RU2572357C1 - Method of forming three-dimensional image of earth's surface in on-board four-channel doppler radar set - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: method of forming a three-dimensional image of the earth's surface in an on-board four-channel Doppler radar set includes determining spatial coordinates of reflecting surface elements situated in range resolution elements and Doppler frequency, and is based on combined application of selection on Doppler frequency and a phase method of measuring coordinates.

EFFECT: forming a three-dimensional image of a surface in the visibility range of a radar station in the form of a set of spatial coordinates of reflecting elements of the surface with high accuracy of determining coordinates and wider visibility range of the radar station.

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Description

The invention relates to radar, and in particular to airborne radar systems for monitoring the earth's surface based on the Doppler radar station (radar) with a four-element antenna array (AR).

A three-dimensional image of a portion of the earth’s surface is formed as a set of spatial coordinates of the earth’s reflection elements in the radar visibility zone, 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.

A method is known coordinate measuring elements of the earth surface in the vehicle four-Doppler radar [1] receiving elements whose centers are located on the antenna plane at the points with coordinates (x _l, y ₁₎ = (d, d), (x _2, y ₂₎ = (-d, d), (x ₃ , y ₃ ) = (- d, -d), (x ₄ , y ₄ ) = (d, -d), where 2d is the base distance between the centers of neighboring elements. This method allows to obtain a three-dimensional image of the earth's surface in the radar visibility range, limited by the narrow (of the order of 1 ° - 3 ° at the power level 0.5) circular antenna radiation pattern (BOTTOM) at a radial range R of the order of 1-10 km, typical for low altitude flight carrier radar. The method is the closest in technical essence and consists in the following.

на заданном промежутке времени t синтезирования одновременно в q-x измерительных каналах (номер канала совпадает с номером q приемного элемента антенны: q=1,2,3,4). Затем эти сигналы селектируют в i-x элементах разрешения дальности R_i по задержке времени прихода отраженного сигнала. В результате из $${\dot{S}}_q(t)$$

выделяют i-е составляющие $${\dot{S}}_q(i,t)$$

, i=1, 2, …, m, по числу элементов дальности m.1. Given the position of the antenna line of sight corresponding to the anterolateral view of the airborne radar, complex path signals are received $${\dot{S}}_q(t)$$

for a given period of synthesis time t simultaneously in qx measuring channels (the channel number coincides with the q number of the receiving element of the antenna: q = 1,2,3,4). Then these signals are selected in ix range resolution elements R _i according to the delay in the arrival time of the reflected signal. As a result of $${\dot{S}}_q(t)$$

distinguish i components $${\dot{S}}_q(i,t)$$

, i = 1, 2, ..., m, by the number of range elements m.

преобразуют во временные последовательности $${\dot{S}}_q(i,t)$$

, $$j=\overline{\mathrm{1,}N}$$

(N - число временных отсчетов на промежутке синтезирования), которые подвергают дискретному преобразованию Фурье (ДПФ). Тем самым селектируют сигнал по доплеровской частоте f_j в каждом q-м канале. В результате из $${\dot{S}}_q(i,t)$$

выделяют j-е составляющие $${\dot{S}}_q(i,f_j)$$

, j=1, 2 …, N, в q-x каналах, q=1, 2, 3, 4, где N становится числом элементов разрешения по частоте. Данные операции выполняют одновременно (параллельно) в 4-х каналах.2. In each i-th element of range with a value of R _i signals $${\dot{S}}_q(i,t)$$

convert to time sequences $${\dot{S}}_q(i,t)$$

, $$j=\overline{\mathrm{one,}N}$$

(N is the number of time samples in the synthesis interval), which are subjected to discrete Fourier transform (DFT). Thereby, the signal is selected by the Doppler frequency f _j in each qth channel. As a result of $${\dot{S}}_q(i,t)$$

distinguish j components $${\dot{S}}_q(i,f_j)$$

, j = 1, 2 ..., N, in qx channels, q = 1, 2, 3, 4, where N becomes the number of frequency resolution elements. These operations are performed simultaneously (in parallel) in 4 channels.

превышает порог обнаружения во всех q-x каналах. Такие элементы разрешения соответствуют элементам отражения земной поверхности.3. Of the N frequency resolution elements, only those n elements (n << N) are considered, on which the signal amplitude $$U_q\left(i,j\right)=\left|{\dot{S}}_q\left(i,f_j\right)\right|$$

exceeds detection threshold in all qx channels. Such resolution elements correspond to earth reflection elements.

4. The estimates of the angular coordinates φ - azimuth and θ - elevation angle are carried out by the single-pulse method in the antenna coordinate system. Namely:

, q=1, 2, 3, 4, вычисляют комплексный суммарный $${\dot{S}}_{\Sigma }$$

и комплексные разностные сигналы $${\dot{S}}_{\varphi }$$

, $${\dot{S}}_{\theta }$$

по формулам:4.1) for each i, jth four measurements $${\dot{S}}_q={\dot{S}}_q\left(i,f_j\right)$$

, q = 1, 2, 3, 4, calculate the complex total $${\dot{S}}_{\Sigma }$$

and complex difference signals $${\dot{S}}_{\varphi }$$

, $${\dot{S}}_{\theta }$$

according to the formulas:

, $${\dot{S}}_{\varphi }={\dot{S}}_2+{\dot{S}}_3-{\dot{S}}_1-{\dot{S}}_4$$

, $${\dot{S}}_{\theta }={\dot{S}}_3+{\dot{S}}_4-{\dot{S}}_1-{\dot{S}}_2$$

; $${\dot{S}}_{\Sigma }={\dot{S}}_{\mathrm{one}}+{\dot{S}}_2+{\dot{S}}_3+{\dot{S}}_{\mathrm{four}}$$

, $${\dot{S}}_{\varphi }={\dot{S}}_2+{\dot{S}}_3-{\dot{S}}_{\mathrm{one}}-{\dot{S}}_{\mathrm{four}}$$

, $${\dot{S}}_{\theta }={\dot{S}}_3+{\dot{S}}_{\mathrm{four}}-{\dot{S}}_{\mathrm{one}}-{\dot{S}}_2$$

;

, мнимые части разностных сигналов $$\mathrm{Im}\left\{{\dot{S}}_{\varphi }\right\}$$

, $$\mathrm{Im}\left\{{\dot{S}}_{\theta }\right\}$$

и вычисляют пеленгационные характеристики:4.2) allocate the real part of the total signal $$\mathrm{Re}\left\{{\dot{S}}_{\Sigma }\right\}$$

imaginary parts of difference signals $$\mathrm{Im}\left\{{\dot{S}}_{\varphi }\right\}$$

, $$\mathrm{Im}\left\{{\dot{S}}_{\theta }\right\}$$

and calculate direction-finding characteristics:

, $$U_{\theta }=-\mathrm{Im}\left\{{\dot{S}}_{\theta }/{\dot{S}}_{\Sigma }\right\}$$

; $$U_{\varphi }=-\mathrm{Im}\left\{{\dot{S}}_{\varphi }/{\dot{S}}_{\Sigma }\right\}$$

, $$U_{\theta }=-\mathrm{Im}\left\{{\dot{S}}_{\theta }/{\dot{S}}_{\Sigma }\right\}$$

;

4.3) find the angular coordinates of the center of the reflection element according to the formulas:

φij = kU _φ , θij = kU _θ , k = λ / (2πd),

where λ is the wavelength;

4.4) calculate the rectangular coordinates of the centers of i, j-x elements of the reflection of the earth's surface for a narrow bottom by the formulas:

x _ij = φ _ij Ri, y _ij = θ _ij R _i , z _i = R _i .

5. The set of coordinates x _{i, j} , y _ij , z _i obtained on the set of values i, j, gives a three-dimensional image of the earth's surface along the width of the bottom, which is displayed on the screen of the pilot indicator of the aircraft. However, this method has the following disadvantages: 1) the accuracy of coordinate measurement by the single-pulse method is lower than the accuracy of coordinate measurement by the phase method (phase method, for example, [2, p. 424]);

2) the radar field of view is limited by the width of a narrow BOTTOM of the order of 1 ° - 3 °.

The technical result is aimed at forming a three-dimensional image of the surface in the radar visibility zone with the elimination of these drawbacks, namely, increasing the accuracy of determining spatial coordinates and expanding the radar visibility zone.

сигналов отражения в i-x элементах разрешения дальности R_i (i=1, 2,…, m, где m - число элементов дальности) на j-x частотах (j=1, 2,…, N, где N - число элементов разрешения по частоте) одновременно в четырех измерительных каналах (q=1, 2, 3, 4, где q - номер канала), определении тех j-x частот, на которых амплитуда $$U_q\left(i,j\right)=\left|{\dot{S}}_q\left(i,j\right)\right|$$

сигнала $${\dot{S}}_q(i,j)$$

превышает порог обнаружения во всех каналах, и последующей обработке полученных измерений $${\dot{S}}_q(i,j)$$

, отличающийся тем, что центры приемных элементов антенны располагают на плоскости антенны в точках с координатами (x_l,y_l)=(d,0), (x₂,y₂)=(0,d), (x₃,y₃)=(-d,0), (х₄,y₄)=(0,-d), и для каждой i,j-й четверки измерений $${\dot{S}}_q={\dot{S}}_q\left(i,j\right)$$

, q=1, 2, 3, 4, полученных в q-x каналах, берут аргументы комплексных величин $${\dot{S}}_q$$

- фазы $${\psi }_q=\arg \left\{{\dot{S}}_q\right\}$$

, q=1, 2, 3, 4, вычисляют разности фаз по азимуту φ и углу места θ: Δψ_φ=ψ₁-ψ₃, Δψ_θ=ψ₂-ψ₄ и находят прямоугольные координаты точек отражения:The technical result of the proposed technical solution is achieved by the fact that the method of forming a three-dimensional image 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 $${\dot{S}}_q(i,j)$$

reflection signals in ix range resolution elements R _i (i = 1, 2, ..., m, where m is the number of range elements) at jx frequencies (j = 1, 2, ..., N, where N is the number of frequency resolution elements) simultaneously in four measuring channels (q = 1, 2, 3, 4, where q is the channel number), determining those jx frequencies at which the amplitude $$U_q\left(i,j\right)=\left|{\dot{S}}_q\left(i,j\right)\right|$$

signal $${\dot{S}}_q(i,j)$$

exceeds the detection threshold in all channels, and the subsequent processing of the received measurements $${\dot{S}}_q(i,j)$$

, characterized in that the centers of the receiving elements of the antenna are located on the plane of the antenna at points with coordinates (x _l , y _l ) = (d, 0), (x ₂ , y ₂ ) = (0, d), (x ₃ , y ₃ ) = (- d, 0), (x ₄ , y ₄ ) = (0, -d), and for each i, jth four measurements $${\dot{S}}_q={\dot{S}}_q\left(i,j\right)$$

, q = 1, 2, 3, 4, obtained in qx channels, take the arguments of complex quantities $${\dot{S}}_q$$

- phases $${\psi }_q=\arg \left\{{\dot{S}}_q\right\}$$

, q = 1, 2, 3, 4, the phase differences are calculated in azimuth φ and elevation angle θ: Δψ _φ = ψ ₁ -ψ ₃ , Δψ _θ = ψ ₂ -ψ ₄ and find the rectangular coordinates of the reflection points:

, k=R_iλ/(4πd), λ - длина волны, которые на множестве значений i,j дают трехмерное изображение участка земной поверхности по ширине узкой ДНА, затем смещают линию визирования антенны последовательно по азимуту и углу места на ширину ДНА и повторяют указанные операции. Способ осуществляют следующим образом.x _ij = kΔψ _φ , y _ij = kΔψ _θ , $$z_{ij}=\sqrt{R_i^2-x_{ij}^2-y_{ij}^2}\approx R_i$$

, k = R _i λ / (4πd), λ is the wavelength, which on a set of values i, j give a three-dimensional image of a piece of the earth’s surface along the width of a narrow BOTTOM, then shift the line of sight of the antenna sequentially in azimuth and elevation to the width of the BOTTOM and repeat specified operations. The method is as follows.

1. The centers of the receiving elements of the antenna are located on the plane of the antenna at points with coordinates (x _l , y ₁ ) = (d, 0), (x ₂ , y ₂ ) = (0, d), (x ₃ , y ₃ ) = (-d, 0), (x ₄ , y ₄ ) = (0, -d), where 2d is the base distance between the centers of the receiving elements located on the same axis.

на заданном промежутке времени t синтезирования одновременно в q-x каналах: горизонтальных (для 1-го и 3-го приемных элементов) и вертикальных (для 2-го и 4-го приемных элементов).2. At this position of the antenna line of sight corresponding to the anterolateral view of the airborne radar, complex path signals are received $${\dot{S}}_q(t)$$

on a given synthesis time t at the same time in qx channels: horizontal (for the 1st and 3rd receiving elements) and vertical (for the 2nd and 4th receiving elements).

селектируют в i-x элементах разрешения дальности R_i по задержке времени прихода отраженного сигнала. В результате из $${\dot{S}}_q(t)$$

выделяют i-е составляющие $${\dot{S}}_q(i,t)$$

, i=1, 2,…, m, по числу элементов дальности m.3. Signals $${\dot{S}}_q(t)$$

select in ix range resolution elements R _i according to the delay in the arrival time of the reflected signal. As a result of $${\dot{S}}_q(t)$$

distinguish i components $${\dot{S}}_q(i,t)$$

, i = 1, 2, ..., m, by the number of range elements m.

преобразуют во временные последовательности $${\dot{S}}_q(i,t_j)$$

, $$j=\overline{\mathrm{1,}N}$$

(N - число временных отсчетов на промежутке синтезирования), которые подвергают дискретному преобразованию Фурье (ДПФ). Тем самым селектируют сигнал по доплеровской частоте f_j в каждом q-м канале. В результате из $${\dot{S}}_q(i,t)$$

выделяют j-е составляющие $${\dot{S}}_q(i,f_j)$$

, j=1, 2 …, N, в q-x каналах, q=1, 2, 3, 4, где N становится числом элементов разрешения по частоте. Данные операции выполняют одновременно (параллельно) в 4-х каналах.4. In each i-th element of range with a value of R _i signals $${\dot{S}}_q(i,t)$$

convert to time sequences $${\dot{S}}_q(i,t_j)$$

, $$j=\overline{\mathrm{one,}N}$$

(N is the number of time samples in the synthesis interval), which are subjected to discrete Fourier transform (DFT). Thereby, the signal is selected by the Doppler frequency f _j in each qth channel. As a result of $${\dot{S}}_q(i,t)$$

distinguish j components $${\dot{S}}_q(i,f_j)$$

, j = 1, 2 ..., N, in qx channels, q = 1, 2, 3, 4, where N becomes the number of frequency resolution elements. These operations are performed simultaneously (in parallel) in 4 channels.

превышает порог обнаружения во всех q-x каналах. Такие элементы разрешения соответствуют элементам отражения земной поверхности.5. Of the N frequency resolution elements, only those n elements (n << N) are considered, on which the signal amplitude $$U_q\left(i,j\right)=\left|{\dot{S}}_q\left(i,f_j\right)\right|$$

exceeds detection threshold in all qx channels. Such resolution elements correspond to earth reflection elements.

, q=1, 2, 3, 4, находят пространственные координаты i,j-го отражающего элемента, а именно:6. For each i, jth four measurements $${\dot{S}}_q={\dot{S}}_q\left(i,f_j\right)$$

, q = 1, 2, 3, 4, find the spatial coordinates of the i, jth reflecting element, namely:

- фазы $${\psi }_q=\arg \left\{{\dot{S}}_q\right\}$$

, q=1, 2, 3, 4 и вычисляют разности фаз по азимуту φ для горизонтальных каналов (1 и 3) и по углу места θ для вертикальных каналов (2 и 4):6.1) take arguments of complex quantities $${\dot{S}}_q$$

- phases $${\psi }_q=\arg \left\{{\dot{S}}_q\right\}$$

, q = 1, 2, 3, 4 and phase differences are calculated in azimuth φ for horizontal channels (1 and 3) and elevation angle θ for vertical channels (2 and 4):

Δψ _φ = ψ ₁ -ψ ₃ , Δψ _θ = ψ ₂ -ψ ₄ ;

6.2) for the obtained phase differences find estimates of the angular coordinates:

φ _ij = kΔψ _φ , θ _ij = kΔψ _θ , k = λ / (4πd).

6.3) estimates of the angular coordinates are recalculated into spatial rectangular coordinates, which for a narrow BOTTOM are calculated by the formulas:

.x _ij = φ _ij R _i , y _ij = θ _ij R _i , $$z_{ij}=\sqrt{R_i^2-x_{ij}^2-y_{ij}^2}\approx R_i$$

.

The set of coordinates x _ij , y _ij , x _ij on the set of values i, j gives a three-dimensional image of a portion of the earth's surface along the bottom of the bottom.

7. The line of sight of the antenna is successively shifted in azimuth and elevation to the width of the bottom and the operations are repeated. 2-6. The result is a three-dimensional image of the earth's surface in the extended visibility of the radar.

Settlement part

, µ=1, 2, …, N, на входе ДПФ в каждом q-м канале (q=1, 2, 3, 4) в антенной системе координат [1] имеет видTime sequence model $${\dot{s}}_q\left(t_{\mu }\right)$$

, µ = 1, 2, ..., N, at the input of the DFT in each qth channel (q = 1, 2, 3, 4) in the antenna coordinate system [1] has the form

where U (φ _j , θ _j ) = ρ (φ _j , θ _j ) U ₀ is the amplitude of the signal from the j-th reflecting element of the earth’s surface with angular coordinates φ _j , θ _j corresponding to the j-th resolution element in Doppler frequency with center frequency f _j ; ρ is the reflection coefficient depending on φ _j , θ _j ; U ₀ is the amplitude of the probe signal; D (φ, θ) is the amplitude characteristic of the DND for radiation and reception, for example:

комплексный белый шум с нулевым средним (шум аппаратуры) и дисперсией $${\sigma }_p^2$$

; γ_q - мультипликативная помеха с единичным средним, моделирующая флуктуации сигналов в q-x каналах.k ₀ is the known coefficient (k ₀ = 2.78); Δ _φ and Δ _θ - bottom width in azimuth and elevation at the level of 0.5 power; i is the imaginary unit; δ _q (φ, θ) - delay or phase advance of the received reflected signal from the element with angular coordinates φ, θ in the qth receiving element of the antenna compared to the center of the antenna; ξ - phase component of the element range resolution: ξ = -4πR / λ + φ ₀ + η; ϕ ₀ is the initial phase; η is a random variable uniformly distributed on [0.2π] and describing the reflection uncertainty in the range element (η changes its value with respect to the range elements); $${\dot{\rho }}_q\left(t_{\mu }\right)$$

complex white noise with zero mean (instrument noise) and dispersion $${\sigma }_p^2$$

; γ _q is the unit mean multiplicative noise modeling the fluctuations of signals in qx channels.

The summation in (1) is carried out over n Doppler frequency resolution elements corresponding to n successively located earth reflection elements within the BOTTOM width in this range resolution element R. The time t _µ is counted with a sampling frequency f _d that ensures that there is no "spreading of frequencies" at DFT, i.e. for each frequency f _j the equality holds: f _j = qf _d / N, where q is an integer.

. Или ортом вектора нормали $${\overrightarrow{n}}_0=\left(\cos \theta \sin \varphi ,\sin \theta ,\cos \theta \cos \varphi \right)$$

, совпадающим с ортом радиус-вектора $$\overrightarrow{r}=\left(x,y,z\right)$$

точки M(x,y,z) - центра элемента отражения. Считаем, что плоский фронт волны с таким же нормальным вектором достигает центра остальных приемных элементов антенны. Тогда величина δ_q определится как отклонение центра q-го приемного элемента (точки с координатами x_q,y_q,0) от плоскости, проходящей через начало координат с вектором нормали $${\overrightarrow{n}}_0$$

, по формуле: δ_q=x_qcosθsinφ+y_qsinθ, или с учетом cosθsinφ=x/R, sinθ=y/R:The quantity δ _q (φ, θ) is defined as the difference in distances: δ _q = RR _q , where R is the distance of the center of the reflecting surface element with coordinates x, y, z from the center of the antenna; R is the removal of the center of the same element from the center of the qth receiving element of the antenna with known coordinates x _q , _q and z _q = 0. For the practical calculation of δ _q, we assume the assumption. Imagine the spherical front of the reflected wave reaching the central element of the antenna with a tangent plane (flat front) with a normal vector $$\overrightarrow{n}=\left(x,y,z\right)=R\left(\cos \theta \sin \varphi ,\sin \theta ,\cos \theta \cos \varphi \right)$$

. Ormt normal vector $${\overrightarrow{n}}_0=\left(\cos \theta \sin \varphi ,\sin \theta ,\cos \theta \cos \varphi \right)$$

coinciding with the unit vector of the radius vector $$\overrightarrow{r}=\left(x,y,z\right)$$

points M (x, y, z) - the center of the reflection element. We believe that the plane wave front with the same normal vector reaches the center of the remaining receiving elements of the antenna. Then the value of δ _q is defined as the deviation of the center of q-th receiving element (the points with coordinates x _q, y _q, 0) of the plane passing through the origin with the normal vector $${\overrightarrow{n}}_0$$

, by the formula: δ _q = x _q cosθsinφ + y _q sinθ, or taking cosθsinφ = x / R into account, sinθ = y / R:

Formula (3) gives a linear dependence of δ _q on x, y for the known R. For the coordinates of the centers of the receiving elements of the antenna indicated above

- орта вектора скорости $$\overrightarrow{v}$$

движения носителя РЛС и $${\overrightarrow{r}}^0=\left(\cos \theta \sin \varphi ,\sin \theta ,\cos \theta \cos \varphi \right)$$

- орта радиус-вектора $$\overrightarrow{r}=\left(x,y,z\right)$$

точки отражения:The relationship of the angular φ, θ and, accordingly, rectangular x, y coordinates with the Doppler frequency f _{d is} obtained as follows. For the Doppler beam narrowing (DOL) mode, we have [3, p. 22, p. 52]: f _d = (2v / λ) cosα, where cosα is found using the scalar product of two vectors: $${\overrightarrow{v}}^0=\left(v_x,v_y,v_z\right)$$

- orth of the velocity vector $$\overrightarrow{v}$$

radar carrier movements and $${\overrightarrow{r}}^0=\left(\cos \theta \sin \varphi ,\sin \theta ,\cos \theta \cos \varphi \right)$$

- orth radius vector $$\overrightarrow{r}=\left(x,y,z\right)$$

reflection points:

Equation (5) for fixed v and f _d is a nonlinear equation of the Doppler frequency line (isodope) at a distance R in the angular coordinates φ, θ. Or a linear equation in the rectangular coordinates x, y, z (for a fixed R):

(λ / 2v) f _d = (v _x x + v _y y + v _z z) / R.

, $$\mu =\overline{\mathrm{1,}N}$$

одновременно в q-x каналах (q=1, 2, 3, 4) преобразуются в частотные последовательности $${\dot{s}}_q^{\ast }\left(f_j\right)$$

, j=1, 2, …, N. Для n доплеровских частот n<<N, соответствующих отражающим элементам поверхности и расположенным в общей полосе частот ДПФ, принимается модель:As a result of the DFT, time sequences $${\dot{s}}_q\left(t_{\mu }\right)$$

, $$\mu =\overline{\mathrm{one,}N}$$

simultaneously in qx channels (q = 1, 2, 3, 4) are converted into frequency sequences $${\dot{s}}_q^{\ast }\left(f_j\right)$$

, j = 1, 2, ..., N. For n Doppler frequencies n << N corresponding to reflective surface elements and located in the common frequency band of the DFT, the model is adopted:

j = 1, 2, ..., n, where δ _{q are} defined in (4).

From model (6) it is seen that the angular coordinates φ, θ of the centers of the reflecting elements are contained in the amplitude and phase parts of the processed signals. Moreover, for the measured phases ψ _q = (2π / λ) δ _q + ξ their differences:

where ε ₁ and ε ₂ are the errors of measurement of the phase difference.

The desired coordinates are found from (7), neglecting ε ₁ and ε ₂ :

, где σ_ε - СКО ошибок ε.In this case, the standard deviation of the estimation errors φ, θ is defined as $${\sigma }_{\varphi }={\sigma }_{\theta }={\sigma }_{\epsilon }\frac{\lambda }{\mathrm{four}\pi d}$$

, where σ _ε is the standard deviation of errors ε.

Note that the phase differences taken without taking into account the errors of their measurement:

where Δ _φ = δ _l -δ _3, Δ _θ = δ ₂ -δ _4, at small angles φ, θ is uniquely determined by the value Δ _φ and Δ _θ. Thus, if Δ _φ is changed within 0≤Δ _φ ≤λ, which corresponds to small angles φ, θ, the phase difference varies 0≤Δψ _φ ≤2π or -π≤ψ≤π, and Δ _φ between and set Δψ _φ unique correspondence (9). However, for large angles φ, θ, ambiguity arises. So, if λ <Δ _φ ≤2λ, which corresponds to large angles φ, θ, Δψ _φ again varies in the range 0≤Δψ _φ ≤2π. The same for 2λ <Δ _φ ≤3λ, etc. The elimination of the ambiguity is solved algorithmically and constructively by introducing the fifth central element of the antenna with an asymmetric arrangement of the remaining receiving elements of the antenna along the x and y axes. In this case, coarse and accurate channels are formed [2, p. 424]. However, for a narrow DND characteristic of a phased AR, signals are received from the directions of an unambiguous phase measurement. Also, the correction for the sphericity of the wave front at a specified range of R.

Simulation results

. На дальности R=1000 м моделировалась полоса склона земной поверхности. При ширине круговой ДНА 2° на дальности R высота склона по оси oy составляла 34 м, протяженность по оси ох также 34 м. Центры элементов отражения общим числом n=25 шли с шагом 1,36 м по осям x и у в сторону уменьшения высоты склона. Оценке подлежали пространственные координаты этих центров. Зондирующие импульсы числом N=5000 при моделировании отражались от центров элементов полосы поверхности с коэффициентом ρ=1. При длине волны λ=0,01 м отраженные сигналы принимались в 4-х элементах антенной решетки с базовым расстоянием 2d=0,1 м и после прохождения тракта первичной обработки в 4-х каналах формировались в соответствии с моделью (1). При частоте дискретизации f_д=100 кГц получались 4 временные последовательности длиной N=5000 каждая, которые подвергались ДПФ. В общей полосе частот [0,100 кГц] полоса доплеровских частот, соответствующая отражающим элементам поверхности, составляла [13,9 кГц; 14,4 кГц] с разрешением по частоте 20 Гц. Полученные в результате ДПФ спектральные последовательности подавались на вход алгоритмов 1 и 2 обработки данных. Алгоритм 1 соответствовал способу-прототипу, основанному на моноимпульсном методе, алгоритм 2 - предлагаемому способу, основанному на фазовом методе. Результаты моделирования представлены ниже.The prototype method and the proposed method were compared in the anterolateral view by mathematical modeling. The speed of the aircraft and the unit vector of the velocity vector were set: v = 100 m / s, $${\overrightarrow{v}}^0=\left(\mathrm{one}/\sqrt{2};0;\mathrm{one}/\sqrt{2}\right)$$

. At a distance of R = 1000 m, a strip of the slope of the earth's surface was simulated. With a circular bottom bottom width of 2 ° at a distance R, the slope height along the oy axis was 34 m, the length along the oh axis was also 34 m. The centers of the reflection elements with a total number of n = 25 walked with a step of 1.36 m along the x and y axes in the direction of decreasing height slope. The spatial coordinates of these centers were subject to assessment. The probe pulses with the number N = 5000 in the simulation were reflected from the centers of the surface strip elements with the coefficient ρ = 1. At a wavelength of λ = 0.01 m, the reflected signals were received in 4 elements of the antenna array with a base distance of 2d = 0.1 m and, after passing through the primary processing path in 4 channels, they were formed in accordance with model (1). At a sampling frequency f _d = 100 kHz, 4 time sequences of length N = 5000 each were obtained, which were subjected to DFT. In the common frequency band [0.100 kHz], the Doppler frequency band corresponding to the reflective surface elements was [13.9 kHz; 14.4 kHz] with a frequency resolution of 20 Hz. The spectral sequences obtained as a result of the DFT were fed to the input of data processing algorithms 1 and 2. Algorithm 1 corresponded to the prototype method based on the single-pulse method, algorithm 2 to the proposed method based on the phase method. The simulation results are presented below.

в модели (1) на точность работы алгоритмов 1, 2. Даны зависимости средней ошибки определения пространственных координат центров элементов отражения и оценок СКО этих ошибок от отношения сигнал-шум С/Ш=201g(U₀/σ_р).Tables 1, 2 show the effect of additive noise. $${\dot{\rho }}_q\left(t_{\mu }\right)$$

in the model (1) on the accuracy of algorithms 1, 2. The dependences of the average error in determining the spatial coordinates of the centers of reflection elements and the RMSE estimates of these errors on the signal-to-noise ratio S / N = 201g (U ₀ / σ _p ) are given.

You can see the advantage of algorithm 2 in the accuracy of determining the coordinates. Tables 3, 4 show the effect of the multiplicative interference γ _q at a fixed ratio S / N = 60 dB. The action of γ _{q was} modeled by a random change in γ _q along the qth channels with a deviation of the indicated percentage relative to its average value.

You can also see the advantage of algorithm 2 of the proposed method. This method can find implementation in existing airborne systems for monitoring the earth's surface in order to improve the safety of low-altitude flights.

Literature

1. A positive decision on the application No. 2013119344/07 (028620).

2. Finkelstein M.I. Basics of radar: Textbook for universities. M .: Radio and communications, 1983. 536 p.

3. Kondratenkov G.S., Frolov A.Yu. Radio vision. Earth Remote Sensing Radar Systems: Textbook for High Schools / Ed. G.S. Kondratenkova, Moscow: Radio Engineering, 2005.368 s.

Claims (1)

A method of forming a three-dimensional image of the earth’s surface in an onboard four-channel Doppler radar, which consists in the formation of a radar image of a plot of the earth’s surface in the form of a set of complex amplitudes

reflection signals in ix range resolution elements R _i (i = 1, 2, ..., m, where m is the number of range elements) at jx frequencies (j = 1, 2, ..., N, where N is the number of frequency resolution elements) simultaneously in four measuring channels (q = 1, 2, 3, 4, where q is the channel number), determining those jx frequencies at which the amplitude

signal

exceeds the detection threshold in all channels, and the subsequent processing of the received measurements

, characterized in that the centers of the receiving elements of the antenna are located on the antenna plane at points with coordinates (x ₁ , y ₁ ) = (d, 0), (x ₂ , y ₂ ) = (0, d), (x ₃ , y ₃ ) = (- d, 0), (x ₄ , y ₄ ) = (0, -d) and for each i, jth four measurements

, q = 1, 2, 3, 4, obtained in qx primary processing channels, take the arguments of complex quantities

- phases

, q = 1, 2, 3, 4, the phase differences are calculated in azimuth φ and elevation angle θ: Δψ _φ = ψ ₁ -ψ ₃ , Δψ _θ = ψ ₂ -ψ ₄ and find the rectangular coordinates of the reflection points:
x _ij = kΔψ _φ , y _ij = kΔψ _θ ,

, k = R _i λ / (4πd),
λ is the wavelength, which on a set of values of i, j give a three-dimensional image of a piece of the earth’s surface along the width of a narrow antenna pattern, then shift the line of sight of the antenna sequentially in azimuth and elevation by the width of the radiation pattern and repeat these operations.