RU2539558C1 - Method of forming three-dimensional image of earth's surface and air environment using antenna array - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: method of forming a three-dimensional image of the earth's surface and air environment using an antenna array includes successive scanning of a scanning with displacement of the antenna beam by the beam pattern width and forming, at each position of the beam, a three-dimensional image of reflection objects via two-step processing of a matrix of complex measurements, received in channels of the antenna array, which enables to estimate the amplitude of the reflection field in angular elements of discretisation of the visibility zone of the antenna in all range resolution elements and obtain spatial coordinates of all reflecting elements in the visibility zone.

EFFECT: forming a three-dimensional image of reflection objects in a visibility zone using a cheap two-step procedure of increasing resolution of the antenna array on angular coordinates.

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Description

The invention relates to radar, and in particular to airborne radar systems (radar) for monitoring the earth's surface and the air situation, working in real beam (RL) based on a flat antenna array (AR) [1]. The radar mode is notable for its simplicity of implementation (in comparison with the aperture synthesis mode), the absence of restrictions on the movement of the radar carrier, and the possibility of maneuvering and observing forward along the flight course [2]. However, the low resolution of the radar mode, determined by the width of the radiation pattern (BH) of the antenna, limits its use to a small observation range at low altitude flight (MVP).

To improve the safety of the profit center, it is necessary to form a three-dimensional image of the terrain at the flight rate in real time. When observing the air situation, it becomes necessary to distinguish between several equally distant aerial objects located within the antenna beam width (detection of group air objects). In this case, three tasks arise: increasing the resolution of the antenna, forming a three-dimensional image and increasing the speed of data processing. The invention is directed to the solution of these problems.

The known method of two-stage image recovery in multichannel radar and radiolocation stations [3], which has increased speed. In relation to the radar, in [3], the radar mode with MD, which is divided by angular variables, is considered. This property of the ND allows, when forming a radar image, to process the measurement matrix first in rows and then in columns using one-dimensional summation of measurements with weight coefficients. The advantage of the method [3] in speed compared to conventional processing of the measurement matrix using two-dimensional summation with the same number of channels due to a more efficient organization of calculations is shown. However, in [3] a description is given of a scanning radar, in which the effect of increasing the resolution in angles is based on the sequential displacement of the radar beam in rows and columns by the size of the sampling element (pixel of the image matrix). Scanning leads to an increase in processing time and a random change in the phase of the received signal upon repeated emission, which significantly reduces the accuracy of image reconstruction and, accordingly, its clarity (resolution). Also, in [3], it is not indicated for which antenna the property of dividing the beam by angular variables is fulfilled.

, принятые в k-x каналах ФАР ( $$k=\overline{1,N}$$

, N - число каналов), суммируют с весовыми коэффициентами

рассчитанными методом восстановления n угловых составляющих поля отражения от земной поверхности в пределах ширины ДН ФАР (n<N), и осуществляют оценивание j-х комплексных амплитуд

поля отражения по формулеThe closest in technical essence is a way to increase the resolution of a phased array antenna (PAR) of an airborne station [4], which consists in forming an N-channel phased array antenna using calculated complex weight coefficients, characterized in that when receiving a probe signal reflected from the earth's surface with directions θ, φ elevation angle θ and azimuth φ complex signals $${\dot{y}}_k$$

received in kx channels of PAR ( $$k=\overline{\mathrm{one},N}$$

, N is the number of channels), summarized with weights

calculated by the method of reconstructing the n angular components of the reflection field from the earth's surface within the width of the beam headlamp (n <N), and j-complex amplitudes are estimated

reflection fields according to the formula

и получают амплитудное изображение

элементов поверхности, наблюдаемых в пределах ширины ДН с повышенным в n раз угловым разрешением.then take assessment modules

and get the amplitude image

surface elements observed within the limits of the width of the beam with an angular resolution increased by a factor of n.

The summation in formula (1) is carried out over all j-th elements of a linear or flat headlamp. For a flat headlamp, whose DN has the property of dividing by angular variables, formula (1), as in [3], is disclosed as an economical two-stage procedure (restoration of the image matrix first by the ith rows and then by the jth columns) :

- комплексные измерения в q,k-x каналах ФАР

и

- элементы матриц весовых коэффициентов W_A и W_B.where m and n are the number of discretization elements along the angular coordinates θ and φ (m <M, n <N); $${\dot{y}}_{q,k}$$

- complex measurements in q, kx channels of the PAR

and

- elements of the matrices of weights W _A and W _B.

However, this method has the following disadvantages.

1. For the coordinate system considered in [4], the headlamps are not separated by angular variables (azimuth and elevation). Therefore, the claimed two-stage procedure in such a coordinate system is not applicable.

2. The method is limited to considering flat (in angular coordinates) images, while radar observations allow us to measure the range and on this basis to form more informative three-dimensional images of reflection objects.

3. The method is limited to considering only one angular direction of the antenna beam, while the field of view contains many angular directions.

The technical result is aimed at forming a three-dimensional image of reflection objects in the field of view using an economical two-stage procedure for increasing the resolution of the AR in the corners.

значения комплексных амплитуд принимаемых сигналов $${\dot{y}}_{q,k}$$

, формируют из этих амплитуд M×N-матрицу измерений Y с элементами

и далее обрабатывают,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 and the air environment using the antenna array in the form of an M × N matrix of receiving elements is that when observing the earth's surface or the air situation using a beam scanning at angles antennas in the field of view are measured at each beam position in the q, kx measuring channels

values of the complex amplitudes of the received signals $${\dot{y}}_{q,k}$$

form from these amplitudes an M × N measurement matrix Y with elements

further processed

измеряют в каждом l-м элементе разрешения дальности ( $$l=\overline{1,L}$$

, L - число таких элементов), запоминают их в M×N-матрице измерений Y и обрабатывают в антенной системе координат, при этом умножают матрицу Y слева на рассчитанную заранее m×M-матрицу весовых коэффициентов W_A и получают m×N-матрицу S восстановленного по строкам изображения: S=W_AY, далее матрицу S умножают справа на рассчитанную заранее N×n-матрицу весовых коэффициентов W_B и получают m×n-матрицу U восстановленного по строкам и столбцам изображения с повышенным в mn раз (m<N, n<N) угловым разрешением: U=SW_B, затем вычисляют модули

комплексных элементов матрицы

повторяют операции для всех l-х элементов дальности

и запоминают координаты тех i,j,l-x пространственных элементов, амплитуды которых превышают порог γ₀ обнаружения полезного сигнала: u(i,j,l)>γ₀, в результате получают трехмерное изображение объектов отражения в виде совокупности их прямоугольных координат x_j,y_j,z_l в зоне видимости антенны, затем повторяют операции для всех положений луча и получают трехмерное изображение в полной зоне обзора.characterized in that during scanning the beam is sequentially shifted by the width of the antenna pattern (at the level of 0.5 power) line by line in the field of view, complex amplitudes

measured in each l-th element of range resolution ( $$l=\overline{\mathrm{one},L}$$

, L is the number of such elements), store them in the M × N measurement matrix Y and process it in the antenna coordinate system, while multiplying the Y matrix on the left by the previously calculated m × M matrix of weight coefficients W _A and obtain an m × N matrix S of the row-reconstructed image: S = W _A Y, then the matrix S is multiplied on the right by the N × n matrix of weight coefficients W _B calculated in advance, and an m × n matrix U of the image reconstructed in rows and columns is obtained with an increase in mn times (m <N, n <N) angular resolution: U = SW _B , then the modules are calculated

complex matrix elements

repeat operations for all l-range elements

and remember the coordinates of those i, j, lx spatial elements whose amplitudes exceed the useful signal detection threshold γ ₀ : u (i, j, l)> γ ₀ , as a result, a three-dimensional image of reflection objects is obtained in the form of a combination of their rectangular coordinates x _j , y _j , z _l in the visibility range of the antenna, then repeat the operations for all positions of the beam and get a three-dimensional image in the full viewing area.

The method is as follows.

1. The antenna beam, using electronic control, scans the field of view, moving in azimuth and elevation line by line to the width of the beam (at the level of 0.5 power).

, М и N - число элементов по строке и столбцу).2. After sending the probe pulses, the reflected signals are received by the q, kth AR elements (single or grouped), which are located in the AR plane in matrix order along the qth rows and kth columns (

, M and N - the number of elements by row and column).

, проходят в них тракт первичной обработки (стробирование по дальности, фазовое детектирование, фильтрацию на низкой частоте [5]), в результате которой на видеочастоте выделяются комплексные амплитуды

принимаемых сигналов

в каждом l-м элементе разрешения по дальности ( $$l=\overline{1,N}$$

, L - число таких элементов).3. Received signals arrive at q, ke receive channels

pass through them the primary processing path (range gating, phase detection, low-frequency filtering [5]), as a result of which complex amplitudes are emitted on the video frequency

received signals

in each l-th element of range resolution ( $$l=\overline{\mathrm{one},N}$$

, L is the number of such elements).

помещаются в М×N-матрицу измерений Y в каждом l-м элементе дальности. Дальнейшая обработка осуществляется в l-х элементах дальности независимо и параллельно в антенной системе угловых координат φ_x, θ_y.4. Complex amplitudes

placed in the M × N-matrix of measurements Y in each l-th element of range. Further processing is carried out in l-range elements independently and in parallel in the antenna system of angular coordinates φ _x , θ _y .

5. The matrix Y is multiplied on the left by the m × M matrix of weight coefficients W _A calculated in advance. The result is an m × N matrix S of a row-reconstructed image: S = W _A Y.

6. The matrix S is multiplied on the right by the pre-calculated N × n matrix of weight coefficients W _B. It turns out the m × n matrix U of the image reconstructed from rows and columns with an increased mn times (m <N, n <N) angular resolution: U = SW _B.

комплексных элементов матрицы

и запоминаются номера i,j амплитуд u(i,j,l), которые превышают порог обнаружения полезного сигнала γ₀: u(i,j,l)>γ₀ в l-м элементе дальности.7. Modules are calculated

complex matrix elements

and the numbers i, j of amplitudes u (i, j, l) that exceed the detection threshold of the useful signal γ ₀ : u (i, j, l)> γ ₀ in the l-th range element are stored.

для запомненных номеров i,j,l, имеющих угловые координаты θy(i), φ_x(j) и дальность r(l), вычисляются прямоугольные координаты x=φ_x(j)r(l), y=θ_y(i)r(l), z=r(l), совокупность которых представляет трехмерное изображение объектов отражения в зоне видимости АР.8. On the set of l-range elements

for the memorized numbers i, j, l having angular coordinates θy (i), φ _x (j) and range r (l), rectangular coordinates x = φ _x (j) r (l), y = θ _y (i ) r (l), z = r (l), the combination of which represents a three-dimensional image of reflection objects in the AR visibility zone.

9. For all positions of the scanning beam of the antenna, a three-dimensional image is obtained in the form of a set of points with coordinates x, y, z in the full viewing area.

10. The resulting coordinates are converted into a global coordinate system for the purpose of spatio-temporal image processing.

Settlement part

Observation of the earth's surface or air situation is carried out in a rectangular antenna coordinate system o, x, y, z, the oz axis coincides with the central direction of radiation and reception of reflected signals. The antenna system also uses the coordinate system r, φ _x , θ _y , where r is the slant range; φ _x is the angle between the oz axis and the geometric projection of the radar beam on the horizontal plane o, x, z; θ _y is the angle between the oz axis and the geometric projection of the beam onto the vertical plane o, y, z.

- вектор луча отражения от точки M; α - угол между вектором

и вектором скорости

движения носителя РЛС.The figure 1 shows the following: the shaded part is the plane of the antenna; o, x, y, z - rectangular antenna coordinates; φ, θ - spherical angular coordinates (azimuth and elevation); φ _x = φ is the azimuth and θ _y is the elevation angle in the projection onto the coordinate plane o, y, z;

is the vector of the reflection beam from point M; α is the angle between the vector

and velocity vector

radar carrier movements.

работающими на излучение и прием отраженных сигналов. Центры приемных элементов антенны расположены в точках М(x_k,y_q) с координатами x_k, y_q.The antenna is made in the form of a flat M × N-array with q, k elements located in matrix order

working on the radiation and reception of reflected signals. The centers of the receiving elements of the antenna are located at points M (x _k , y _q ) with coordinates x _k , y _q .

представлена двойной суммой:Comprehensive signal model

represented by a double sum:

Where

- комплексная амплитуда принимаемого сигнала в l-м элементе разрешения дальности с углового направления θ_y(i), φ_x(j); множитель i под знаком экспоненты - мнимая единица; ξ_l - изменение фазы сигнала при приеме в l-м элементе дальности; u(i,j,l) - амплитуда сигнала отражения в i,j-м угловом направлении и l-м элементе дальности, характеризующая отражающую способность i,j,l-го пространственного элемента разрешения (ненулевая для элемента отражения); ε - неизвестное изменение фазы в l-м элементе дальности, которое в l-м элементе можно считать неизменным, а на множестве значений l - случайным, равномерно распределенным на [0,2π]; λ - длина волны;

- комплексная нормированная ДН q,k-го приемного элемента АР, амплитудная часть которой g(i,j) - известная функция θ_y(i) и φ_x(j) (µ - известный коэффициент); Δ - ширина круговой ДН антенны; δ_q,k=δ_q,k(i,j) - известное опережение или запаздывание по фазе сигнала, принимаемого с i,j-го углового направления в q,k-м приемном элементе по сравнению с центром антенны;

- комплексный гауссовский белый шум с нулевым математическим ожиданием и дисперсией

действительной и мнимой части.Where

- the complex amplitude of the received signal in the l-th element of range resolution from the angular direction θ _y (i), φ _x (j); the factor i under the sign of the exponent is an imaginary unit; ξ _l is the phase change of the signal when received in the l-th element of range; u (i, j, l) is the amplitude of the reflection signal in the i, jth angular direction and the lth range element, which characterizes the reflectivity of the i, j, lth spatial resolution element (nonzero for the reflection element); ε is the unknown phase change in the l-th element of range, which in the l-th element can be considered unchanged, and on the set of values of l - random, uniformly distributed on [0,2π]; λ is the wavelength;

- the complex normalized DN q of the kth receiving element of the AR, the amplitude part of which g (i, j) is the known function θ _y (i) and φ _x (j) (μ is the known coefficient); Δ is the width of the circular bottom antenna; δ _{q, k} = δ _{q, k} (i, j) - a known advance or phase delay of the signal received from the i, jth angular direction in the q, kth receiving element compared to the center of the antenna;

- complex Gaussian white noise with zero expectation and dispersion

real and imaginary parts.

The summation in (3) is carried out over the i, jth discretization elements of the goniometric region {(θ, φ)} within the BOTTOM.

или

The calculation of δ _{q, k} = δ _{q, k} (i, j) in the angular antenna coordinates θ _y (i), φ _x (j) reduces to the following. For a plane wave front, the normal vector

or

Using the formula for the distance from the point M (x _q , y _k ) of the center q, of the kth element of the antenna to the plane of the wave passing through the center of the antenna, we obtain

For a beam width Δ of the order of 1 ⁰ -2 ⁰ ° (in radians this is a small value compared to unity), formula (4) can be simplified:

Then the complex pattern of each q, kth element of the AR is divided by the angular variables φ _x and θ _y as follows:

Where

In view of (6), model (3) takes the form of a repeated sum:

or in matrix form:

where Y is the M × N measurement matrix

A - M × m matrix of coefficients

U is the m × n matrix of the desired amplitudes;

записанная в транспонированном виде по отношению к матрице A; P - М×N-матрица помех

B - m × N matrix of coefficients

recorded in transposed form with respect to matrix A; P - M × N interference matrix

матрицы U находим по критерию минимума следа матрицы (Y-AUB)^H(Y-AUB) по формуле [3, 4]:Optimal grade

the matrices U are found by the criterion of the minimum trace of the matrix (Y-AUB) ^H (Y-AUB) by the formula [3, 4]:

where H is the symbol for the transpose and pairing operation; I is the identity matrix; δ is the regularization parameter.

It is convenient to perform operations (9) in the form of a two-stage procedure:

- матрицы комплексных весовых коэффициентов. Для круговой ДН (m=n): В=A^H.Where

- matrices of complex weights. For a circular pattern (m = n): B = A ^H.

Estimates (10) can be represented as a linear combination of measurements with weighting coefficients according to formula (2). Thus, the solution to the problem of reconstructing a two-dimensional image U reduces to the sequential solution of two one-dimensional problems.

элементов комплексной матрицы оценок

, превышающие порог обнаружения полезного сигнала, по совокупности значений i, j дают амплитудное изображение объектов отражения в l-м элементе дальности в зоне видимости АР. На множестве значений l получаем трехмерное изображение поверхности в виде совокупности точек с координатами x=φ_x(j)r(l), y=θ_y(i)r(l), z=r(l) в антенной прямоугольной системе.Modules

elements of an integrated assessment matrix

exceeding the detection threshold of the useful signal, in terms of the combination of i, j values give an amplitude image of the reflection objects in the l-th range element in the AR visibility range. On the set of values of l, we obtain a three-dimensional image of the surface in the form of a set of points with coordinates x = φ _x (j) r (l), y = θ _y (i) r (l), z = r (l) in a rectangular antenna system.

. Наоборот, при заданном предельном значении СКО ошибки оценивания находятся числа m и n, определяющие угловую разрешающую способность трехмерного изображения.The accuracy of the estimates of the amplitudes for a given number m, n of discretization elements of the goniometric region {(θ, φ)} is determined by the number and relative position of the elements of the antenna array and, accordingly, the structure of the matrices A and B. The covariance matrix Coν of the estimation errors at each estimation stage (10) can be approximately determine by the formula

. On the contrary, for a given limit value of the standard deviation of the estimation error, the numbers m and n are found, which determine the angular resolution of the three-dimensional image.

Literature

1. Monzingo R.A., Miller T.U. Adaptive Antenna Arrays: Introduction to Theory / Per. from English - M .: Radio and communications, 1986. 448 p.

2. Active phased antenna arrays / Ed. DI. Voskresensky and A.I. Kanaschenkova.- M .: Radio engineering. 2004.487 s.

3. Patent RU 2379705 C2.

4. Patent RU 2464680 C1.

5. Radar stations with digital synthesis of the antenna aperture / A.N. Antipov, V.T. Goryainov, A.N. Culin et al .; under the editorship of V.T. Goryainova.- M.: Radio and Communications, 1988. 304 p.

Claims (1)

The method of forming a three-dimensional image of the earth's surface and the air environment using an antenna array in the form of an M × N matrix of receiving elements, which consists in the fact that when observing the earth's surface or the air situation using an antenna beam scanning at angles, the antennas in the field of view are measured at each position beam in q, kx measuring channels $$(q=\overline{\mathrm{one},M},k=\overline{\mathrm{one},N})$$

values of the complex amplitudes of the received signals $${\dot{y}}_{q,k}$$

form from these amplitudes an M × N measurement matrix Y with elements $${\dot{y}}_{q,k},$$

$$q=\overline{\mathrm{one},M},$$

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

further processed
characterized in that during scanning the beam is sequentially shifted by the width of the antenna pattern (at the level of 0.5 power) line by line in the field of view, complex amplitudes $${\dot{y}}_{q,k}(l)$$

measured in each l-th element of range resolution ( $$l=\overline{\mathrm{one},L}$$

, L is the number of such elements), store them in the M × N measurement matrix Y and process it in the antenna coordinate system, while multiplying the Y matrix on the left by the previously calculated m × M matrix of weight coefficients W _A and obtain an m × N matrix S of the row-reconstructed image: S = W _A Y, then the matrix S is multiplied on the right by the N × n matrix of weight coefficients W _B calculated in advance, and an m × n matrix U of the image reconstructed in rows and columns is obtained with an increase in mn times (m <N, n <N) angular resolution: U = SW _B , then the modules are calculated $$u(i,j,l)=\left|\dot{u}(i,j,l)\right|$$

i, j-x complex elements of the matrix $$U(i=\overline{\mathrm{one},m},j=\overline{\mathrm{one},n})$$

repeat operations for all l-x range elements $$(l=\overline{\mathrm{one},L})$$

and remember the coordinates of those i, j, lx spatial elements whose amplitudes exceed the useful signal detection threshold γ ₀ : u (i, j, l)> γ ₀ , as a result, a three-dimensional image of reflection objects is obtained in the form of a combination of their rectangular coordinates x _j , y _j , z _l in the visibility range of the antenna, then repeat the operations for all positions of the beam and get a three-dimensional image in the full viewing area.