CN106054132B - A kind of ISM methods based on the selection of effective subband and detection statistic weighting - Google Patents
A kind of ISM methods based on the selection of effective subband and detection statistic weighting Download PDFInfo
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Abstract
The present invention provides a kind of ISM methods based on the selection of effective subband and detection statistic weighting, it is related to array signal processing field, subband azimuth spectrum vector is obtained according to the wideband data that basic matrix receives, effective subband is selected in the subband azimuth spectrum therefrom obtained, the azimuth spectrum of effective subband is weighted, each corresponding detection statistic of effective subband is taken as the power of oneself, summation is weighted to the azimuth spectrum on each subband, obtain final broadband azimuth spectrum, the present invention can reflect the size of subband signal-to-noise ratio indirectly, improve the detectability to small-signal, improve the snr gain of wide-band processing, the Broadband DOA Estimation result finally obtained is compared to traditional ISM methods, there are better angular resolution and lower context class.
Description
Technical Field
The invention relates to the field of array signal processing, in particular to a broadband target azimuth estimation method.
Background
In the field of array-based wideband object orientation estimation (DOA) technology, the Incoherent Signal-subspace method (ISM) and coherent Signal-subspace method (CSM) are two main processing Methods at present. The CSM method divides the received broadband data into each sub-band component, focuses each sub-band component on a reference sub-band by constructing a focusing matrix, and finally performs the azimuth estimation by using a narrow-band subspace algorithm, for example, the MUSIC algorithm and the ISM method divide the received data into each sub-band component, then performs the azimuth estimation on each sub-band component by using the narrow-band subspace algorithm, and finally performs the weighted average of the azimuth spectrum of each sub-band to obtain the final broadband DOA estimation. The ISM method does not need target position pre-estimation, and has the advantages of simple principle, easy implementation and the like compared with the CSM method, but has the defects of poor angular resolution and the like under the condition of low signal-to-noise ratio.
In an actual working environment, energy distribution of broadband signals received by an array on each frequency band (also called sub-band) is often uneven, and under uniform background noise, signal-to-noise ratios on each sub-band are different, so that the performance of the ISM method can be improved by selecting sub-bands with high signal-to-noise ratios to synthesize a broadband azimuth spectrum. In recent years, some ISM improvement methods are provided, a method for selecting frequency points based on maximum power is provided, only a sub-band with the maximum power is selected for processing, effective information on other frequency bands in received broadband data is lost, and further some target azimuth information may be missed. The industry proposes an improved method based on subband energy weighting, which has a certain improvement effect, but has little effect on low snr signals due to the use of used subbands including low snr subbands.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for selecting and weighting effective sub-bands to further synthesize a final broadband azimuth spectrum aiming at the defects of an ISM method in the existing broadband signal processing.
The method utilizes the sub-band azimuth spectrum to construct the detection statistic on each sub-band, selects the sub-band according to the detection statistic, calls the selected sub-band as an effective sub-band, takes the detection statistic of the effective sub-band as a weight, and finally outputs the weight to the effective sub-band to synthesize the broadband azimuth spectrum. Because the constructed detection statistics and the array output signal-to-noise ratio of the subband signals are in positive correlation, the invention can reserve the subbands with high signal-to-noise ratio as much as possible, and simultaneously abandon the subbands without signals or with low signal ratio, thereby improving the processing performance of the broadband array. Therefore, the method provided by the invention has great improvement on the condition that the performance is reduced when the ISM method is used for target resolution under low signal-to-noise ratio.
The technical scheme adopted by the invention for solving the existing problems can be divided into the following 3 steps:
step 1: obtaining sub-band azimuth spectrum vector according to wideband data received by array
For the broadband receiving data obtained by sampling the receiving matrix which is a uniform horizontal linear array with the array element number of M and the array element spacing of d, the sampling frequency is assumed to be fsThe receiver processing band range is [ f ]L,fH]With a bandwidth of [ f ]L,fH]The digital filter band-pass filters the broadband received data and then passes through discrete Fourier transformThe transformation divides the broadband received data into sub-band components, and selects the sub-band frequency falling on [ f [ ]L,fH]Taking J subband components in between as subbands to be processed, obtaining azimuth spectrum estimation of each subband component by using a Conventional Beamforming (CBF) algorithm for each subband component, uniformly scanning K directions within a range of-90 degrees to 90 degrees relative to a normal direction of a matrix by using the azimuth spectrum estimation, obtaining azimuth spectrum estimation values in the K directions to form Kx 1 subband azimuth spectrum vectors, wherein the J subbands have J azimuth spectrum vectors in total;
step 2: selecting effective sub-band from sub-band azimuth spectrum obtained in step 1
Supposing that the noise is white Gaussian noise with uniformly distributed space, recording an azimuth spectrum obtained by a CBF algorithm when only the noise exists in broadband receiving data and no signal exists as a noise azimuth spectrum, uniformly scanning K directions in a range of-90 degrees relative to a normal direction of a matrix for the noise azimuth spectrum, taking spectral values of the K directions to form a K multiplied by 1 noise azimuth spectrum vector, obtaining the noise azimuth spectrum vector by computer simulation, taking an average value for at least 1000 times as a final result, taking a cosine value of an included angle between a sub-band azimuth spectrum vector and the noise azimuth spectrum vector as a T0Constructing the detection statistic T1-T on each sub-band0Setting false alarm probability PFAObtaining a detection threshold value gamma by a Monte Carlo repeated test for at least 10000 times, selecting a sub-band with a detection statistic value larger than the detection threshold value gamma as an effective sub-band, and entering the step 3;
and step 3: weighting the azimuth spectrum of the effective sub-bands obtained by the processing in the step 2, taking the detection statistic T corresponding to each effective sub-band as the weight of the effective sub-band, and carrying out weighted summation on the azimuth spectrum on each sub-band to obtain the final broadband azimuth spectrum:
in the formula (1), g corresponds to the effective sub-bandjValue 1, non-significant subband pairThe corresponding sub-band is 0, TjAnd weighting the corresponding effective sub-band to obtain a final broadband azimuth spectrum after weighting, thereby obtaining a target azimuth estimation result.
The method has the advantages that the cosine value of the included angle between the sub-band orientation spectral vector and the noise orientation spectral vector is adopted to construct the detection statistic, the constructed detection statistic is in positive correlation with the signal-to-noise ratio on the sub-band, and the signal-to-noise ratio of the sub-band can be indirectly reflected; the constructed detection statistic and the array output signal-to-noise ratio are in positive correlation, so that the array gain is utilized, and the detection capability of weak signals is improved; selecting effective sub-bands by using the detection statistics, and abandoning noise sub-bands, thereby finally improving the signal-to-noise ratio gain of broadband processing; the weighting is carried out on each sub-band by using the value of the detection statistic on each sub-band, so that the background level of the broadband azimuth spectrum can be further reduced, and compared with the traditional ISM method, the finally obtained broadband DOA estimation result has better angular resolution and lower background level.
Drawings
FIG. 1 is a schematic diagram of a receiving array according to the present invention.
Fig. 2 is a flow chart of the steps involved in the present invention.
FIG. 3 is a diagram illustrating the effect of the present invention under single-target, uncorrelated noise.
FIG. 4 is a diagram illustrating the effect of the present invention under multiple targets and correlated noise.
Fig. 5 is a diagram illustrating the effect of different narrow-band DOA estimation algorithms according to the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
The main contents of the invention are:
and constructing detection statistics on each sub-band based on an included angle between the sub-band orientation spectrum vector and the noise orientation spectrum vector, setting a detection threshold according to the false alarm probability, and selecting the corresponding sub-band with the detection statistic value larger than the threshold value as an effective sub-band.
And selecting the corresponding detection statistic value of the effective sub-band as a weight, and carrying out weighted synthesis on the azimuth spectrum of the effective sub-band to obtain a final broadband azimuth spectrum.
The method provided by the invention is verified through computer numerical simulation, and the great improvement effect of the method provided by the invention on the traditional ISM method is proved.
The target signal is a sound wave, and the propagation speed of the sound wave under water is 1500 m/s. The number of array elements of the receiving array is 32, and the spacing between the array elements is 0.5 m. The processing bandwidth of the receiver is 50 Hz-1000 Hz. The sampling frequency is 4kHz, the time length of each sampling data segment is 1s, and 64 data segments are taken in each processing. The target signal is composed of a continuous spectrum (a wide-band gaussian signal) and a line spectrum signal. The target frequency band range is 450 Hz-650 Hz, line spectrums of 459Hz and 551Hz are contained, and the target direction is 10 degrees; the target two-frequency band range is 550 Hz-750 Hz, line spectrums of 587Hz and 703Hz are contained, and the target direction is 20 degrees. The spectral level signal-to-noise ratio is defined as In order to be the power of the signal,is the noise power.
In the implementation, the false alarm probability is set to be 0.001, and the Monte Carlo test is repeated 10000 times to obtain the value of the detection threshold. Taking the process of passive sonar target position estimation in a typical underwater acoustic environment as an example, an implementation example of the invention is given.
Step 1: obtaining sub-band azimuth spectrum vector according to wideband data received by array
For the broadband receiving data obtained by sampling the receiving matrix which is a uniform horizontal linear array with the array element number of M and the array element spacing of d, the sampling frequency is assumed to be fsThe receiver processing band range is [ f ]L,fH]With a bandwidth of [ f ]L,fH]The digital filter performs band-pass filtering on the broadband received data, then divides the broadband received data into each sub-band component through discrete Fourier transform, and selects the frequency of the sub-band falling on [ f [)L,fH]Taking J subband components in between as subbands to be processed, obtaining azimuth spectrum estimation of each subband component by using a Conventional Beamforming (CBF) algorithm for each subband component, uniformly scanning K directions within a range of-90 degrees to 90 degrees relative to a normal direction of a matrix by using the azimuth spectrum estimation, obtaining azimuth spectrum estimation values in the K directions to form Kx 1 subband azimuth spectrum vectors, wherein the J subbands have J azimuth spectrum vectors in total;
and performing band-pass filtering on the time domain data received by the array, and dividing the time domain data into L data blocks, wherein the length of each data block is N. Performing discrete Fourier transform on each data block and according to the processing bandwidth [ fL,fH]J subband components are selected, and the jth subband component matrix can be expressed as
X(fj)＝[x1(fj),…,xl(fj),…,xL(fj)](2)
Wherein,has a center frequency of fjThe L (L ═ 1, …, L) frequency domain snapshot vector on the subband of (a), T is the transposition operation, and the CBF algorithm is used to obtain the center frequency fjThe azimuth spectrum of the sub-band of (a),
wherein,is a space domain scanning vector, theta is an included angle between a signal incidence direction and a normal line, c is a propagation speed in a medium, d is an array element interval,for covariance matrix estimation, uniformly scanning theta in K directions within the range of-90 DEG to obtain the central frequency fjThe sub-band azimuth spectral vector of
pj＝[pj(θ1)，…,pj(θk),…,pj(θK)](4)
J subband direction spectral vectors can be obtained by sequentially calculating according to the formula (2) and the formula (3).
Step 2: selecting effective sub-band from sub-band azimuth spectrum obtained in step 1
Supposing that the noise is white Gaussian noise with uniformly distributed space, recording an azimuth spectrum obtained by a CBF algorithm when only the noise exists in broadband receiving data and no signal exists as a noise azimuth spectrum, uniformly scanning K directions in a range of-90 degrees relative to a normal direction of a matrix for the noise azimuth spectrum, taking spectral values of the K directions to form a K multiplied by 1 noise azimuth spectrum vector, obtaining the noise azimuth spectrum vector by computer simulation, taking an average value for at least 1000 times as a final result, taking a cosine value of an included angle between a sub-band azimuth spectrum vector and the noise azimuth spectrum vector as a T0Constructing the detection statistic T1-T on each sub-band0Setting false alarm probability PFAObtaining a detection threshold value gamma by a Monte Carlo repeated test for at least 10000 times, selecting a sub-band with a detection statistic value larger than the detection threshold value gamma as an effective sub-band, and entering the step 3;
considering that a narrow-band random signal exists on a certain sub-band with the center frequency f, and the incoming wave direction is theta0With a power ofThe received noise of each array element is assumed to be Gaussian noise with uniformly distributed space and zero mean value, the received noise of each array element is uncorrelated, and the noise power isThe noise is uncorrelated with the signal, the subband signal can be represented as
x(t,f)＝s(t,f)+n(t) (5)
Wherein,in order to be a component of the signal,is an array pair theta0Direction vector of direction, amplitude A0(t), phaseAre all of slow variation, n (t) ═ n1(t),…,nM(t)]TThe covariance matrix R of the subband signal as the noise componentsubCan be expressed as:
Rsub＝Rs+Rn(6)
wherein R iss＝E[s(t,f)·sH(t,f)]As a signal covariance matrix, E [. cndot]Indicating the desired operation, superscript H indicates the conjugate transpose,i is an M × M identity matrix, I is a noise covariance matrix.
Note ps(θ)＝aH(θ)Rsa (theta) is the signal azimuth spectrum, pn(θ)＝aH(θ)Rna (theta) is a noise azimuth spectrum, whereinIs a scan vector, theAzimuth spectrum p of sub-bandsub(theta) can be represented as
psub(θ)＝aH(θ)Rsuba(θ)＝ps(θ)+pn(θ) (7)
Then R iss，RnSubstitution calculation Ps(θ)，Pn(theta) the amount of the compound (a) is available,
uniformly scanning theta in K directions within the range of-90 degrees to obtain a signal azimuth spectrum vector, a noise azimuth spectrum vector and a receiving sub-band azimuth spectrum vector of
Ps＝[ps(θ1),…,ps(θK)]
Pn＝[pn(θ1),…,pn(θK)]
Psub＝[psub(θ1),…,psub(θK)](9)
Wherein p issub(θk)＝ps(θk)+pn(θk) K is 1, …, K. Note PsubAt PnIs at an included angle ofCosine value of included angle is recordedThen there is
Wherein | · | | represents vector modulo operation, formula (7), (8), (9) is substituted into formula (10), and input signal-to-noise ratio is recordedCan obtain the product
The snr is calculated and recorded by the formula (11)Can obtain the product
Comparison b2In relation to the magnitude of Ka, there are
Wherein Y is (Y)1,…,yK) D (-) means variance calculation, and D (Y) is greater than or equal to 0 as known from statistical knowledge, and by integrating (12) and (13), for snr > 0,the same theory can proveThus T0Decreases with increasing number of array elements and input signal-to-noise ratio. In equation (11), M.snr can be understood as the array output signal-to-noise ratio, hence T0Decreasing as the output signal-to-noise ratio of the array increases.
For a certain sub-band with center frequency f, there are
T＝1-T0(14)
From the above derivation, it can be seen that when the number of array elements M is constant, T increases with the increase of the input snr and the number of array elements M. That is, T increases with increasing array output signal-to-noise ratio. In practice, the snr of the received data is unknown, so T can be considered as a detection statistic for detecting whether a signal exists on a subband, and a detection threshold γ can be set. If T is more than gamma, the signal is considered to exist on the sub-band; otherwise, the subband is considered to have no signal.
The combination of the formulas (4), (9), (10) can obtain the center frequency fjThe sub-band of detection statistics of
For the jth sub-band, carrying out Monte Carlo repeated test and setting false alarm probability so as to obtain a detection threshold gammaj. Substituting the sub-band azimuth spectrum vector elements obtained by calculation in the step 1) into the formula (14) to obtain a detection statistic TjAnd is combined with a threshold gammajAnd (6) comparing. If Tj＞γjIf yes, selecting it as effective sub-band, and recording gj1 is ═ 1; if Tj≤γjIf so, the subband is discarded and g is recordedj＝0。
And step 3: weighting the azimuth spectrum of the effective sub-bands obtained by the processing in the step 2, taking the detection statistic T corresponding to each effective sub-band as the weight of the effective sub-band, and carrying out weighted summation on the azimuth spectrum on each sub-band to obtain the final broadband azimuth spectrum:
in the formula (1), g corresponds to the effective sub-bandjThe value is 1 and the sub-band corresponding to the non-valid sub-band is 0, so that the valid sub-band, T, can be selectedjRepresenting the weighting of the corresponding active sub-bands, as described aboveKnowing TjAnd weighting to obtain a final broadband azimuth spectrum and further obtain a target azimuth estimation result, wherein the larger the corresponding signal-to-noise ratio of the larger sub-band is.
1) For the case of single target and uncorrelated noise, only a target one is assumed in the received signal, the noise is gaussian noise, and the received noise of each array element is uncorrelated. The continuous spectral signal-to-noise ratio is-15 dB, and the line spectral signal-to-noise ratio is-10 dB. Computer simulation was performed according to the steps of the above technical solution, and the result is shown in fig. 3. FIG. 3 shows the effect of the traditional ISM method (ISM-CBF), the ISM method (ISM-CBF-effective subband), and the ISM method (ISM-CBF-effective subband-weighted) wideband DOA estimation. Fig. 3 shows that the method proposed by the present invention has a great improvement effect on the angular resolution and background level of the conventional ISM method, and simultaneously, the background level can be further reduced by using the weighting of the detection statistics.
2) For the situation of multiple targets and correlated noise, a first target and a second target exist in a received signal at the same time, the noise is Gaussian noise, and correlation exists between the received noise of each array element. The continuous spectral signal-to-noise ratio is-15 dB, and the line spectral signal-to-noise ratio is-10 dB. Computer simulation is performed according to the steps of the above technical solution, and the correlated noise in the simulation is generated by the algorithm proposed by e.habets and s.gannot, and the result is shown in fig. 4. It can be known from fig. 4 that the conventional ISM method cannot achieve the position estimation of the target, and the method proposed by the present invention can be used to distinguish the positions of the two targets. In practical situations, the background noise is usually correlated noise, and the result of fig. 4 shows that the method provided by the present invention also has a great improvement effect on the target resolution performance under the interference of correlated noise.
3) The method provided by the invention is suitable for other narrow-band DOA algorithms. Under the condition of multiple targets and related noise, in the step 1) of the technical scheme, the MVDR algorithm is used for calculating the azimuth spectrum vector of each sub-band, and other steps are unchanged. Through computer simulation, fig. 5 shows the implementation effect of the CBF algorithm and the MVDR algorithm on the method provided by the present invention. As can be seen from fig. 5, it is clear that better target orientation resolution can be achieved when the MVDR method is used. It is therefore contemplated that a high resolution narrow band DOA estimation algorithm may be used in the present invention in an attempt to achieve better performance.
According to the implementation example, compared with the traditional ISM method, the method provided by the invention can greatly improve the angular resolution of the target and reduce the background level, and has a better improvement effect on the traditional ISM method under the condition of relevant noise, so that the method can be effectively applied to the field of broadband target direction estimation.
The basic principle of the method is derived theoretically, the implementation scheme is verified by computer numerical simulation, and the result shows that compared with the traditional ISM method, the method provided by the invention can effectively improve the angular resolution of the broadband DOA estimation and well reduce the background level.
Claims (1)
1. An ISM method based on active subband selection and detection statistic weighting, comprising the steps of:
step 1: obtaining sub-band azimuth spectrum vector according to wideband data received by array
For the broadband receiving data obtained by sampling the receiving matrix which is a uniform horizontal linear array with the array element number of M and the array element spacing of d, the sampling frequency is assumed to be fsThe receiver processing band range is [ f ]L,fH]With a bandwidth of [ f ]L,fH]Digital filter of for receiving digital signal in wide bandPerforming band-pass filtering, dividing the broadband received data into sub-band components by discrete Fourier transform, and selecting the frequency of the sub-band falling on [ f [)L,fH]Taking J subband components in between as subbands to be processed, using a CBF algorithm to each subband component to obtain azimuth spectrum estimation of each subband component, uniformly scanning K directions within a range of-90 degrees relative to a normal direction of a matrix to obtain azimuth spectrum estimation values in the K directions to form K multiplied by 1 subband azimuth spectrum vectors, wherein J subbands have J azimuth spectrum vectors;
step 2: selecting effective sub-band from sub-band azimuth spectrum obtained in step 1
Supposing that the noise is white Gaussian noise with uniformly distributed space, recording an azimuth spectrum obtained by a CBF algorithm when only the noise exists in broadband receiving data and no signal exists as a noise azimuth spectrum, uniformly scanning K directions in a range of-90 degrees relative to a normal direction of a matrix for the noise azimuth spectrum, taking spectral values of the K directions to form a K multiplied by 1 noise azimuth spectrum vector, obtaining the noise azimuth spectrum vector by computer simulation, taking an average value for at least 1000 times as a final result, taking a cosine value of an included angle between a sub-band azimuth spectrum vector and the noise azimuth spectrum vector as a T0Constructing the detection statistic T1-T on each sub-band0Setting false alarm probability PFAObtaining a detection threshold value gamma by a Monte Carlo repeated test for at least 10000 times, selecting a sub-band with a detection statistic value larger than the detection threshold value gamma as an effective sub-band, and entering the step 3;
and step 3: weighting the azimuth spectrum of the effective sub-bands obtained by the processing in the step 2, taking the detection statistic T corresponding to each effective sub-band as the weight of the effective sub-band, and carrying out weighted summation on the azimuth spectrum on each sub-band to obtain the final broadband azimuth spectrum:
in the formula (1), g corresponds to the effective sub-bandjThe value is 1, the sub-band corresponding to the non-effective sub-band is 0, TjRepresenting the weighting of the corresponding effective sub-band, and obtaining the final broadband azimuth spectrum after weightingAnd further obtaining the target azimuth estimation result.
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