij R, z i = R i .

Analysis of computational costs indicates the possibility of implementing this method on a modern elemental base in real time with parallelization of operations. The computational costs in parts 1 to 4 coincide with the computational costs of the prototype due to the identity of the operations. The number of elementary operations when evaluating the angular coordinates (paragraphs 5 and 6) in the proposed method is several times less than the number of elementary operations of the prototype.

A positive difference of the proposed method from the known methods [5] and [6] is as follows.

1. The ability to measure the angular coordinates of reflective surface elements with a small number (Q = 4) of radar measuring channels.

2. Independence of the operations of estimating the angular coordinates from the instability trajectory and approximation errors of the dependence of L j and f j .

3. Greater profitability.

Settlement part

We consider an antenna in the form of a 4-element flat array (Q = 4) with a circular bottom beam (bottom width at 0.5 power level Δ δ = Δ θ = Δ is 1 ° -3 °). The centers of the antenna receiving elements are located at the points M 1 (d, d, 0), M 2 (-d, d, 0), M 3 (-d, -d, 0), M 4 (d, -d, 0) in the rectangular antenna coordinate system o a , x a , y a , z a . Earth surface observation is carried out in angular antenna coordinates: φ x , θ y are the angles between the axis o a z a and the geometric projections of the vector o a M

Figure 00000027
(a reflection beam from a point M on the earth's surface) onto the horizontal plane o a , x a , z a and the vertical plane o a , y a , z a .

After passing through the primary processing path, including phase detection, low-pass filtering and fast Fourier transform, complex signals are obtained in parallel in qx channels S ˙ q ( i , j )

Figure 00000006
, q = 1, 2, 3, 4, in ix range elements (i = 1, 2, ..., m) at j-Doppler frequencies (j = 1, 2, ..., n).

The frequencies f j correspond to the angle α j of the deviation of the reflection beam relative to the vector ν

Figure 00000028
path velocity of the radar carrier, for example, for the “Doppler firing” mode [1]: f j ≈ (2ν / λ) cosα j , and cosα j ≈ν x φ + ν y θ + ν z , where ν x , ν y , ν z - coordinates of the unit vector ν 0
Figure 00000029
of vector ν
Figure 00000030
. Therefore, the choice of frequencies is consistent with the angular coordinates φ, θ of the radar visibility over the width of its bottom. The approximation errors of the dependences f j and φ, θ do not affect the accuracy of estimating the angular coordinates φ, θ.

Signal Model S ˙ q ( i , j )

Figure 00000006
, q = 1, 2, 3, 4, in the antenna angular coordinates φ, θ without indices i, j has the following form:

S ˙ one = U ( ϕ , θ ) G ˙ ( ϕ , θ ) exp { - i μ ( ϕ + θ ) } + P ˙ one , ( one )

Figure 00000031

S ˙ 2 = U ( ϕ , θ ) G ˙ ( ϕ , θ ) exp { - i μ ( - ϕ + θ ) } + P ˙ 2

Figure 00000032
,

S ˙ 3 = U ( ϕ , θ ) G ˙ ( ϕ , θ ) exp { - i μ ( - ϕ - θ ) } + P ˙ 3

Figure 00000033
,

S ˙ four = U ( ϕ , θ ) G ˙ ( ϕ , θ ) exp { - i μ ( ϕ - θ ) } + P ˙ four

Figure 00000034
,

G ˙ ( ϕ , θ ) = exp { - k ( ϕ 2 + θ 2 ) / Δ 2 } exp { i ξ }

Figure 00000035
, μ = (4π / λ) d,

where U (φ, θ) is the amplitude of the reflection signal in the direction φ, θ is the beam; G ˙ ( ϕ , θ )

Figure 00000036
- normalized complex DND; k is the coefficient (for example, k = 2.78 [1]); ξ is the random component of the phase of the reflected signal (phase of rereflection) uniformly distributed on [0.2π]; P ˙ q
Figure 00000037
- complex Gaussian white noise with zero mean.

The total and difference signals are formed from (1) as follows:

S ˙ Σ = S ˙ one + S ˙ 2 + S ˙ 3 + S ˙ four , S ˙ ϕ = S ˙ 2 + S ˙ 3 - S ˙ one - S ˙ four , S ˙ θ = S ˙ 3 + S ˙ four - S ˙ one - S ˙ 2 . ( 2 )

Figure 00000038

Neglecting the effects of noise p . q

Figure 00000039
(when added to (2), their level decreases) and the random component ξ, we write the real and imaginary parts (2):

Re { S ˙ Σ } = four U 0 cos ( μ ϕ ) cos ( μ θ )

Figure 00000040
, Im { S ˙ ϕ } = four U 0 sin ( μ ϕ ) cos ( μ θ )
Figure 00000041
,

Im { S ˙ θ } = four U 0 cos ( μ ϕ ) sin ( μ θ )

Figure 00000042
.

We obtain the following direction-finding characteristics for small angles φ, θ:

Im { S ˙ ϕ } / Re { S ˙ Σ } = tan ( μ ϕ ) μ ϕ , ( 3 )

Figure 00000043

Im { S ˙ θ } / Re { S ˙ Σ } = tan ( μ θ ) μ θ

Figure 00000044
.

Estimates of the angular coordinates follow from (3):

ϕ = ( one / μ ) Im { S ˙ ϕ } / Re { S ˙ Σ }

Figure 00000045
, θ = ( one / μ ) Im { S ˙ θ } / Re { S ˙ Σ }
Figure 00000046
.

In a rectangular antenna system o a , x a , y a , z a the coordinates of the reflection point, taking into account the small angles φ x and θ y, are determined as follows:

x = φR, y = θR, z = R.

On the set of values i = 1, 2, ..., m, j = 1, 2, ..., n, we have a set of coordinates x ij , y ij , z i of reflection points that represent a three-dimensional image of the surface in the radar visibility range (along the bottom width )

Literature

1. Kondratenkov G.S., Frolov A.Yu. Radio vision. Earth remote sensing radar systems. Textbook for universities / Ed. G.S. Kondratenkova. - M.: Radio Engineering, 2005.368 s.

2. Leonov A.I., Fomichev K.I. Monopulse radar. - M .: Radio and communications, 1984. 312 p.

3. Patent RU 2299448 C2.

4. Patent RU 2334250 C1.

5. Patent RU 2373551 C1.

6. Patent RU 2416809 C1.

Claims (1)

  1. A method for measuring the coordinates of the elements of the earth’s surface in an onboard four-channel Doppler radar consists in the formation of a radar image of a portion of the earth’s surface in the form of a set of complex amplitudes S ˙ q ( i , t )
    Figure 00000004
    reflection signals in the i-th range resolution elements (i = 1,2, ..., m, where m is the number of range elements) at j-Doppler frequencies (j = 1,2, ..., n, where n is the number of Doppler frequencies ) simultaneously in four measuring channels (q = 1, 2, 3, 4), determining those j-th frequencies at which the amplitude U q ( i , j ) = | | | S ˙ q ( i , j ) | | |
    Figure 00000008
    signal S ˙ q ( i , j )
    Figure 00000007
    exceeds the detection threshold, and subsequent processing of the set of measurements S ˙ q ( i , j )
    Figure 00000007
    characterized in that for each i, jth four of the measurements obtained S ˙ q = S ˙ q ( i , j )
    Figure 00000010
    , q = 1, 2, 3, 4, calculate the complex total S ˙ Σ
    Figure 00000011
    and complex difference signals S ˙ ϕ
    Figure 00000012
    , S ˙ θ
    Figure 00000013
    according to the formulas
    S ˙ Σ = S ˙ one + S ˙ 2 + S ˙ 3 + S ˙ four
    Figure 00000014
    , S ˙ ϕ = S ˙ 2 + S ˙ 3 - S ˙ one - S ˙ four
    Figure 00000015
    , S ˙ θ = S ˙ 3 + S ˙ four - S ˙ one - S ˙ 2
    Figure 00000016
    ,
    then extract the real part of the total signal Re { S ˙ Σ }
    Figure 00000017
    imaginary parts of difference signals Im { S ˙ ϕ }
    Figure 00000018
    , Im { S ˙ θ }
    Figure 00000019
    and make up the relationship Im { S ˙ ϕ } / Re { S ˙ Σ } = tan ( μ ϕ )
    Figure 00000020
    , Im { S ˙ θ } / Re { S ˙ Σ } = tan ( μ θ )
    Figure 00000021
    ,
    meaningful direction-finding characteristics with a known coefficient μ, on the linear part of which the estimates of the angular coordinates φ and θ are calculated by the formulas
    ϕ i j = ( one / μ ) Im { S ˙ ϕ } / Re { S ˙ Σ }
    Figure 00000022
    , θ i j = ( one / μ ) Im { S ˙ θ } / Re { S ˙ Σ }
    Figure 00000023
    ,
    these operations are performed independently (in parallel) for all values of i, j and thereby determine the angular coordinates φ ij , θ ij of all i, jx surface elements in the radar visibility range, which, together with the range measurements R i, give a three-dimensional image of the earth's surface as a set points with coordinates x ij = φ ij R i , y ij = θ ij R, z i = R i in the antenna rectangular system.
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