Rapid adaptive beam forming method for cylindrical array band focusing

Abstract

The invention provides a rapid adaptive beam forming method for cylindrical array sub-band focusing, and provides a sub-band focusing covariance matrix estimation method through the characteristics of phase modal domain signals, and covariance matrixes corresponding to all frequency points in a certain frequency band can be focused into a covariance matrix at a center frequency through the method. And self-adaptive beam forming is carried out through the sub-band focusing covariance matrix. Because the modal intensity change of the frequency points in the sub-bands is small, the problem that the low-frequency high-order modal intensity is sharply reduced can be avoided by focusing on the central frequency points of the sub-bands, the analyzable phase modal domain decomposition order is improved, and more information is reserved as much as possible; in addition, due to the fact that time accumulation and frequency point accumulation in the frequency band are carried out at the same time, the problem that covariance inversion is not stable is solved, the number of times of inversion calculation is greatly reduced, and calculation efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of acoustic arrays, and mainly relates to a fast adaptive beamforming method with cylindrical element sub-band focusing. Background Art

[0002] In the civilian and defense fields, cylindrical arrays are widely used in devices such as voice microphone arrays, radars, and sonars. Such arrays generally adopt traditional beamforming methods, that is, the conventional beamforming method (CBF) of summing delays of each channel, or the adaptive beamforming method. Currently, a large number of studies have been carried out on the beamforming method in the phase modal domain of circular arrays. The beamforming in the phase modal domain can obtain high directivity and relatively high processing gain in the low-frequency band with a small aperture. However, due to the complex noise affecting the acoustic array, the processing performance in the phase modal domain is greatly limited.

[0003] The beamforming method in the phase modal domain is mainly used for various types of arrays such as circular arrays, cylindrical arrays, and spherical shell arrays. By harmonic decomposition (such as spherical harmonic decomposition), the element signals are transformed into the phase modal domain, and the high directivity inherent in the phase modal domain is used to achieve high-performance beamforming. In current research, the beamforming method closest to the present invention, namely the phase modal domain MVDR beamforming method, mainly consists of steps such as covariance matrix estimation and inversion in the phase modal domain, and calculation of beamforming weighting vectors. Based on the phase modal domain MVDR beamforming method, the present invention further optimizes the covariance matrix estimation and inversion, and the beamforming weighting vector calculation method, improving the calculation efficiency and the robustness of matrix inversion.

[0004] To cope with the influence of complex noise, a large number of studies have been carried out on the adaptive beamforming in the phase modal domain, mainly including beamforming methods such as LCMV and MVDR. However, in the low-frequency band, these methods are first limited by the decomposition order in the phase modal domain. Since the intensity of high-order modes in the low-frequency band decreases sharply, high-order decomposition will amplify white noise, resulting in a decline in beamforming performance. Secondly, in these methods, the construction methods of the covariance matrix in the phase modal domain and the covariance matrix in the element domain are similar, and it is easy to suffer from the problem of unstable inversion due to a small number of beats. Finally, these methods face the problem of a large amount of matrix inversion calculation, and the engineering implementation is difficult. Summary of the Invention

[0005] The technical problem solved by the present invention is to provide a fast adaptive beamforming method with cylindrical element sub-band focusing for the problems of covariance matrix estimation in the phase modal domain adaptive beamforming of cylindrical arrays and improving the beamforming calculation efficiency.

[0006] The object of the present invention is accomplished by the following technical solutions. A fast adaptive beamforming method with cylindrical element sub-band focusing includes the following steps:

[0007] Step 1, Phase Modal Domain Transformation: The cylindrical array receives signals, and performs phase modal domain transformation on the element frequency domain signals;

[0008] Step 2, Modal Intensity Calculation: Calculate the modal intensity for each frequency point;

[0009] Step 3, Sub-band Focused Phase Modal Domain Signal and Covariance Estimation: Perform frequency focusing in the phase modal domain to realize the construction of the sub-band covariance matrix;

[0010] Step 4, Sub-band Focused Adaptive Beamforming: Realize adaptive beamforming by inverting the sub-band covariance matrix.

[0011] Further, in the said Step 1, the specific steps are as follows:

[0012] After the array received signals are sorted in the order of each circle of elements, the frequency domain signal arrangement vector is defined as follows:

[0013]

[0014] In the formula, the element p q represents the measured value of the signal received by the q-th element of a certain circle of the cylindrical array at a certain frequency f;

[0015] Define the transformation matrix

[0016]

[0017] where m = -n,... n, N = 2n + 1, Ω q is the angle corresponding to the q-th hydrophone, and Y is the phase modal domain transformation matrix when the element coordinates are given;

[0018] Y m (Ω) = e imΩ

[0019] Phase modal domain signal:

[0020] P m (f) = (Y QN ) H P Q (f).

[0021] Further, in the said Step 2, the specific steps are as follows: Calculate the modal intensity for each frequency point:

[0022] Sound transmission through the cylinder: b m (kr) = i m j m (kr)

[0023] Rigidity of the cylinder:

[0024] j n (kr) represents the Bessel function of the nth order, and j n '(kr) is its derivative; represents the Hankel function of the second kind of the nth order, represents the derivative of the Hankel function; the modal intensities b m (kr) and b m (k0r) at the analysis frequency point f and the center frequency point f0 of the frequency band are obtained respectively through the above formula.

[0025] Further, in the third step, the specific steps are as follows:

[0026] Calculate the phase modal domain signal of sub-band focusing:

[0027]

[0028] and its estimated sub-band focusing covariance matrix:

[0029]

[0030] t represents the accumulation of the signal within a period of time, and f is the frequency identifier within the sub-band.

[0031] Further, in the fourth step, the specific steps are as follows: Calculate the inverse matrix R -1 of the sub-band focusing covariance matrix, and according to the corrected modal intensity b m (k0r), the phase modal domain signal P m (f, f0) of sub-band focusing, calculate the beamforming result in the φ direction at this frequency point through the following formula:

[0032]

[0033] where V = [Y -N (φ)(b -N (k0r)) * Y -N (φ)(b -N+1 (k0r)) * … Y -N (φ)(b N (k0r)) * T The broadband beamforming result within the sub-band is represented by the following formula:

[0034]

[0035] ​The beneficial effects of the present invention are as follows: Based on the characteristics of the phase modal domain signal, the present invention provides a method for estimating the sub-band focused covariance matrix. By this method, the covariance matrices corresponding to all frequency points within a certain frequency band can be focused into the covariance matrix at the center frequency, and then adaptive beamforming is performed using the sub-band focused covariance matrix. Since the modal intensity variation of the frequency points within the sub-band is small, focusing on the center frequency of the sub-band can avoid the problem of the sharp decrease in the intensity of the low-frequency high-order modes, improve the analyzable order of the phase modal domain decomposition, and retain as much information as possible. In addition, by accumulating in time and accumulating the frequency points within the frequency band simultaneously, the problem of non-robust covariance inversion is solved, and the number of inversion calculations is greatly reduced, thus improving the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] To clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for the embodiments. Obviously, the drawings described below are only some embodiments of the present invention, and those skilled in the art or ordinary technicians can obtain other drawings based on these drawings without creative efforts.

[0037] Figure 1 It is the signal processing flow chart of the present invention.

[0038] Figure 2 It is the comparison diagram of the effects between the method of the present invention and conventional beamforming.

[0039] Figure 3 It is the beam time history of the 3 - trial data and the comparison diagram of the effects between the method of the present invention and conventional beamforming. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the protection scope of the present invention.

[0041] As shown in the figure, the present invention proposes a fast adaptive beamforming method for cylindrical dipole sub-band focusing, which improves the analyzable order of the phase modal domain, enhances the robustness of covariance matrix estimation, realizes the improvement of target detection and resolution capabilities, and simultaneously reduces the computational complexity of beamforming.

[0042] Mechanism of the present invention:

[0043] 1) Construction of the sub-band covariance matrix in the phase modal domain: Frequency focusing is performed in the phase modal domain to realize the construction of the sub-band covariance matrix;

[0044] 2) Sub-band focused adaptive beamforming: Adaptive beamforming is achieved by inverting the sub-band covariance matrix.

[0045] The signal processing flow chart is as Figure 1 shown, and this method includes the following steps:

[0046] (1) Phase-mode domain transformation

[0047] For the signals received by the cylindrical array, the phase-mode domain transformation is performed on the element frequency-domain signals. After the array received signals are sorted in the order of each circle of elements, the arrangement vector of its frequency-domain signals is defined as follows:

[0048]

[0049] In the formula, the element p q represents the measured value of the signal received by the q-th element of a certain circle of the cylindrical array at a certain frequency f. In the implementation, without loss of generality, it is assumed that the signal processing frequency band is 500Hz - 2000Hz, 1024 sampling points are processed each time, and there are 68 frequency points in the frequency band, which are respectively expressed as f1, f2,... f 68 , and the center frequency f0 is defined as 1000Hz. Define the transformation matrix

[0050]

[0051] where, m = -n,... n, N = 2n + 1, Ω q is the angle corresponding to the q-th hydrophone, and Y is the phase-mode domain transformation matrix when the element coordinates are given.

[0052] Y m (Ω) = e imΩ

[0053] Phase-mode domain signal:

[0054] P m (f) = (Y QN ) H P Q (f)

[0055] (2) Modal intensity calculation

[0056] Calculate the modal intensity for each frequency point:

[0057] Sound transmission through the cylinder: b m (kr) = i m j m (kr)

[0058] Cylinder rigidity:

[0059] j n$(kr)$ represents the Bessel function of the first kind of order $n$, $J_{n}$ n '$(kr)$ is its derivative; $H_{n}^{(2)}(kr)$ represents the Hankel function of the second kind of order $n$, $H_{n}^{(2)'}(k_{0}r)$ represents the derivative of the Hankel function. The modal strengths $b_{n}(kr)$ and $b_{n}(k_{0}r)$ at the analysis frequency point $f$ and the center frequency point $f_{0}$ of the frequency band are obtained respectively through the above formulae. m $b_{n}$ m $(k_{0}r)$.

[0060] (3) Subband focusing phase modal domain signal and covariance estimation

[0061] Calculate the subband focusing phase modal domain signal:

[0062]

[0063] and its estimated subband focusing covariance matrix:

[0064]

[0065] $t$ represents the accumulation of the signal within a period of time, and $f$ is the frequency identifier within the subband. By this method, the focusing covariance matrices corresponding to all frequency points within the subband can be estimated simultaneously. On the one hand, it enhances the robustness of the covariance estimation and avoids the influence of the non - robustness of covariance inversion in the adaptive algorithm. On the other hand, multiple frequency points within the subband share a covariance matrix, greatly reducing the number of times of covariance matrix inversion and improving the calculation efficiency.

[0066] Generally, phase modal domain processing requires calculating Due to the extremely small value of the low - frequency high - order $b_{n}$ m (kr), it is easy to amplify the white noise signal in the phase modal domain signal amplification array, affecting the low - frequency processing performance. In the present invention, by utilizing the characteristic that the difference in frequency modal strengths within the subband is small, reasonably setting the center frequency and the analysis order, and controlling within the range of 0.1 - 10, the low - frequency signal processing order is greatly improved on the premise of minimizing the amplification of the high - order signal noise component, laying a foundation for improving the beamforming performance.

[0067] For a general cylindrical array, the number of array elements per circle is generally about 4 to 128, and the total order of the phase modal domain is generally not higher than 128. Since the cumulative sample number of the covariance matrix is TK, generally T = 64 and K = 68 in this example, and the total cumulative sample number of the covariance is 4352. Therefore, the inverse matrix of the focused covariance matrix estimated by this method is computationally robust, which can avoid the problem of the degradation of beamforming performance caused by the non-robust covariance in the adaptive algorithm under the condition of a small number of beats. On the other hand, multiple frequency points within a sub-band share a covariance matrix, which greatly reduces the number of times of inverting the covariance matrix. In this example, the number of times of inverting the covariance matrix is reduced to 1 / 68 of the original, which greatly improves the computational efficiency.

[0068] (4) Sub-band focused adaptive beamforming

[0069] Based on the previous step, calculate the inverse matrix \(R^{-1}\) of the sub-band focused covariance matrix -1 , according to the modified modal intensity \(b\) m (\(k_0r\)), the sub-band focused phase modal domain signal \(P\) m (\(f,f_0\)), calculate the beamforming result in the \(\varphi\) direction at this frequency point through the following formula:

[0070]

[0071] where \(V = [Y\) -N (\(\varphi\))(\(b\) -N (\(k_0r\))) * \(Y\) -N (\(\varphi\))(\(b\) -N+1 (\(k_0r\))) * … \(Y\) -N (\(\varphi\))(\(b\) N (\(k_0r\))) * T , the broadband beamforming result within the sub-band can be expressed by the following formula:

[0072]

[0073] It should be noted that the formula of the sub-band focused adaptive beamforming in the present invention is similar in form to the MVDR beamforming, but due to the use of the sub-band focused covariance matrix in the phase modal domain, the steering vector in the phase modal domain and the two elements of the sub-band focused phase modal domain signal are completely different from the conventional MVDR beamforming or the disclosed phase modal domain MVDR beamforming.

[0074] Figure 2 ​The beamforming result diagram of a certain cylindrical array is given, and a comparison of the effects between the method of the present invention (the red line in the upper figure and the lower figure) and the conventional beamforming (the blue line in the upper figure and the middle figure) is presented. It can be seen from the figure that compared with the traditional method, the target resolution ability and detection ability of the method of the present invention are significantly improved. Figure 3 The beam time history of the three test data is given, and a comparison of the effects between the method of the present invention (the right figure) and the conventional beamforming (the left figure) is presented. It can be seen that compared with the traditional method, the beamforming performance of the method of the present invention is significantly improved, and the weak target detection ability within the gray frame is stronger.

[0075] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A fast adaptive beamforming method with a cylindrical dipole and focusing, characterized in that: It includes the following steps: Step 1, phase modal domain transformation: The cylindrical array receives signals, and performs phase modal domain transformation on the element frequency domain signals; Step 2, modal strength calculation: Calculate the modal strength for each frequency point; Step 3, sub-band focused phase modal domain signal and covariance estimation: Perform frequency focusing in the phase modal domain to realize the construction of the sub-band covariance matrix; Step 4, sub-band focused adaptive beamforming: Realize adaptive beamforming by inverting the sub-band covariance matrix.

2. The fast adaptive beamforming method with a cylindrical dipole array and focusing according to claim 1, characterized in that: In the said Step 1, the specific steps are as follows: After the array received signals are sorted in the order of each circle of elements, the frequency domain signal arrangement vector is defined as follows: where the element p q represents the measurement value of the received signal of the q-th element in a certain ring of the cylindrical array at a certain frequency f; Define the transformation matrix where m = -n,...n, N = 2n + 1, Ω q is the angle corresponding to the q-th hydrophone, and Y is the phase modal domain transformation matrix when the array element coordinates are given; Y m (Ω) = e imΩ Phase modal domain signal: P m (f) = (Y QN ) H P Q (f).

3. The fast adaptive beamforming method with a cylindrical dipole array focusing according to claim 2, wherein: In the said Step 2, the specific steps are as follows: Calculate the modal strength for each frequency point: Cylindrical sound transmission: b m (kr) = i m j m (kr) Cylinder rigidity: j n (kr) represents the Bessel function of the nth order, and j n '(kr) is its derivative; represents the Hankel function of the second kind of the nth order, represents the derivative of the Hankel function; the modal intensities b m (kr) and b m (k0r) of the analysis frequency point f and the center frequency point f0 of the frequency band are obtained respectively through the above formula.

4. The method for fast adaptive beamforming with a cylindrical dipole array having focusing according to claim 3, characterized in that: In the said Step 3, the specific steps are as follows: Calculate the sub-band focused phase modal domain signal: And its estimated sub-band focused covariance matrix: t represents the accumulation of signals over a period of time, and f is the frequency identifier within the sub-band.

5. The method for fast adaptive beamforming with a cylindrical dipole array having focusing according to claim 4, characterized in that: In the fourth step, the specific steps are as follows: calculate the inverse matrix R of the subband focusing covariance matrix -1 , according to the corrected modal intensity b m (k0r), the subband focusing phase modal domain signal P m (f, f0), calculate the beamforming result in the φ direction at this frequency point through the following formula: where V = [Y -N (φ)(b -N (k0r)) * Y -N (φ)(b -N+1 (k0r)) * … Y -N (φ)(b N (k0r)) * T , the wideband beamforming result within the subband is expressed by the following formula:​

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