RU2456631C1 - Method for adaptive spatial compensation of interference during monopulse amplitude integral-differential direction finding and presence of receiving channel calibration errors - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method involves receiving signals from the current observation direction using an antenna system with integral (with number j=1), azimuth-differential (with number j=2), elevation angle-differential (with number j=3) channels and antennae q=1, 2,…Q compensation channels, coordinated processing of signals of each channel using Q+3 identical receiving channels, analogue-to-digital conversion of signals of each receiving channel and processing the digitised signals of each channel by calculating vectors of weight coefficients of the integral, azimuth-differential and elevation angle-differential channels and weighted summation of signals of the integral and compensation, azimuth-differential and compensation and elevation angle-differential and compensation channels, characterised by that, in order to calculate vectors of weight coefficients, constraint matrices for the shape of the resultant beam pattern of the integral, azimuth-differential and elevation angle-differential channels are formed first for all possible directions of observations in form of readings of values of the beam pattern of the integral, azimuth-differential, elevation angle-differential and compensation channels in r=1, 2,…, R constraint points, wherein for an odd number of constraint points, one of them lies in the given direction of observation, and the rest of the constraint points lie symmetrically about it and the direction finding planes; for an even number of constraint points, their positions lie symmetrically about the direction of observation and the direction finding planes; deviation of constraint points from the direction of observation is selected based on the minimum root-mean-square value of the error in estimating angular coordinates of the direction finding signal for the expected distributions of values of angular coordinates of arrival directions and power of the directing finding signal and noise; the constraint matrices are stored in constraint matrix memory; when processing digital signals of each channel, covariance matrices are formed for the integral, azimuth-differential, elevation angle-differential and compensation channels; the values of the constraint matrices for the integral, azimuth-differential and elevation angle-differential for the current observation direction are read from the constraint matrix memory, and to eliminate the effect of calibration errors, i=1, 2,…, I values of the regularisation parameter

are generated in form of a geometrical progression with the quotient Δµ=2…3 and initial value equal to the level of inherent noise of receiving channels; values of vectors of weight coefficients for the integral, azimuth-differential and elevation angle-differential channels corresponding to each regularisation parameter are generated based on the constraint matrices in accordance with a defined expression; the sum of squares of magnitudes of the weight coefficients for the integral, azimuth-differential and elevation angle-differential channels is then calculated for each value of the regularisation parameter; weighted summation of signals of the integral and compensation, azimuth-differential and compensation and elevation angle-differential and compensation channels is carried out and estimates of angular coordinates of the useful signal source are calculated for all values of vectors of weight coefficients for different values of the regularisation parameter; values of squares of angular distance between the angular coordinate estimates are calculated for neighbouring values of the regularisation parameter; values of angular coordinate estimates are calculated, which correspond to the first, in ascending order of the regularisation parameter, minimum square of angular distance between angular coordinate estimates provided the sum of squares of magnitudes of weight coefficients exceed an upper threshold value, and in the absence of said minimum, the angular coordinate estimates are those values which correspond to the value of the regularisation parameter where the sum of squares of magnitudes of the weight coefficient is closest to the lower threshold value without exceeding it.

EFFECT: high accuracy of direction finding.

6 dwg

Description

The invention relates to the field of radar technology and can be used to adaptively compensate the directional patterns of the total and difference channels of the monopulse amplitude total-difference direction finder of natural and deliberate interference during stabilization of parameters (eliminating zero displacement and changing slope) of its direction-finding characteristic and compensating for the effect calibration errors of the receiving channels.

A known method of monopulse total-differential direction finding [Reference radar ed. M. Skolnik, vol. 4. M .: Sov. Radio, 1978, pp. 16-21], which consists in receiving signals from a three-channel monopulse system containing a total and two difference channels, transferring the input signals of each channel to an intermediate frequency, amplifying the signals of the total and difference channels using a common automatic gain control system with the aim of ensuring independence of the signals of the sum and difference channels from the input signal level and phase detection of the signals of the difference channels when using the sum channel as a reference signal ala. At the output of the phase detectors, error signals are generated along the difference channels, the magnitude and sign of which determine the target offset from the equal-signal direction.

The disadvantage of the considered method of monopulse amplitude total-differential direction finding is its low noise immunity with respect to interference acting on the side lobes of the radiation pattern of the total and difference channels, leading to the appearance of systematic direction finding errors, the level of which depends on the signal-to-noise and noise / noise ratios "at the input of the direction finder and the level of the radiation patterns of the channels in the direction of the sources of interference [Bykov VV, Brodsky SV, Ovchinnikov GN The accuracy and stability of the angular tracking of the target under the influence of multipoint interference on monopulse radars along the far side lobes of the antenna radiation pattern, Radio engineering, No. 10, 2000].

A known method for the joint formation of rays in the total and difference radiation patterns of monopulse antenna arrays [RF patent 2120161, IPC H01Q 3/26, 1998], based on the weighting of the signals received by each emitter, their separation into two channels, the summation of the signals received from the outputs of the same name dividers with respectively progressive increasing and decreasing phase shift, providing a deviation of each beam in the generalized coordinate by ± ΔU, where ΔU is the distance of the beam maxima to the equal signal direction, and osleduyuschem formation of the sum and difference patterns. The weighting coefficients of the signals received by each emitter are chosen equal to the algebraic sum of the weighting coefficients for a given emitter, providing the formation of a basic radiation pattern with a maximum oriented in the direction of U _o and four radiation patterns compensating for each interference acting from the direction of U _p , of which two radiation patterns are oriented respectively in the directions (U _p + ΔU) and (U _p -ΔU), and the other two radiation patterns are mirror symmetric with respect to the natural direction and oriented respectively in the directions (2U _о -U _п -ΔU) and (2U _о -U _п + ΔU), and the weights of symmetric pairs of compensating radiation patterns are chosen the same. In this case, almost complete elimination of distortions of the direction-finding characteristic of the meter is achieved. The disadvantage of this method is the need for a priori information about the direction of the interference, which, as a rule, is not performed in practice.

Adaptive methods and compensation devices implementing them are known that exclude the possibility of distorting the shape of the radiation pattern when receiving a useful signal, as well as its partial suppression. These systems use angle restriction methods that can be divided into three groups.

The first group includes methods and compensating devices that implement them, in which restrictions on the shape of the radiation pattern are introduced using pilot signals [Monzingo R.A., Miller T.U. Adaptive antenna arrays. - M.: Radio and Communications, 1986, pp. 226-228]. In the framework of these methods, it is required to have a large dynamic range of elements of the compensation system, as well as filtering pilot signals at the output, which are significant drawbacks of the methods of this group.

The second group includes methods and compensation devices that implement them, which use “preliminary” (up to the adaptive processor) spatial filtering to protect the main lobe of the radiation pattern [R. Monzingo, T.U. Miller Adaptive antenna arrays. - M .: Radio and communications, 1986, p. 228-230; RF patent 2013833, H01Q 25/02, H01Q 21/00, 1994]. These methods reduce the influence of the useful signal on the formation of the resulting radiation pattern in a rather narrow spatial region relative to the expected direction of arrival of the useful signal and are highly sensitive to hardware implementation errors — differences of the real amplitude-phase distribution from the system aperture from the given a priori [Jablon N.K. Adaptive beamforming with the generalized sidelobe canceller in the presence of array imperfections IEEE Trans. Antennas and Propag. 1986. Vol. 34, No. 8, p. 996-1012].

The third group includes methods and compensation devices that implement them, using restrictions introduced directly into the control loop using a spatial-matrix filter [Monzingo RA, Miller T.U. Adaptive antenna arrays. - M.: Radio and Communications, 1986, pp. 163-165, 231-237]. The disadvantage of the methods of this group is their high sensitivity to calibration errors, which are understood as errors in determining (aligning) the characteristics of the receiving channels in amplitude and phase. To counter the influence of these errors, a method is known based on the use of regularized procedures for adaptive tuning of spatial filters [Abramovich Yu.I., Kachur V.G. Protection methods that differ from the reference useful signal in adaptive procedures with an unclassified training set. Radio engineering and electronics, volume 35, No. 6, 1990, p. 1235-1242], however, the method for determining the regularization parameter is not defined.

Closest to the proposed method (prototype) is a method of compensating for interference with a monopulse amplitude total-differential direction finding, implemented using a monopulse direction finder as part of a digital homing radar [Veksin S.I. Compensation for side lobe interference in Doppler homing heads. Radio engineering, No. 9, 2002, p. 76 ... 86; Veksin S.I. Processing of radar signals in Doppler homing heads. MAI Publishing House, 2005, pp. 212-224].

, разностных по азимуту

и углу места

и компенсационных

каналов поступают на аналого-цифровые преобразователи, где подвергаются преобразованию в цифровую форму. Выборку цифровых отсчетов сигналов обрабатывают в устройстве формирования результирующих сигналов и вычисления пеленгов путем последовательной реализации следующих операций:The essence of the method lies in the fact that useful (direction-finding) signals and interference are received by the main antenna system and the antennas of the compensation channels, amplified, transferred (if necessary) to the intermediate frequency, and coordinated intra-pulse processing is carried out in identical receiving channels. After consistent processing, the total

difference in azimuth

and corner of the place

and compensatory

channels are fed to analog-to-digital converters, where they are converted to digital form. A sample of digital samples of signals is processed in the device for generating the resulting signals and calculating bearings by sequentially implementing the following operations:

путем попарного перемножения сигналов, принимаемых различными компенсационными антеннами, и усреднения полученных результатов за заданный интервал времени;1.1) form the covariance matrix of the signals received by the compensation channels with elements

by pairwise multiplying the signals received by various compensation antennas, and averaging the results for a given time interval;

;1.2) calculate the covariance vectors of the signals of the total, difference and compensation channels with elements

;

1.3) calculate the vectors of the weighting coefficients of the total and difference channels

w _j = - (Φ ^* ) ^-1 G _j ;

1.4) carry out the weighted summation of the signals of the total and compensation and difference and compensation channels

.

.

The obtained compensated signals of the total and difference channels are used to calculate the estimates of the angular coordinates of the direction finding signal according to the formulas [Leonov A.I., Fomichev K.I. Monopulse radar. M .: Sov. Radio, 1970, pp. 22-26]

- среднее значение квадрата амплитуды сигнала суммарного канала за заданный интервал времени усреднения.where µ _{α (β)} is the steepness of the direction-finding characteristic along the azimuth channel and elevation angle, respectively;

- the average value of the square of the amplitude of the signal of the total channel for a given interval of averaging time.

The disadvantages of the prototype are the low accuracy of direction finding in the case of the formation of a covariance matrix of interference of the compensation channels and vector columns of the covariances of the signals of the total, difference and compensation channels for a sample containing, along with the interference, a useful direction-finding signal, zero offsets and changes in the steepness of direction-finding characteristics in the azimuthal and elevation planes, which are the dependences of the mathematical expectations of the estimation of the angular positions of the useful signal at the output of the direction finder in two planes bones of direction finding from angular deviations of the source of the useful signal from the direction of the maximum of the total channel (equal signal direction), when forming a covariance interference matrix for a sample containing only interference when exposed from separate directions. In the case of the formation of a covariance interference matrix for a sample containing, in addition to interference, a useful direction finding signal, a “failure” in the resulting radiation pattern of the sum and difference channels will be generated not only in the direction of interference, but also in the useful signal itself, as a result of which useful information will be lost in the meter about its angular coordinates. In the second case, the formation of dips in the resulting radiation pattern of difference channels can lead to a shift of their zeros, and the total channel to a change in its level, which in turn will lead to a change in the normalization conditions when calculating the angular coordinates when implementing the total-difference processing and a change in the steepness of direction finding characteristics.

The technical result of the invention is to increase the accuracy of direction finding by compensating for the interference on the side lobes of the total and differential channels of the direction finder due to the preservation of the positions of zeros and steepness of direction finding characteristics in the presence of calibration errors of the receiving channels.

в виде геометрической прогрессии со знаменателем Δ_µ=2…3 и начальным значением, равным уровню собственных шумов приемных каналов пеленгатора, формируют соответствующие каждому параметру регуляризации значения векторов весовых коэффициентов суммарного, разностного по азимуту и разностного по углу места каналов с учетом матриц ограничений в соответствии с выражениемThis result is achieved by the fact that in the method of compensating for noise during a monopulse amplitude total-differential direction finding, which consists in receiving signals by an antenna system with a total (with number j = 1), difference in azimuth (with number j = 2) and difference in elevation ( with number j = 3) and antennas q = 1, 2, ..., Q of compensation channels, coordinated processing of signals of each channel using Q + 3 identical receiving channels, analog-to-digital conversion of signals of each receiving channel and processing of digitized signals of each receiving channel in the device for generating the resulting signals and calculating bearings with the calculation of the vectors of the weight coefficients of the total and difference channels and the weighted summation of the signals of the total and compensation, difference in azimuth and compensation, difference in elevation and compensation channels, constraint matrices are preliminarily formed for calculating the weight vectors on the shape of the resulting radiation pattern of the total, difference in azimuth and difference in angle of elevation of the channel catch for all possible directions of observation in the form of readings of the values of the radiation patterns of the total, difference in azimuth, difference in elevation and compensation channels at r = 1, 2, ..., R constraint points, while with an odd number of restriction points, one of them is located in a given direction of observation, and the remaining restriction points are located symmetrically relative to it and the direction finding planes, with an even number of limit points their positions are located symmetrically relative to the direction of observation and the direction finding, deviations of the restriction points from the direction of observation are selected based on the minimum mean square error of the estimate of the angular coordinates of the direction finding signal for the expected distributions of the values of the angular coordinates of the directions of arrival and the strengths of the direction finding signal and interference, the restriction matrices are stored in the memory of the restriction matrixes, and each of the digitized signals is processed channel form covariance matrices total, difference in azimuth, difference in elevation and compensation ka bins, read the values of the restriction matrices of the sum, difference in azimuth and difference in elevation channels for the current direction of observation from the memory device of the restriction matrices, form i = 1, 2, ..., I values of the regularization parameter

in the form of a geometric progression with the denominator Δ _µ = 2 ... 3 and the initial value equal to the level of the intrinsic noise of the receiving channels of the direction finder, form the values of the vectors of the weight coefficients of the total, difference in azimuth and difference in angle of elevation channels corresponding to each regularization parameter in accordance with the restriction matrices in accordance with expression

,

,

- текущее значение параметра регуляризации;where Ф _j - covariance matrix of received signals for the j-th channel; I is the unit diagonal matrix;

- the current value of the regularization parameter;

- матрица ограничений для j-го канала;

- matrix of constraints for the j-th channel;

- вектор-столбец ограничений для j-го канала, образуемый из значений первой строки матрицы C_j;

;

- отсчеты значений диаграмм направленности j-го суммарного или разностного и q-го компенсационного каналов в точках ограничений; «+» - знак эрмитова сопряжения, вычисляют сумму квадратов модулей весовых коэффициентов суммарного, разностного по азимуту и разностного по углу места каналов для каждого из значений параметра регуляризации, проводят весовое суммирование и вычисляют оценки угловых координат полезного сигнала для всех значений векторов весовых коэффициентов при различных значениях параметра регуляризации, рассчитывают значения квадратов углового расстояния между оценками угловых координат для соседних значений параметра регуляризации, определяют значения оценок угловых координат, соответствующих первому в порядке возрастания параметра регуляризации минимуму квадрата углового расстояния между оценками угловых координат при условии непревышения суммы квадратов модулей весовых коэффициентов верхнего порогового значения, а при отсутствии указанного минимума в качестве оценок угловых координат принимают значения, соответствующие значению параметра регуляризации, при котором сумма квадратов модулей весовых коэффициентов наиболее близка к нижнему пороговому значению, не превышая его.

is the constraint column vector for the j-th channel, formed from the values of the first row of the matrix C _j ;

;

- counts of the values of the radiation patterns of the j-th total or difference and q-th compensation channels at the constraint points; “+” Is the sign of the Hermitian conjugation, the sum of the squared modules of the weight coefficients of the total, difference in azimuth and difference in elevation of the channels for each of the values of the regularization parameter is calculated, weight summation is carried out and estimates of the angular coordinates of the useful signal for all values of the vectors of the weight coefficients for various values of the regularization parameter, calculate the squares of the angular distance between the estimates of the angular coordinates for adjacent values of the regularization parameter, determine beginning of estimates of the angular coordinates corresponding to the first in the order of increasing regularization parameter minimum of the squared angular distance between the estimates of the angular coordinates provided that the sum of the squared modules of the weight coefficients of the upper threshold value does not exceed, and in the absence of the specified minimum, the values corresponding to the value of the regularization parameter are taken as the estimates of the angular coordinates, in which the sum of the squared moduli of the weighting coefficients is closest to the lower threshold value, not exceed nd it.

и угла места

в двух реализациях моделирования работы пеленгатора с компенсацией помех от параметра регуляризации. На фиг.5 приведены зависимости величины

- суммы квадратов производных оценок азимута и угла места пеленгуемого сигнала по параметру регуляризации, от самого параметра регуляризации. На фиг.6 приведены результаты расчетов нормированной к ширине главного лепестка суммарного канала среднеквадратической величины ошибки оценки угловых координат пеленгуемого сигнала от нормированных к ширине диаграммы направленности суммарного канала отклонений ограничений от направления наблюдения.Figure 1 shows the structural diagram of a device that implements the inventive method. Figure 2 shows the dependence of the sum of the squares of the weight coefficients and normalized to the maximum value of the coefficient of directional action of the total channel in power in the direction of the useful signal from the regularization parameter. Figure 3 shows the dependence of the interference compensation coefficient in the total channel on the regularization parameter. Figure 4 shows the dependence of the azimuth estimates

and elevation

in two implementations of direction finder simulation with interference compensation from the regularization parameter. Figure 5 shows the dependence of the value

- the sum of the squares of the derived estimates of the azimuth and elevation of the direction-finding signal with respect to the regularization parameter, from the regularization parameter itself. Figure 6 shows the results of calculations normalized to the width of the main lobe of the total channel of the root mean square value of the error in estimating the angular coordinates of the direction finding signal from the deviations of the restrictions from the direction of observation normalized to the width of the radiation pattern of the total channel.

A device that implements the inventive method (figure 1), contains the main monopulse antenna system 1 and q = 1, 2, ..., Q antennas 2.1 ... 2.Q compensation channels, the outputs of which are connected to Q + 3 in series with identical receiving channels 3.1 ... 3.Q + 3 and analog-to-digital converters 4.1 ... 4.Q + 3, the outputs of which are connected to the calculator of covariance matrices 5 and the first signal inputs i = 1, 2, ..., I of the calculators of vectors of weight coefficients 6.1 ... 6.I, output the covariance matrix calculator is connected to the second signal inputs of the vector calculators weight coefficients 6.1 ... 6.I, to the information inputs of which a constraint matrix memory device is connected 7. The first outputs of the weight vector calculators 6.1 ... 6.I are connected to the inputs of the device for calculating the difference of squares of estimates of angular coordinates 8. Outputs of the device for calculating the difference of squares of estimates of angular coordinates and the second outputs of the weight vector calculators 6.1 ... 6.I are connected to the logical selection unit 9.

Implementation of the proposed method for adaptive spatial interference compensation during monopulse amplitude total-differential direction finding with stabilization of the direction-finding characteristic parameters and in the presence of calibration errors of the receiving channels is as follows.

на форму результирующей диаграммы направленности суммарного, разностного по азимуту и разностного по углу места каналов видаPreliminarily (when adjusting and calibrating the direction finder) for all possible s = 1, 2, ..., S directions of observation (angular directions of the mechanical or electronic orientation of the maximum of the main lobe of the total channel of the main monopulse antenna system 1) with angular coordinates (α _S , β _S ) block 7 form the matrix of constraints

on the form of the resulting radiation pattern of the total, difference in azimuth and difference in elevation of the channel type

,

), и запоминают их в устройстве памяти матриц ограничений 7.which are the readings of the values of the directivity patterns of the total, difference in azimuth, difference in elevation and compensation channels at r = 1, 2, ..., R points of limitations that are separated in azimuth and elevation from the direction of observation (α _S , β _S ) at (

,

), and store them in the memory device of the matrix of constraints 7.

, разностных по азимуту

и углу места

и компенсационных

каналов поступают на аналого-цифровые преобразователи 4.1…4.Q+3, где подвергаются преобразованию в цифровую форму. Выборки цифровых отсчетов сигналов поступают на устройство формирования ковариационных матриц 5, где осуществляется вычисление ковариационных матриц помех суммарного и разностных каналов с элементами

;

;

, и первые сигнальные входы вычислителей векторов весовых коэффициентов 6.1…6.I.Useful (direction-finding) signals and interference are received by the main antenna system 1 and the antennas of the compensation channels 2.1 ... 2.Q, they carry out coordinated intra-pulse processing in identical receiving channels 3.1 ... 3.Q + 3. After consistent processing, the total

difference in azimuth

and corner of the place

and compensatory

channels are fed to analog-to-digital converters 4.1 ... 4.Q + 3, where they are converted to digital form. The samples of the digital samples of the signals are fed to the covariance matrix generation device 5, where the covariance interference matrices of the total and difference channels with elements are calculated

;

;

, and the first signal inputs of the weight vector calculators 6.1 ... 6.I.

The covariance matrices of the total and difference channels formed in the covariance matrix 5 forming device 5 are processed in the calculators of the weight coefficients vectors 6.1 ... 6.I by sequential implementation of the following operations:

, где i - порядковый номер вычислителя векторов весовых коэффициентов; Δ_µ - шаг изменения параметра регуляризации;

- начальное значение параметра регуляризации, равное мощности собственных шумов приемных каналов пеленгатора;calculate the regularization parameter

where i is the serial number of the weight vector calculator; Δ _µ is the step of changing the regularization parameter;

- the initial value of the regularization parameter, equal to the power of the own noise of the receiving channels of the direction finder;

read the values of the constraint matrices of the total, difference in azimuth and difference in the elevation angle of the channels for the current direction of observation (α _S , β _S ) of the form

from the memory device of the matrix of restrictions 7;

calculate the vectors and the sum of the squares of the modules of the weight coefficients of the total and difference channels

,

,

- вектор-столбец ограничений для j-го канала, образуемый из значений первой строки матрицы C_j, и значения суммы квадратов модулей весовых коэффициентовWhere

is the column vector of constraints for the j-th channel, formed from the values of the first row of the matrix C _j , and the values of the sum of the squared modules of the weight coefficients

- норма вектора;total and difference channels for various values of the regularization parameter, where

is the norm of the vector;

,

) угловых координат пеленгуемого сигналаcarry out the weighted summation of the signals of the total and compensation and difference and compensation channels and calculate the estimates (

,

) angular coordinates of the direction finding signal

и

and

,

) поступают на первые, а величины w_Σi - на вторые выходы вычислителей векторов весовых коэффициентов 6.1…6.I.Values (

,

) arrive at the first, and the quantities w _Σi - at the second outputs of the calculators of vectors of weight coefficients 6.1 ... 6.I.

In the device for calculating the difference of the squares of the estimates of the angular coordinates 8, the calculation of the values

,

,

representing the squares of the angular distances between the estimates of the angular coordinates for adjacent values of the regularization parameter.

,

), соответствующего первому минимуму Δ_i при условии

, где

- верхнее (при поиске минимума) значение максимальной суммы квадратов модулей весовых коэффициентов; при отсутствии минимума Δ_i осуществляется выбор значения (

,

), соответствующего

, где

- нижнее (при отсутствии минимума) значение максимальной суммы квадратов модулей весовых коэффициентов.In the logical selection block 9, a value is selected (

,

) corresponding to the first minimum Δ _i under the condition

where

- the upper (when searching for the minimum) value of the maximum sum of squares of the modules of weight coefficients; in the absence of a minimum Δ _i , the value (

,

) corresponding to

where

- the lower (in the absence of a minimum) value of the maximum sum of squares of the modules of weight coefficients.

Let us justify the content of the distinctive operations of the proposed method for adaptive spatial interference compensation during monopulse amplitude total-difference direction finding and the presence of calibration errors of the receiving channels. In this case, calibration errors are understood to mean any types of errors that occur during the setup and operation of the receiving channels, recalculated to the input of the channel antennas and leading to differences in the true and stored in the matrices of the limitations of the samples of the values of the radiation patterns of the sum, difference and compensation channels.

The proposed method is characterized by a strong interconnection of operations implemented in the compensation of interference and actually monopulse direction finding, and has the following features allowing to achieve this goal.

Since the vectors of the weighting coefficients of the total and difference channels are formed taking into account the stored matrix of constraints, the elements of which satisfy the systems of equations

,

,

и компенсационных каналов

в точках ограничений и ошибки калибровки указанных уровней

,

удовлетворяют соотношениямradiation pattern levels of the total (j = 1), differential (j = 2, 3)

and compensation channels

at the points of limitations and calibration errors of the indicated levels

,

satisfy the relations

и

,

and

,

and the location of the constraint points is selected from the condition of the minimum of the mean square error of the estimate of the angular coordinates of the direction finding signal in a given spatial region

,

,

Where

- средний квадрат ошибки в заданной пространственно-энергетической ситуации при усреднении по ансамблям реализаций полезного сигнала и помех;

- угол между векторами (

,

) оценки и истинным (α₀, β₀) значением пространственных координат пеленгуемого сигнала в заданной пространственно-энергетической ситуации и реализациях сигнала и помех; W_c(α₀, β₀, Р₀), W_п(α_п, β_п, P_п) - законы распределения пространственно-энергетических параметров полезного сигнала и помех соответственно, исключается существенное изменение амплитудно-фазовых соотношений между мгновенными значениями напряжений полезного сигнала на выходах суммарного и разностных каналов при реализации компенсации помех при приходе полезного сигнала с угловых направлений, соответствующих точкам ограничений и близких к ним [Монзинго Р.А., Миллер Т.У. Адаптивные антенные решетки. М.: Радио и связь, 1986, стр.123; Фрост. Алгоритм линейно-ограниченной обработки сигналов в адаптивной решетке. ТИИЭР, т.60, №8, 1972, стр.5-16]. Отметим, что величина

включает в себя как смещение оценки, обусловленное искажениями результирующих диаграмм направленности суммарного и разностных каналов, так и флуктуационную составляющую, обусловленную взаимодействием и случайным характером полезного сигнала, помех и внутренних шумов в приемных каналах пеленгатора.- the mean square error of the estimation of the angular coordinates of the direction-finding signal when averaging over a variety of spatio-energy situations and ensembles of realizations of the useful signal and interference;

- the average square of the error in a given spatio-energy situation when averaging over ensembles of realizations of the useful signal and interference;

is the angle between the vectors (

,

) estimates and the true (α ₀ , β ₀ ) value of the spatial coordinates of the direction-finding signal in a given spatial-energy situation and the implementation of the signal and interference; W _c (α ₀ , β ₀ , P ₀ ), W _p (α _p , β _p , P _p ) are the distribution laws of the spatial and energy parameters of the useful signal and interference, respectively, a significant change in the amplitude-phase relations between the instantaneous values of the useful voltages is excluded the signal at the outputs of the total and difference channels in the implementation of compensation for interference upon arrival of a useful signal from angular directions corresponding to the points of limitations and close to them [Monzingo R.A., Miller T.U. Adaptive antenna arrays. M .: Radio and communications, 1986, p. 123; Frost Algorithm of linearly-limited signal processing in the adaptive lattice. TIIER, vol. 60, No. 8, 1972, pp. 5-16]. Note that the quantity

It includes both the estimation bias due to distortions in the resulting radiation patterns of the sum and difference channels, and the fluctuation component due to the interaction and random nature of the useful signal, noise, and internal noise in the receiving channels of the direction finder.

We show the need for regularization and selection of estimates of the angular coordinates based on the minimum of Δ _i in the presence of calibration errors of the receiving channels.

If there are no calibration errors, the conditions are fulfilled (to simplify the recording, it is accepted that the current direction of observation is α _s = β _s = 0)

,

и

,

,

and

,

where F _j (α _i , β _i ) = (F _пj (α _i , β _i ), Fк ₁ (α _i , β _i ), ..., Fк _Q (α _i , β _i )) ^T ; (α _i , β _i ) - angular directions of arrival of interference; m = 1, 2, ..., M are the numbers of interference sources; (α ₀ , β ₀ ) is the angular direction of arrival of the useful signal.

, где F_искj(α_m,β_m)=F_j(α_m,β_m)+ΔF_j(α_m,β_m) - искаженный вектор амплитудно-фазового распределения;If there are calibration errors for m = 1, 2, ..., M interference (not protected by restrictions) directions, the conditions are satisfied

where F _{claim j} (α _m , β _m ) = F _j (α _m , β _m ) + ΔF _j (α _m , β _m ) is the distorted amplitude-phase distribution vector;

,

- ошибки калибровки j-го суммарного или разностных и q-го компенсационного каналов соответственно.ΔF _j (α _im , β _m ) = (ΔF _пj (α _m , β _m ), ΔFк ₁ (α _m , β _m ), ..., ΔFк _Q (α _m , β _m )) ^T is the vector of calibration errors for j channel

,

- calibration errors of the jth total or difference and qth compensation channels, respectively.

In the direction (α ₀ , β ₀ ) we represent the vector ΔF _j (α ₀ , β ₀ ) in the form

- составляющая, коллинеарная неискаженному вектору амплитудно-фазового распределения; χ(w_j) - коэффициент пропорциональности; ΔF_xj(α₀, β₀) - дополнительная составляющая.Where

- component collinear to the undistorted vector of the amplitude-phase distribution; χ (w _j ) is the coefficient of proportionality; ΔF _xj (α ₀ , β ₀ ) is an additional component.

The power of the useful signal at the output of the j-th total or differential channel:

достигается при χ(w)→-1 и

. Физически это соответствует такому представлению вектора искажений, что

Regardless of the sign of the second term in (2) global minimum (P → _O 0) of the output power when both of the limit conditions

is achieved when χ (w) → -1 and

. Physically, this corresponds to such a representation of the distortion vector that

Thus, in the presence of calibration errors and the arrival of a useful signal from the direction of limitation or close to it, a fictitious noise source arises, the physical compensation of which occurs by setting the “zeros” of the resulting diagrams of the total and difference channels, taking into account calibration errors in the direction of arrival of the useful signal when the restrictions are met relatively undistorted diagrams of the total and difference channels.

до определенного значения

имеет место стабилизация значения результирующей (компенсированной) диаграммы направленности в направлении на полезный сигнал при сохранении эффективного подавления помех. При дальнейшем возрастании

эффективность подавления помех снижается [Абрамович Ю.И., Качур В.Г. Методы защиты отличающегося от опорного полезного сигнала в адаптивных процедурах с неклассифицированной обучающей выборкой. Радиотехника и электроника, том 35, №6, 1990, стр.1235-1242]. Исходя из этой закономерности, в моноимпульсных измерителях должна существовать область стабильных оценок угловых координат пеленгуемого сигнала, близких к случаю измерений в беспомеховой обстановке и при отсутствии компенсации помех.When carrying out regularization of a linearly bounded filter with increasing parameter

to a certain value

there is a stabilization of the value of the resulting (compensated) radiation pattern in the direction of the useful signal while maintaining effective interference suppression. With further increase

interference suppression efficiency is reduced [Abramovich Yu.I., Kachur V.G. Protection methods that differ from the reference useful signal in adaptive procedures with an unclassified training set. Radio Engineering and Electronics, Volume 35, No. 6, 1990, pp. 1235-1242]. Based on this regularity, in monopulse meters, there should be a region of stable estimates of the angular coordinates of the direction-finding signal, close to the case of measurements in an interference-free environment and in the absence of interference compensation.

каждая располагались симметрично относительно плоскостей пеленгации по краям основной антенной системы, М=1 источник помех с эквивалентным отношением сигнал/внутренний шум

, где

- мощность внутренних шумов приемных каналов, для случая воздействия по максимуму главного лепестка суммарного канала, находился на угловом направлении, соответствующем максимуму первого бокового лепестка суммарного канала, направление прихода полезного сигнала соответствовало направлению наблюдения (центру пеленгационной характеристики), нормированное к ширине главного лепестка суммарного канала отклонение ограничений от направления наблюдения принималось равным ν=0,14. Исследовались зависимости суммы квадратов весовых коэффициентов

и коэффициента направленного действия суммарного канала по мощности в направлении полезного сигнала

(фиг.2), коэффициента компенсации помехи в суммарном канале К_п (фиг.3), оценок азимута

и угла места

(фиг.4) и величины

(фиг.5) от параметра регуляризации

, j=1, 2, 3. Независимые ошибки калибровки суммарного и разностных каналов формировались как ошибки множителя синфазной решетки при независимых нормально распределенных амплитудных и фазовых ошибках каждого элемента решетки со среднеквадратическими отклонениями σ_φ=15° и σ_А=15% соответственно. Независимые ошибки калибровки компенсационных каналов соответствовали ошибкам в синфазной решетке при аналогичных суммарному и разностным каналам ошибкам элементов. Результаты вычислительного эксперимента приведены для двух (1, 2) реализаций ошибок калибровки. Нанесенные на рисунке величины (

,

) и (

,

) представляют собой оценки угловых координат моноимпульсным пеленгатором в присутствии ошибок калибровки суммарного и разностных каналов в двух реализациях при отсутствии внешних помех и отключенной пространственной компенсации. При

полезный сигнал практически полностью подавляется (G→0), что подтверждает существенное влияние ошибок калибровки на амплитудные и фазовые соотношения напряжений полезного сигнала на выходе суммарного и разностных каналов при проведении пространственной компенсации помех.The presence of this pattern was confirmed during the computational experiment. The implementation of the method using a monopulse main antenna system, based on a square antenna array of 21 × 21 elements with an inter-element distance λ / 2, where λ is the wavelength, Q = 8 compensation antennas with square apertures of size

each were located symmetrically with respect to direction finding planes along the edges of the main antenna system, M = 1 interference source with an equivalent signal / internal noise ratio

where

- the power of the internal noise of the receiving channels, for the case of exposure to the maximum of the main lobe of the total channel, was in the angular direction corresponding to the maximum of the first side lobe of the total channel, the direction of arrival of the useful signal corresponded to the direction of observation (the center of the direction-finding characteristic) normalized to the width of the main lobe of the total channel the deviation of the restrictions from the direction of observation was taken equal to ν = 0.14. The dependences of the sum of squared weights were studied.

and the directional coefficient of the total channel power in the direction of the useful signal

(Fig.2), the interference compensation coefficient in the total channel K _p (Fig.3), azimuth estimates

and elevation

(figure 4) and values

(Fig. 5) from the regularization parameter

, j = 1, 2, 3. Independent calibration errors of the total and difference channels were formed as errors of the common-mode grating multiplier for independent normally distributed amplitude and phase errors of each grating element with standard deviations σ _φ = 15 ° and σ _A = 15%, respectively. Independent calibration errors of the compensation channels corresponded to errors in the in-phase grating with element errors similar to the total and difference channels. The results of a computational experiment are presented for two (1, 2) implementations of calibration errors. The values plotted in the figure (

,

) and (

,

) are estimates of the angular coordinates by a single-pulse direction finder in the presence of calibration errors of the total and difference channels in two implementations in the absence of external interference and spatial compensation disabled. At

the useful signal is almost completely suppressed (G → 0), which confirms the significant influence of calibration errors on the amplitude and phase ratios of the voltage of the useful signal at the output of the sum and difference channels during spatial interference compensation.

Based on the above regularities, a criterion of the form can be used to calculate the regularization parameter for a single-pulse amplitude total-difference direction finding

at

- значения аргумента, соответствующие минимумам функции

;

- верхнее (при поиске минимума) значение максимальной суммы квадратов модулей весовых коэффициентов;

- максимальное значение параметра регуляризации, определяемое ожидаемой максимальной мощностью полезного сигнала и величиной ошибок калибровки. Дополнительные условия (4), (5) соответствуют отсечению локальных минимумов

при малых и больших значениях параметра регуляризации соответственно.Where

- argument values corresponding to function minima

;

- the upper (when searching for the minimum) value of the maximum sum of squares of the modules of weight coefficients;

- the maximum value of the regularization parameter, determined by the expected maximum power of the useful signal and the magnitude of the calibration errors. Additional conditions (4), (5) correspond to cutting off local minima

for small and large values of the regularization parameter, respectively.

,

критерий (3) может быть заменен наWith a sufficiently small (Δ _µ = 2 ... 3) step of changing the regularization parameter in a multi-channel scheme

,

criterion (3) can be replaced by

- значения аргумента, соответствующие минимумам величины

;under additional conditions corresponding to (4), (5), where

are the values of the argument corresponding to the minima of the quantity

;

,

- оценки азимута и угла места, определяемые для соответствующих значений

.

,

- azimuth and elevation estimates determined for the corresponding values

.

пороговому значению, не превышая его. В качестве

может быть выбрано верхнее значение суммы квадратов весовых коэффициентов для наиболее сложных ситуаций, характеризующихся равенством числа степеней свободы системы компенсации и числа воздействующих помех.In the absence of a minimum in (3), for example, with small distortions in certain directions or the influence of noise, as estimates of the angular coordinates, we take the values corresponding to the value of the regularization parameter, at which the sum of the squared modules of the weight coefficients is closest to the lower

threshold value, not exceeding it. As

the upper value of the sum of the squares of the weighting coefficients can be selected for the most difficult situations, characterized by the equality of the number of degrees of freedom of the compensation system and the number of interfering interference.

The optimal values of the upper and lower threshold levels can be found empirically or using mathematical modeling on a variety of predicted signal-noise situations.

Define the remaining parameters of the method.

Given the fact that the introduction of restrictions leads to a decrease in the number of degrees of freedom of the compensation system from Q + 1 to Q + 1-R, a rational number of restrictions should be minimal and may be R = 4, 5. A larger number of restrictions (R = 7, 9 etc.) can be used with increased requirements for measurement accuracy, taking into account the hardware capabilities of the device. The symmetric arrangement of restrictions with respect to direction finding planes and the peculiarities of their location when they are even or odd are determined by the need to ensure symmetry of the direction finding characteristic of the meter.

по результатам математического моделирования могут быть выбраны Δ_µ=2…3 и

, где α_иск - среднеквадратическая величина нормированной ошибки калибровки каналов; P_max - ожидаемая максимальная мощность полезного сигнала.The step of changing the regularization parameter Δ _µ and the maximum value of the regularization parameter

according to the results of mathematical modeling can be selected Δ _µ = 2 ... 3 and

where α _lawsuit is the root mean square value of the normalized calibration error of the channels; P _max - the expected maximum power of the desired signal.

от параметра

, где ϑ_α, ϑ_β - ширины диаграммы направленности суммарного канала по азимуту и углу места соответственно;

, для различных значений ошибок калибровки, определяемых среднеквадратическими амплитудными σ_A и фазовыми σ_φ ошибками в элементах решетки, при наличии М=1 и М=3 источников помех. Результаты приведены для реализации способа с использованием моноимпульсной основной антенной системы на базе квадратной антенной решетки из 21×21 элементов с межэлементным расстоянием λ/2, где λ - длина волны, и Q=8 компенсационных антенн с квадратными апертурами размером

каждая, расположенными симметрично относительно плоскостей пеленгации по краям основной антенной системы, нормировка при вычислении пеленга - мгновенная. Отношения полезный сигнал/шум и помеха/шум при их приеме полезного сигнала и помех по максимуму диаграммы направленности принимались равными

;

. Направление прихода полезного сигнала считалось распределенным равновероятно в пределах полуширины диаграммы направленности суммарного канала по азимуту и углу места, направление прихода помех - в пределах ±(1…5) от ширины диаграммы направленности суммарного канала. Ковариационная матрица помех формировалась с учетом полезного (пеленгуемого) сигнала (неклассифицированная выборка). Шаг изменения параметра регуляризации принимался равным Δ_µ=2, число ограничений R=5. Верхнее и нижнее пороговые значения суммы квадратов модулей весовых коэффициентов принимались равными

и

.Let us illustrate the gain of the proposed method for adaptive spatial interference compensation with monopulse amplitude total-difference direction finding and the presence of calibration errors of receiving channels for direction finding accuracy in comparison with the prototype, as well as monopulse amplitude total-direction finding without spatial interference compensation. Figure 6 shows the results of calculations normalized to the width of the main lobe of the total channel of the root mean square value of the error of direction finding

from parameter

, where ϑ _α , ϑ _β are the beam widths of the total channel in azimuth and elevation, respectively;

, for various values of calibration errors determined by the root mean square amplitude σ _A and phase σ _φ errors in the grating elements, in the presence of M = 1 and M = 3 sources of interference. The results are presented for implementing the method using a monopulse main antenna system based on a square antenna array of 21 × 21 elements with an inter-element distance λ / 2, where λ is the wavelength, and Q = 8 compensation antennas with square apertures of size

each, located symmetrically with respect to the direction finding planes at the edges of the main antenna system, normalization when calculating the bearing is instantaneous. The ratios of the useful signal / noise and interference / noise when they receive the useful signal and noise along the maximum radiation pattern were taken equal

;

. The direction of arrival of the useful signal was considered distributed equally within the half-width of the directivity pattern of the total channel in azimuth and elevation, the direction of arrival of interference within ± (1 ... 5) of the width of the directivity pattern of the total channel. The covariance interference matrix was formed taking into account the useful (direction-finding) signal (unclassified sample). The step of changing the regularization parameter was taken equal to Δ _µ = 2, the number of restrictions R = 5. The upper and lower threshold values of the sum of the squared modules of the weighting coefficients were taken equal

and

.

As follows from the calculation results, the optimal location of the constraints corresponds to ν = 0.1 ... 0.15, and in the given spatial-energy situations, the method of monopulse amplitude total-difference direction finding without spatial interference compensation is completely inoperative, that is, errors in determining coordinates can significantly exceed the width of the radiation pattern in each of the direction finding planes, and the prototype is inoperative with an unclassified sample. With a classified sample for the prototype, the normalized mean square displacements of the estimates of the angular coordinates in typical signal-noise situations are 5 ... 10 times higher than the corresponding values for the proposed method.

в виде геометрической прогрессии со знаменателем Δ_µ=2…3 и начальным значением, равным уровню собственных шумов приемных каналов пеленгатора, формируют наборы векторов весовых коэффициентов суммарного и разностных каналов с учетом ограничений на форму их результирующей диаграммы направленности и различных значений единого для всех каналов параметра регуляризации ковариационных матриц помех, вычисляют сумму квадратов модулей весовых коэффициентов суммарного и разностных каналов для каждого из значений параметра регуляризации, вычисляют выходные сигналы суммарного и разностных каналов и осуществляют оценки угловых координат источника полезного сигнала для всех значений векторов весовых коэффициентов суммарного и разностных каналов при различных значениях параметра регуляризации, рассчитывают значения квадратов углового расстояния между оценками угловых координат для соседних значений параметра регуляризации и определяют значения оценок угловых координат, соответствующих первому минимуму квадрата углового расстояния между оценками угловых координат для соседних значений параметра регуляризации при условии непревышения суммы квадратов модулей весовых коэффициентов верхнего порогового значения, а при отсутствии указанного минимума в качестве оценок угловых координат принимают значения, соответствующие значению параметра регуляризации, при котором сумма квадратов модулей весовых коэффициентов наиболее близка к нижнему пороговому значению, не превышая его.The proposed method is new, because from publicly available information the method of adaptive spatial interference compensation is not known for monopulse amplitude total-difference direction finding and the presence of calibration errors of the receiving channels, which consists in receiving signals by the main antenna system with the total difference in azimuth, difference in elevation channels, antennas q = 1, 2, ..., Q compensation channels, consistent processing of the signals of each channel using Q + 3 identical receive channels, analog-to-digital transforming the signals of each receiving channel and processing the digitized signals of each receiving channel by calculating the vectors of weight coefficients of the total and differential channels and weighted summation of the signals of the total and compensation, difference in azimuth and compensation, difference in elevation and compensation channels, characterized in that they additionally carry out preliminary formation of matrices of restrictions on the shape of the resulting radiation pattern of the total, difference in azimuth and p channel-dependent difference in the elevation angle for all possible directions of observation in the form of readings of the values of the radiation patterns of the total, difference in azimuth, difference in elevation and compensation channels at r = 1, 2, ..., R restriction points, and the location of the restriction points is chosen based on the minimum the root-mean-square error of the estimation of the angular coordinates of the direction-finding signal for the expected distributions of the values of the angular coordinates of the directions of arrival and the strengths of the direction-finding signal and interference, remember the matrix matrices eny device memory constraints matrices, and to eliminate the influence of the calibration error form i = 1, 2, ..., I values of the regularization parameter

in the form of a geometric progression with the denominator Δ _µ = 2 ... 3 and the initial value equal to the level of the intrinsic noise of the receiving channels of the direction finder, form sets of vectors of weight coefficients of the total and difference channels, taking into account restrictions on the shape of their resulting radiation pattern and different values of a parameter common to all channels the regularization of the covariance interference matrices, calculate the sum of the squared modules of the weight coefficients of the total and difference channels for each of the values of the regularization parameter, output signals of the total and difference channels and estimate the angular coordinates of the source of the useful signal for all values of the vectors of the weight coefficients of the total and difference channels for various values of the regularization parameter, calculate the squares of the angular distance between the estimates of the angular coordinates for adjacent values of the regularization parameter and determine the values of the estimates of the angular coordinates corresponding to the first minimum of the square of the angular distance between the estimates of the angular coordinates for neighboring values of the regularization parameter provided that the sum of the squared modules of the weight coefficients of the upper threshold values does not exceed, and in the absence of the indicated minimum, the values corresponding to the value of the regularization parameter at which the sum of the squared modules of the weight coefficients are closest to the lower threshold value are not exceeded, not exceeding him.

The proposed technical solutions have an inventive step, since it does not explicitly follow from the published scientific data and the known technical solutions that the claimed sequence of operations is the preliminary generation and storage of restriction matrices, the reception of signals by the main antenna with total and difference channels and compensation antennas, consistent signal processing in identical receiving channels, analog-to-digital signal conversion, the formation of the values of the regularization parameter and vector weighting coefficients of the total and difference channels, taking into account the constraint matrices and for various values of the regularization parameter, weighted summation of the signals of the total, difference and compensation channels, calculating the sum of the squared modules of the weighting coefficients of the total and difference channels for each of the values of the regularization parameter, calculating the output signals of the total and difference channels and estimates of the angular coordinates of the source of the useful signal for all values of the vectors of the weight coefficients of the total and difference channels for different values of the regularization parameter, calculating the squares of the angular distance between the estimates of the angular coordinates for adjacent values of the regularization parameter and determining the values of the estimates of the angular coordinates corresponding to the first minimum of the square of the angular distances between the estimates of the angular coordinates for adjacent values of the regularization parameter, provided that the sum of the squares of the modules does not exceed weighting factors of the upper threshold value, and in the absence of the specified minimum adoption in as estimates of the angular coordinates of the values corresponding to the regularization parameter, at which the sum of the squared modules of the weighting coefficients is closest to the lower threshold value, but does not exceed it, it provides stabilization of parameters (position of the zeros of the difference diagrams and the slope value) of the direction finding characteristic of the meter in the presence of receiving calibration errors channels and achieving compensation acting on the side lobes of the radiation pattern of the total and differential interference channels.

The proposed technical solutions are practically applicable, since antenna devices, demodulators, analog-to-digital converters, read-only memory modules and digital signal processors can be used for their implementation. The presented requirements for the accuracy of the calibration of the direction finder channels, in which the proposed method of spatial interference compensation will be workable, are characterized by relative calibration errors of the order of 1 ... 2 decibels in amplitude and absolute errors of the order of several tens of degrees in phase and are typical requirements for serial direction finding equipment.

The technical and economic efficiency of the proposed method consists in increasing the direction finding accuracy by compensating the total and difference channels of the direction finder interference acting on the side lobes and by preserving the positions of zeros and steepness of direction finding characteristics in the presence of calibration errors in the receiving channels.

Claims (1)

The method of adaptive spatial interference compensation during monopulse amplitude total-differential direction finding and the presence of calibration errors in the receiving paths, which consists in receiving signals from the current direction of observation using an antenna system with a total (with number j = 1), difference in azimuth (with number j = 2 ), difference in elevation (with number j = 3) channels and antennas q = 1, 2, ..., Q compensation channels, consistent processing of signals of each channel using Q + 3 identical receive channels, analog-to-digital conversion using the signals of each receiving channel and processing the digitized signals of each channel by calculating the vectors of weight coefficients of the total, difference in azimuth and difference in elevation of channels and weighted summation of the signals of total and compensation, difference in azimuth and compensation and difference in elevation and compensation channels, different the fact that to calculate the vectors of weighting coefficients pre-form matrices of restrictions on the shape of the resulting radiation pattern total, difference in azimuth and difference in elevation of channels for all possible directions of observation in the form of readings of the values of radiation patterns of total, difference in azimuth, difference in elevation and compensation channels at r = 1, 2, ..., R constraint points, and at an odd number of restriction points, one of them is located in a given direction of observation, and the remaining limit points are located symmetrically relative to it and direction finding planes, with an even number of limit points of their position symmetrically with respect to the direction of observation and direction-finding planes, the deviations of the restriction points from the direction of observation are selected based on the minimum root mean square error of the estimate of the angular coordinates of the direction-finding signal for the expected distributions of the angular coordinates of the directions of arrival and the strengths of the direction-finding signal and interference, the restriction matrices are stored in the device , when processing the digitized signals of each channel, the covariance matrices of the total in azimuth, difference in elevation and compensation channels, the values of the restriction matrices of the sum, difference in azimuth and difference in elevation of the channels for the current direction of observation are read from the memory of the restriction matrix, and i = 1, 2, ..., I values of the regularization parameter

in the form of a geometric progression with the denominator Δ _µ = 2 ... 3 and the initial value equal to the level of the noise floor of the receiving channels, form the values of the vectors of the weight coefficients of the total, difference in azimuth and difference in the elevation angle of the channels corresponding to each regularization parameter taking into account the restriction matrices in accordance with expression

where Ф _j - covariance matrix of received signals for the j-th channel; I is the unit diagonal matrix;

- the current value of the regularization parameter;

- matrix of constraints for the j-th channel;

is the constraint column vector for the j-th channel, formed from the values of the first row of the matrix C _j ;

- counts of the values of the radiation patterns of the j-th total or difference and q-th compensation channels at the constraint points; "+" Is the sign of the Hermitian pairing, the sum of the squared modules of the weight coefficients of the total, difference in azimuth and difference in elevation channels for each of the values of the regularization parameter is calculated, weighted summation of the signals of total and compensation, difference in azimuth and compensation and difference in elevation is carried out and compensation channels and calculate the estimates of the angular coordinates of the source of the useful signal for all values of the vectors of the weighting coefficients for various values of the regular parameter nations, calculate the values of the squares of the angular distance between the estimates of the angular coordinates for adjacent values of the regularization parameter, determine the values of the estimates of the angular coordinates corresponding to the first in the order of increasing the regularization parameter minimum of the square of the angular coordinates between the estimates of the angular coordinates, provided that the sum of the squared modules of the weight coefficients of the upper threshold value does not exceed and in the absence of the specified minimum as estimates of the angular coordinates take values corresponding to which correspond to the value of the regularization parameter, at which the sum of the squared moduli of the weight coefficients is closest to the lower threshold value, not exceeding it.

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