The way multi-channel detection and estimation of the number of radiation sources with adaptive equalization capacity of noise in the channels

 

The invention relates to electrical engineering and can be used in multi-channel RDF, radar, sonar and other systems, passive and active location, using the receiving antenna arrays and methods for multi-channel spatial-temporal signal processing, and systems spatially dispersed and polarization-diversity reception. Achievable technical result is to increase the accuracy of determining the number of spatially-correlated radiation sources and the reliability of detection for eigenvalues of sample correlation matrices of the signals from the outputs of the N sensors of the antenna array when the noise in the channels have different power due to the fact that before you perform the procedure multichannel detection and estimation of the number of spatially-correlated sources of radiation procedure adaptive equalization capacity of noise in the channels, the above procedure is performed as an iterative search procedure of maximizing the minimum eigenvalues of the sample correlation matrix with constraints in the form of equality on the trail of a sample correlation mA is goonline RDF, radar, sonar and other systems, passive and active location, using the receiving antenna arrays and methods for multi-channel spatial-temporal signal processing, and systems spatially dispersed and polarization-diversity reception.

There is a method of multichannel detection and estimation of the number of spatially-correlated radiation sources [1] , is selected as the closest analogue in which the signals are spatially correlated sources take the N sensors of the antenna array, where N is the given number of sensors of the antenna array, compute the sample correlation matrix of the above-mentioned signals, calculate eigenvaluesnthe sample correlation matrix, ordered referred eigenvaluesnin descending order, compare them with the threshold values before comparison with the threshold values of the M first mentioned eigenvaluesnwhere M= N-1, N-2, ...up to N-M=1, subtract the appropriate assessment of noise componentsmentioned eigenvaluesnthresholds for M first mentioned eigenvaluesnobtained by multiplying the normalized thresholds on the average noise power in the channel, which is calculated as the average value extraprise functions for all N mentioned eigenvaluesnif all thresholds are exceeded obtained valuesyou decide that the number of detected spatial-correlated radiation sources is equal to M, if the threshold is not exceeded when M = 1, then decide about the lack of spatially-correlated radiation sources.

The disadvantage of multi-channel detection and estimation of the number of spatially-correlated radiation sources [1] is the lack of accuracy of determining the number of radiation sources M and the lack of detection in cases where the noise in the different channels have different power.

To improve the accuracy of determining the number of spatially-correlated radiation sources and the reliability of detection when the noise in the channels have different power the sources of radiation with adaptive equalization capacity of noise in the channels. Its essence consists in the following: 1. Receive signals from the N sensors of the antenna array (Fig. 1) memorize the signals from the sensors of the antenna array in the storage device, multiply the signals from the outputs of the storage device on the weighting coefficients, calculate the sample correlation matrix (ACM), compute the minimum eigenvalueN(j,w1,w2,...,wN) MCV:where RXX(j) - complex VKM;- complex vector of signals with N sensors of the antenna array;Tsign transpose;+sign Hermitian pairing; xn(k) is a complex signal output from the n-th sensor antenna array, which is remembered in the storage device;+- a complex Hermitian-conjugate vector of the signals from the sensors of the antenna array;is a complex diagonal matrix of weight coefficients;
wn(j) - weighting factor for a signal with the n-th sensor array weights wn(j) are real, positive numbers wn(j)>0);
k is the number of temporal reference frame (k =1,...,K);
To - size sampling signals from the and;
j is the number of steps of iterative procedure adaptive equalization capacity of noise in the channels;
J is the number of the last step of the iterative procedure of the adaptive equalization capacity of noise in the channels.

2. In the first step, j=1 iterative procedure adaptive equalization capacity of noise in the channel weights wn(j) assigns a single value of wn(1)=1, calculate MCV RXX(1) calculate the trace of VKM trRXX(l) and the minimum eigenvalue VKMN(1,w1,w2,...,wNwhere

rnn(1) values of the diagonal elements VKM RXX(1) in the first step.

3. Solve the problem of optimization of the weights [w1,w2,...,wN] on the criteria of maximum minimum Sz VKM limitation in the form of equality on the trail VKM:
N(j,w1,w2,...,wN) _Max, j = 1,...J, (3)
w12(j)r11(1)+w22(j)r22(1)+...+wN2(j)rNN(1)=
=trRxx(1). 4)
4. For the found values of the weights [w1,w2,...,wN] obtained on the last J-th step of the procedure adaptive equalization capacity somigliana.

5. M NW first ACM served on subtractive device (N-M) last NW VKM served on the device extrapolation (Fig. 2) and to provide estimates of "noise" componentsnfor M NW first. On extraprise functions calculate an average noise power in the channel
6. Multiply the normalized values of the threshold on the received average power of noise in the channelssubtract from the first M Sznappropriate assessment "noise" componentsand compare the obtained values ofwith thresholds (Fig. 2).

7. Multichannel detection and estimation of the number of radiation sources is carried out in a step-by-step procedures. In the first step extrapolation doing one last noise Sz when M=N-1. If all thresholds are exceeded, then decide that the number of sources is equal to M, and the procedure of assessment done. If the thresholds for the first Sz M not exceeded, then the extrapolation procedure performed on the last two noise Sz when M=N-2, and so on until M= 1. If the threshold is not exceeded when M=1, then a decision is made about the absence of radiation sources.

FA number of radiation sources with adaptive equalization capacity of noise in the channels, shown in Fig.1. The signals of the radiation source 1 (Fig.1) are N sensors of the antenna array 2, with outputs of the sensors of the antenna array signals are sent to respective N inputs of the storage device 3, the stored signals from the outputs of the storage device 3 are fed to the inputs of the multipliers 4, on the other inputs of the multipliers are served weights to outputs of the device computing the weights 6, the inputs of the device computing the weights 6 do N values of the diagonal elements and the minimum eigenvalue of the output device for calculating MCV and NW VKM 5, the inputs of the computing device VKM and NW VKM 5 receive weighted signals from the outputs of the multipliers 4, sorted in descending order N NW VKM outputs of the computing device VKM and NW VKM 5 arrive at the inputs of the device detection and estimation of the number of AI 7, and the result of the detection-estimation output device detection and estimation of the number of AI 8.

Functional diagram of the device detection and estimation of the number of AI 7 shown in Fig.2. On input device detection and estimation of the number of AI (Fig. 2) are sorted in descending order N NW VKM outputs of the computing device VKM and NW of Voxtropolis 2, (N-M) estimates of "noise" components of Sz with the respective outputs of the device extrapolation 2 served on other inputs subtractive device 1 and the signal output from extrapolator with the measured value of the average noise power in the channel 4 is input to the comparator with threshold 3, on the other M inputs of the comparator with threshold 3 signals from outputs of subtractive device 1, and the result of the detection-estimation output device detection and estimation of the number of AI 5.

The storage device 3 (Fig.1) provides recording and storing complex vectors of signalswith N sensors of the antenna array 2 (Fig.1) taken from sources of radiation 1.

Multipliers 4 (Fig.1) multiply each of the N memorized signals xn(k) the corresponding weighting factor wn(j), j=l,...,J, forming the signals wn(j) x xn(k), which calculates VKM received signals. When using vector-matrix notation the procedure of multiplication is realized in the form of a worka complex vector signalswith N sensors of the antenna array on a complex diagonal matrix of weights W(j).

< The NW VKM in descending order. For vector-matrix notation, the calculation of MCV perform in accordance with formula (1). Calculation NW VKM carried out in two stages in accordance with well-known approach [2] . At the first stage coerce the original MCV to a tridiagonal matrix mean by orthogonal sequence-similar transformations using matrices reflection of householder [2, S. 115]. In the second stage, using the well-known QR-algorithm, which is based on QR decomposition of the matrix, tridiagonal matrix, the matrix is reduced to a diagonal form [2, C. 156]. The values of the diagonal elements of the matrix are desired Sz VKM. The obtained values of Sz VKM are ordered in descending order.

Unit weight calculation 6 (Fig. 1) performs the optimization of the values of weight coefficients [w1,w2,...,wN] on the criteria of maximum minimum Sz VKM (3) when the constraint as equality on the trail VKM (4). The expression (4) can be transformed to mind

where

- the option that preserves the trace VKM when changing the weighting factor wm(j). From (5), (6) shows that the weighting factor wm(j) adopts the m of descent by alternately search for maxima in the interval (7) for each of the weighting coefficients wm(j) with a simultaneous change in the other weighting coefficients in accordance with (5), (6). As the initial values of the weighting coefficients used a single value of wm(j)=1. The search for the maximum of the objective function (3) is carried out using the method of the Golden section [3, S. 54]. Iterative search procedure ends on the last J-th step.

For the found values of the weights [w1,w2,...,wN] obtained on the last J-th step of the procedure adaptive equalization capacity of noise in the channels, compute the sample correlation matrix (1), compute Sz VKM Marshal NW VKM in descending order. Calculation of MCV and NW VKM is executed in the computing device VKM and NW ACM 5 (Fig.1). The obtained values of Sz VKM1,2,...,M,M+1,...,Nserved on the appropriate input device detection and estimation of the number of AI 7 (Fig.1).

Functional diagram of the device detection and estimation of the number of AI shown in Fig. 2.

Subtractive device 1 (Fig.2) perform the subtraction of the M first Sznmg_data/59/598493.gif">expect the device extrapolation 2 (Fig. 2) by extrapolation (N-M) the last-mentioned eigenvaluesn. The extrapolation is performed using exponential functions of the form


the q - parameter, which is calculated from the condition of minimization of mean square error

After finding the value of q is calculated "noise" components for M NW first by the formula (8) for n = 1,...,M

Obtained at the output of subtractive device 1 (Fig. 2) the values ofserved on the inputs of the comparator with threshold 3 (Fig. 2). Thresholds for M the first eigenvalues are obtained by multiplying the normalized thresholds on the average power of noise in the channels. The average noise power in the channel 4 (Fig. 2) calculated as the average value extraprise functions for all N eigenvalues

The normalized threshold values are calculated for a unit average power of noise in the channels. For calculation use a multivariate normal distribution function Sz VKM:

M598501.gif">- average fluctuational component;
n- dispersion fluctuational component.

Average values and dispersion fluctuation components calculated by means of simulation algorithm that implements the method [1]. Modeling performed by noise implementations without signals of radiation sources. The study is carried out for a given number of sensors of the antenna array N and the number of time samples K. the Obtained average values and dispersion fluctuation components Sz VKM stored in a table. Threshold values for each Sz calculated on the basis of (8) from the given values of probability of false alarm.

Device detection and estimation of the number of AI 7 (Fig.1) performs the estimation of the number of radiation sources in the form of step-by-step procedures. In the first step extrapolation doing one last noise Sz when M=N-1. If all thresholds are exceeded, then decide that the number of sources is equal to M and the procedure of assessment done. If the thresholds for the first Sz M not exceeded, then the extrapolation procedure performed on the last two noise Sz when M=N-2, and so on until M=1. If the threshold is not exceeded when M=1, then minimalisation-correlated radiation sources in multichannel detector with adaptive equalization capacity of noise in the channels increases the accuracy of determining the number of radiation sources and increases the reliability of detection in cases when the noise in the different channels have different power.

Sources of information
1. EN 2172962 C1, 20.03.2000.

2. Parlett B. Symmetric problem of eigenvalues. Numerical methods/ Lane. from English. - M.: Mir, 1983. - 384 S.

3. Rekleitis,, Ravindran A., Ragsdell K. Optimization in engineering: In 2 vol./TRANS. from English. - M.: Mir, 1986. - KN. 1.


Claims

Method for detection and estimation of the number of spatially-correlated radiation sources in multichannel detector with adaptive equalization capacity of noise in the channels, namely, that the signals spatially-correlated radiation sources take the N sensors of the antenna array, where N is the given number of sensors of the antenna array, compute the sample correlation matrix of the above-mentioned signals, calculate eigenvaluesnthe sample correlation matrix, where n= 1, . . . N, ordered referred eigenvaluesnin descending order, compare them with the threshold values before comparison with the threshold values of the M first mentioned eigenvaluesnwhere M= N - 1, N - 2, . . . to N - M= 1, vicitynthat calculated by extrapolation (N - M) the last-mentioned eigenvaluesnthresholds for M first mentioned eigenvaluesnobtained by multiplying the normalized thresholds on the average noise power in the channel, which is calculated as the average value extraprise functions for all N mentioned eigenvaluesnif all thresholds are exceeded obtained valuesyou decide that the number of detected spatial-correlated radiation sources is equal to M, if the threshold is not exceeded when M= 1, then decide about the lack of spatially-correlated radiation sources, wherein before calculating the sample correlation matrix of the signals and their valuesnthe sample correlation matrix, the signals from the outputs of the N sensors of the antenna array remember, next by multiplying each of the N stored signals xn(k) the corresponding weighting factor wn(j) when j = 1, . . . , J form C is b>n(j)xn(k) and the minimum eigenvalueN(j,w1,w2,...,wN) mentioned sample correlation matrix when k = 1 . . . , K, where k is the number of temporary reference To the size of the sample signals from the N sensors of the antenna array, j is the number of steps of iterative procedure adaptive equalization capacity of noise in the channels, J - the number of the last step of the above procedure, in the first step, j = 1 iterative procedure adaptive equalization capacity of noise in the channels all weight coefficients wn(j) assigns a single value of wn(1) = 1, compute the sample correlation matrix of the signals R(1), the minimum eigenvalueN(j,w1,w2,...,wN), the diagonal values of r11(1), r22(1), . . . rNN(1) and trace trR(1) the sample correlation matrix R(1), the subsequent steps mentioned procedure carry out the optimization of the values of weight coefficients wn(j) according to the criterion of maximum to minimum eigenvaluesN(j,w1,w2,...,wN) sample correlation matrix with constraints in the form of equality on the trail of a random correlate is 1,...J,
w12(j) r11(1) + w22(j) r22(1) + . . . + wN2(j)rNN(1) = trR(1),
and the decision about the detection of spatially-correlated radiation sources and the estimation of the number of spatially-correlated radiation sources is carried out after the completion of all steps of the iterative procedure of the adaptive equalization capacity of noise in the channels of a multichannel detector, when values of the weighting coefficients (w1, w2, . . . , wN), obtained at the last J-th step.

 

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