CN116846440A - Beam forming method and system for calculating covariance matrix based on singular value decomposition - Google Patents
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Abstract
A beamforming method and system for calculating covariance matrix based on singular value decomposition, the method comprises: calculating a covariance matrix of the observation signals; singular value decomposition is carried out on a covariance matrix of the observation signal, and the noise power is calculated by utilizing the singular value; calculating an inverse matrix of the covariance matrix of the observation signal by using the left singular vector matrix, the right singular vector matrix and the singular values; calculating an interference noise covariance matrix according to the definition of the covariance matrix by utilizing the inverse matrix of the observed signal covariance matrix and the theoretical steering vector of the interference signal; re-calculating the interference noise covariance matrix by using the calculated interference noise covariance matrix and adding the spherical expansion noise covariance matrix and the diagonal loading capacity; calculating a wave beam forming filter coefficient matrix by using the recalculated interference noise covariance matrix and a theoretical steering vector of the target signal and adopting an MVDR method; and obtaining a beam enhanced target signal based on the signal vector received by the sensor array and the filter coefficient matrix.
Description
Technical field:
the invention relates to the field of array signal processing, in particular to a beam forming method and a beam forming system for calculating a covariance matrix based on singular value decomposition, which are used for attenuating interference and noise signals in other directions and enhancing useful signals in a target direction.
The background technology is as follows:
the beam forming technology has wide application in the fields of communication, radar, sonar and the like, and the main principle is that a sensor array is utilized to acquire the space and time information of a physical field, the weighting coefficient of a filter is designed, and the multi-channel physical quantity is filtered, so that the purposes of inhibiting interference signals and other noise signals outside the beam and enhancing useful signals in the target direction are achieved.
The standard Capon beamforming Method (MVDR) can reach theoretical optimum when the interference noise covariance matrix and steering vector are precisely known. However, for the scene with a plurality of interference sources and multi-path propagation effect, the superposition of the target signal, the interference signal and other noise is acquired by the sensor, and the signal sample acquired in real time is limited, so that the interference noise covariance matrix cannot be accurately calculated. In addition, due to errors in sensor position and incoming wave direction estimation, accurate steering vectors are often not obtained. The mismatch of the interference noise covariance matrix and steering vector causes the Capon beamforming method to directly impair the target signal.
In order to increase the robustness of the beamforming method to interference noise covariance matrix and steering vector mismatch, many improvements have been reported. The simplest and most commonly used is the MVDR diagonal loading method, which eliminates the pathogenicity of the matrix by adding regularization coefficients, reducing the damage to the target signal, however, there is a problem in that the diagonal loading is difficult to determine. In the document 1"Robust Adaptive Beamforming Based on Interference Covariance Matrix Reconstruction and Steering Vector Estimation,IEEE Trans.Signal Process, vol.60, no.7, pp.3881-3885,2012, a beamforming method is proposed that integrates the Capon spatial spectrum over the whole spatial region except the directional region where the target signal is located, thereby calculating the interference noise covariance matrix, and improves the steering vector accuracy by solving a quadratic programming problem with quadratic constraints. Chinese patent CN105182298A provides a method for calculating an interference noise covariance matrix for an incoming wave direction error, based on document 1, the integral of the Capon spatial spectrum is rewritten into a sum approximation, and the eigenvalue decomposition is used to reduce the approximation error caused by the sum instead of the integral, then the eigenvector corresponding to the largest eigenvalue is used to replace the steering vector of the interference signal, and the interference noise covariance matrix is calculated according to definition. The method for calculating the interference noise covariance matrix based on the Capon spatial spectrum integration or summation needs to integrate or sum the incoming wave direction area where each interference signal is located on each frequency component, performs twice eigenvalue decomposition calculation and twice matrix inversion operation, has very high calculation complexity, and is not suitable for beam enhancement processing of broadband signals with high real-time requirements.
The invention comprises the following steps:
aiming at the defects of the prior art, the invention provides a beam forming method and a beam forming system for calculating a covariance matrix based on singular value decomposition.
According to the invention, the singular value decomposition is carried out on the covariance matrix of the observed signal, the noise power is calculated by utilizing the singular value, the inverse matrix of the covariance matrix is calculated by utilizing the singular value decomposition, the interference noise covariance matrix is calculated by utilizing the definition of the theoretical steering vector and the covariance matrix, the integral and summation operation is avoided, the inversion operation of a matrix is reduced, the calculation complexity is greatly reduced, and the method is suitable for the real-time wave beam enhancement processing of the broadband signal.
A first aspect of the present invention provides a beamforming method for calculating a covariance matrix based on singular value decomposition, comprising the steps of:
s1, calculating a covariance matrix of an observation signal based on the observation signal acquired by a sensor array and an exponential smoothing method;
s2, singular value decomposition is carried out on a covariance matrix of the observed signal, and noise power is calculated by utilizing the singular value;
s3, calculating an inverse matrix of the covariance matrix of the observation signal by using the left singular vector matrix, the right singular vector matrix and the singular values;
s4, calculating an interference noise covariance matrix according to the definition of the covariance matrix by utilizing an inverse matrix of an observed signal covariance matrix and a theoretical steering vector of an interference signal;
s5, recalculating the interference noise covariance matrix by using the calculated interference noise covariance matrix and adding the spherical expansion noise covariance matrix and the diagonal loading capacity;
s6, calculating a wave beam forming filter coefficient matrix by using the recalculated interference noise covariance matrix and a theoretical steering vector of the target signal and adopting an MVDR method; and obtaining a beam enhanced target signal based on the signal vector received by the sensor array and the filter coefficient matrix.
Further, the formula for calculating the covariance matrix of the observation signal based on the observation signal collected by the sensor array and the exponential smoothing method in step S1 includes:
Φ y (n,f)＝α 1 Φ y (n-1,f)+(1-α 1 )y(n,f)y H (n,f) (1)
wherein n represents a time frame; f represents frequency; alpha 1 The value range is (0, 1) for the exponential smoothing factor, the larger the value is, the larger the effect of the historical prediction data is, and the smaller the effect of the current actual data is;
y(n,f)＝[Y 1 (n,f) Y 2 (n,f)…Y M (n,f)] T (2)
is an Mx1-dimensional acoustic signal vector; y is Y m (n, f) is the signal observed by the mth sensor; [] T Transpose the conventional matrix; and when n=1, Φ y (0, f) is
Φ y (0,f)＝Γ 0,π (f)+εI M (3)
Wherein I is M Is an M-order identity matrix; epsilon is regularization parameter which changes along with frequency, the value range is (0, 1), and the larger the frequency is, the smaller the value is; Γ -shaped structure 0,π (f) A covariance matrix of spherical diffusion noise, wherein the (i, j) element is:
[Γ 0,π (f)] ij ＝sinc(2πf(j-i)τ 0 ) (4)
wherein τ 0 ＝δ/c 0 Delta is the distance between adjacent sensor array elements, c 0 The propagation speed of a physical quantity, sinc (·) is the sampling function.
Further, the process of performing singular value decomposition on the covariance matrix of the observed signal in step S2, and estimating the noise power by using the singular value includes:
observed signal covariance matrix Φ for current time frame y (n, f) singular value decomposition:
Φ y (n,f)＝USV H (5)
wherein U and V are respectively a left singular vector matrix and a right singular vector matrix, which are M multiplied by M unitary matrices; s is a diagonal matrix, and diagonal elements of the diagonal matrix are singular values arranged from large to small; [] H Is the conjugate transpose of the matrix;
calculating the power of noiseIs the average of the smallest (M- (j+d)) singular values, where J is the total number of interfering signals and D is the number of target signals.
Further, the formula for calculating the inverse matrix of the observed signal covariance matrix by using the left singular vector matrix, the right singular vector matrix and the singular values in step S3 includes:
wherein S is -1 Is obtained by inverting the diagonal element of S.
Further, the process of calculating the interference noise covariance matrix according to the definition of the covariance matrix in step S4 by using the inverse matrix of the observed signal covariance matrix and the theoretical steering vector of the interference signal includes:
calculating the power of the jth interfering signalThe formula of (2) is as follows:
wherein d is H (Θ j F) is the theoretical steering vector of the j-th interference signal, Θ j The incoming wave direction vector of the j-th interference signal; in the three-dimensional spherical coordinate system of the system,θ j and phi j Pitch angle and azimuth angle respectively;
calculating interference noise covariance matrix phi according to the definition of covariance matrix ξ The formula of (2) is as follows:
further, the formula for recalculating the interference noise covariance matrix using the calculated interference noise covariance matrix, the spherical expansion noise covariance matrix and the diagonal load in step S5 is as follows:
Φ ε (n,f)＝α 2 Φ ξ (n,f)+(1-α 2 )Φ y (0,f) (9)
wherein alpha is 2 For diagonally loading the weight factor, the value range is (0, 1), and the larger the value is, the more sensitive the value is to the change of the signal.
Further, the process of calculating the filter coefficient matrix of beam forming by using the interference noise covariance matrix and the theoretical steering vector of the target signal in step S6 and using the MVDR method, and obtaining the beam enhanced target signal based on the signal vector and the filter coefficient matrix received by the sensor array includes:
the formula for calculating the beamforming filter coefficients is as follows:
wherein d (Θ) s F) is the theoretical steering vector of the target signal, Θ s The incoming wave direction of the target signal;
the formula for performing beam enhancement filtering calculation on the signals received by the sensor is as follows:
z(n,f)＝w H (n,f)y(n,f) (11)
and multiplying the frequency domain signal z (n, f) after beam enhancement of each frame by a self-defined window function, and performing inverse Fourier transform to obtain a time domain target signal after beam enhancement.
A second aspect of the present invention provides a beamforming system for calculating a covariance matrix based on singular value decomposition, comprising:
the covariance matrix calculation module is used for calculating a covariance matrix of the observation signal based on the observation signal acquired by the sensor array and an exponential smoothing method;
the noise power calculation module is used for carrying out singular value decomposition on the covariance matrix of the observation signal and calculating noise power by utilizing the singular value;
the inverse matrix calculation module of the observed signal covariance matrix calculates an inverse matrix of the observed signal covariance matrix by using the left singular vector matrix, the right singular vector matrix and the singular values;
the interference noise covariance matrix calculation module calculates an interference noise covariance matrix according to the definition of the covariance matrix by utilizing an inverse matrix of the observed signal covariance matrix and a theoretical steering vector of an interference signal;
an interference noise covariance matrix recalculation module that recalculates an interference noise covariance matrix by adding the spherical spread noise covariance matrix and the diagonal load to the calculated interference noise covariance matrix;
the beam enhanced target signal acquisition module calculates a wave beam formed filter coefficient matrix by using the recalculated interference noise covariance matrix and the theoretical steering vector of the target signal and adopting an MVDR method; and obtaining a beam enhanced target signal based on the signal vector received by the sensor array and the filter coefficient matrix.
A third aspect of the present invention provides an apparatus for beamforming based on singular value decomposition to calculate a covariance matrix, comprising one or more processors configured to implement the beamforming method based on singular value decomposition to calculate a covariance matrix described above.
A fourth aspect of the present invention provides a computer readable storage medium having stored thereon a program which, when executed by a processor, is adapted to carry out the beamforming method of calculating a covariance matrix based on singular value decomposition as described above.
The beneficial effects of the invention are as follows: the invention provides a beam forming method for calculating an interference noise covariance matrix by singular value decomposition, which utilizes singular value decomposition to replace eigenvalue decomposition, utilizes singular value decomposition to calculate an inverse matrix of an observation signal covariance matrix, noise power and interference signal power, utilizes definition of a theoretical steering vector and the covariance matrix to calculate the interference noise covariance matrix, utilizes spherical expansion noise covariance matrix and diagonal loading capacity to recalculate the beam forming method of the interference noise covariance matrix, remarkably reduces the calculation complexity of the beam forming method for reconstructing the interference noise covariance matrix based on integral and eigenvalue decomposition, improves the protection performance of the beam forming method on a target signal, and is suitable for real-time beam enhancement processing of broadband signals.
Description of the drawings:
in order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort to a person skilled in the art.
FIG. 1 is a flow chart of a beamforming method for calculating covariance matrix based on singular value decomposition according to the present invention;
FIG. 2 is a schematic block diagram of a flow for calculating a covariance matrix based on singular value decomposition in accordance with the present invention;
fig. 3 is a schematic diagram of time domain waveforms of a target signal and an interference signal before and after a beamforming method based on singular value decomposition to calculate a covariance matrix according to the present invention.
Fig. 4 is a schematic diagram of a target signal beamforming apparatus for calculating a covariance matrix based on singular value decomposition according to the present invention.
Fig. 5 is a schematic diagram of the system architecture of the present invention.
The specific embodiment is as follows:
the steps and advantages of the present invention will be described in detail below with reference to the drawings and specific examples.
Example 1
The invention provides a beam forming method for calculating a covariance matrix based on singular value decomposition, which specifically comprises the following steps of:
s1, calculating a covariance matrix of the observation signals based on the observation signals acquired by the sensor array and an exponential smoothing method.
The number of array elements of the sensor array is M. And performing fast Fourier transform on the time domain signal of the nth (n=1, 2,3 and …) frame received by the sensor array element. For each frequency component, a covariance matrix Φ of the MxM-dimensional observation signal is calculated according to the following formula y ：
Φ y (n,f)＝α 1 Φ y (n-1,f)+(1-α 1 )y(n,f)y H (n,f) (1)
Wherein n represents a time frame; f represents frequency; alpha 1 The value range is (0, 1) for the exponential smoothing factor, the larger the value is, the larger the effect of the historical prediction data is, and the smaller the effect of the current actual data is;
y(n,f)＝[Y 1 (n,f) Y 2 (n,f)…Y M (n,f)] T (2)
is an Mx1-dimensional acoustic signal vector; y is Y m (n, f) is the signal of the mth sensor; [] T Transpose the conventional matrix.
When n=1, Φ y (0, f) is
Φ y (0,f)＝Γ 0,π (f)+εI M (3)
Wherein I is M Is an M-order identity matrix; epsilon is regularization parameter which changes along with frequency, the value range is (0, 1), and the larger the frequency is, the smaller the value is; Γ -shaped structure 0,π (f) A covariance matrix of spherical diffusion noise, wherein the (i, j) element is:
[Γ 0,π (f)] ij ＝sinc(2πf(j-i)τ 0 ) (4)
wherein τ 0 ＝δ/c 0 Delta is the distance between adjacent sensor array elements, c 0 Is the propagation velocity of the physical quantity.
S2, singular value decomposition is carried out on a covariance matrix of the observed signal, and the noise power is calculated by utilizing the singular value.
Observed signal covariance matrix Φ for current time frame y (n, f) singular value decomposition:
Φ y (n,f)＝USV H (5)
wherein U and V are respectively a left singular vector matrix and a right singular vector matrix, which are M multiplied by M unitary matrices; s is a diagonal matrix, and diagonal elements of the diagonal matrix are singular values arranged from large to small; [] H Is the conjugate transpose of the matrix.
Calculating the power of noiseIs the average of the smallest (M- (j+d)) singular values, where J is the total number of interfering signals and D is the number of target signals.
S3, calculating an inverse matrix of the observed signal covariance matrix by using the left singular vector matrix, the right singular vector matrix and the singular values.
The calculation formula of the inverse matrix of the covariance matrix of the observed signal is as follows:
wherein S is -1 Is obtained by inverting the diagonal element of S.
S4, calculating an interference noise covariance matrix according to the definition of the covariance matrix by utilizing an inverse matrix of the observed signal covariance matrix and a theoretical steering vector of the interference signal.
The power calculation formula of the jth interference signal is:
wherein d is H (Θ j F) is the theoretical steering vector of the j-th interference signal, Θ j Is the incoming wave direction vector of the jth interfering signal. In the three-dimensional spherical coordinate system of the system,θ j and phi j Pitch and azimuth, respectively.
Calculating an interference noise covariance matrix Φ using ξ ：
S5, recalculating the interference noise covariance matrix by using the calculated interference noise covariance matrix and adding the spherical expansion noise covariance matrix and the diagonal loading capacity;
the interference noise covariance matrix is recalculated according to the following formula:
Φ ε (n,f)＝α 2 Φ ξ (n,f)+(1-α 2 )Φ y (0,f) (9)
wherein alpha is 2 For diagonally loading the weight factor, the range of values is (0, 1), the larger the value is, the more the value can adapt to the change of the signal, the smaller the value is, and the more the value is close to the fixed beam forming.
S6, calculating a wave beam forming filter coefficient matrix by using the recalculated interference noise covariance matrix and a theoretical steering vector of the target signal and adopting an MVDR method; and obtaining a beam enhanced target signal based on the signal vector received by the sensor array and the filter coefficient matrix.
The MVDR method is adopted to calculate a wave beam forming filter coefficient matrix w (n, f):
wherein d (Θ) s F) is the theoretical steering vector of the target signal, Θ s Is the incoming wave direction vector of the target signal.
Performing beamforming filtering calculation on signals received by the sensor:
z(n,f)＝w H (n,f)y(n,f) (11)
multiplying the obtained frequency domain signal after beam enhancement of each frame by a window function which is set by user, and performing inverse Fourier transform to obtain a time domain signal after beam enhancement.
Taking a uniform annular six-array element sensor array as an example, the sensors are all oriented, M=6, the pitching angles of the sensor array elements are 90 degrees, and the incoming wave direction of a target signal is (theta) s ,φ s ) = (88 °,300 °), the incoming wave direction is (θ 1 ,φ 1 ) = (88 °,240 °), the theoretical steering vector of the circular ring sensor array is
Wherein the method comprises the steps ofH e ＝kr mic ，k＝2πf/c 0 Is the wave number, r mic =0.035 m is the radius of the sensor array, +.>Is the azimuth angle of the sensor array element, and
the fast fourier transform of L points is performed on the n (n=1, 2,3, …) th frame time domain signal received by the sensor array element, in this embodiment, l=256. For each frequency component, a covariance matrix Φ of the MxM-dimensional observation signal is calculated according to the following formula (1) y In the present embodiment, α 1 = (L-1)/(l+1). Calculating an initial signal covariance matrix Φ according to formulas (3) and (4) y (0, f), in this embodiment, the sampling frequency is 1.6kHz, the frequency f ranges from 0 to 8000Hz, and the equal interval is 62.5 Hz; the value of epsilon decreases from 0.01 to 0.001 at equal intervals as the frequency f increases.
The observed signal covariance matrix Φ for the current time frame according to equation (5) y (n, f) singular value decomposition. The inverse of the observed signal covariance matrix is calculated according to equation (6).
Calculating the power of noiseIs the average of the smallest (M- (j+1)) singular values, where J is the total number of interfering signals, in this embodiment j=1.
The power of the jth interfering signal is calculated according to equation (7). Calculating an interference noise covariance matrix phi according to formula (8) ξ . Recalculating the interference noise covariance matrix according to equation (9) using the calculated interference noise covariance matrix, plus the sphere spread noise covariance matrix and the diagonal loading, in this embodiment, α 2 ＝0.90。。
The beamforming filter coefficient matrix w (n, f) is calculated according to formula (10), and the beamforming filter calculation is performed on the signals received by the sensor according to formula (11). Multiplying the obtained frequency domain voice signal after beam enhancement of each frame by a self-defined window function, and performing inverse Fourier transform to obtain a time domain signal after beam enhancement. In this embodiment, the hanning window of the custom window function.
In an embodiment of the present invention, two performance indicators of beamforming enhancement are defined: interference signal attenuation amount xi n And the distortion degree xi of the target signal d . Wherein the attenuation amount of the interference signal is xi n The formula of (2) is as follows:
wherein the method comprises the steps ofIs the variance of the pre-beam interference signal, +.>Is the variance of the post-beam interference signal. Target signal distortion degree ζ d The formula of (2) is as follows:
wherein the method comprises the steps ofFor the variance of the pre-beam target signal, +.>Is the variance of the post-beam target signal.
The unit of the attenuation amount of the interference signal is dB, and the larger the attenuation amount is, the better the suppression performance of the beam forming algorithm on the interference signal is; the distortion degree of the target signal is dimensionless, and the closer the value is to 1, the better the protection of the target signal is indicated. In this embodiment, the mixed signal is collected in the actual environment where reverberation exists, and the beamforming algorithm has a certain dereverberation capability, so ζ d ≠1。
The total time consumption of the observed signal defining the specific duration of the beamforming process is t, and in this embodiment, the total duration of the acquired mixed signal is 3 seconds.
Table 1 shows the suppression performance of the beamforming method of the present invention on interference signals, the protection performance on target signals and the total consumption of processing 3s data compared with other beamforming methods. The beamforming filter coefficients are calculated from the superimposed signal of the interference signal and the target signal. And processing the target signal and the interference sound signal respectively by using the beamforming coefficient, and calculating the attenuation of the interference signal and the distortion of the target signal. It can be seen that the calculation is fastest based on fixed beams, but the interference signal attenuation performance is poor; the adaptive beamforming method without interference noise covariance matrix reconstruction has the advantages that the target signal distortion degree is large; the method of the invention has the interference signal inhibition reaching 10.11dB, which is equivalent to the method in Chinese patent CN105182298A, but the total time consumption of treatment is reduced by 97.8%. In this example, the CPU used for the calculation was Intel Xeon processor icelake, the main frequency was 2.6GHz.
TABLE 1
Fig. 3 is a time domain graph of signals before and after applying the beamforming method of the present invention, wherein (a) in fig. 3 is a time domain waveform diagram before beamforming filtering of a target signal, (b) in fig. 3 is a time domain waveform diagram after beamforming filtering of a target signal, (c) in fig. 3 is a time domain waveform diagram before beamforming filtering of an interference signal, and (d) in fig. 3 is a time domain waveform diagram after beamforming filtering of an interference signal; it can be seen that the interfering signal is greatly suppressed after the beamforming filtering of the present invention, while the target signal is substantially protected.
Corresponding to the embodiment of the beamforming method for calculating the covariance matrix based on singular value decomposition, the invention also provides an embodiment of a beamforming method device for calculating the covariance matrix based on singular value decomposition.
Example 2
Referring to fig. 4, a beamforming apparatus for calculating a covariance matrix based on singular value decomposition according to an embodiment of the present invention includes one or more processors configured to implement the beamforming method for calculating a covariance matrix based on singular value decomposition according to embodiment 1.
The beamforming apparatus for calculating covariance matrix based on singular value decomposition according to the present invention may be applied to any device having data processing capability, such as a computer or the like. The apparatus embodiments may be implemented by software, or may be implemented by hardware or a combination of hardware and software. Taking software implementation as an example, the device in a logic sense is formed by reading corresponding computer program instructions in a nonvolatile memory into a memory by a processor of any device with data processing capability. In terms of hardware, as shown in fig. 3, a hardware structure diagram of an apparatus with any data processing capability where a beamforming device for calculating a covariance matrix based on singular value decomposition is located in the present invention is shown in fig. 3, and in addition to a processor, a memory, a network interface, and a nonvolatile memory shown in fig. 3, any apparatus with any data processing capability in the embodiment generally includes other hardware according to an actual function of the any apparatus with any data processing capability, which is not described herein.
The implementation process of the functions and roles of each unit in the above device is specifically shown in the implementation process of the corresponding steps in the above method, and will not be described herein again.
For the device embodiments, reference is made to the description of the method embodiments for the relevant points, since they essentially correspond to the method embodiments. The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purposes of the present invention. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
Example 3
An embodiment of the present invention provides a computer-readable storage medium having stored thereon a program which, when executed by a processor, implements the beamforming method of embodiment 1 that calculates a covariance matrix based on singular value decomposition.
The computer readable storage medium may be an internal storage unit, such as a hard disk or a memory, of any of the data processing enabled devices described in any of the previous embodiments. The computer readable storage medium may be any device having data processing capability, for example, a plug-in hard disk, a Smart Media Card (SMC), an SD Card, a Flash memory Card (Flash Card), or the like, which are provided on the device. Further, the computer readable storage medium may include both internal storage units and external storage devices of any data processing device. The computer readable storage medium is used for storing the computer program and other programs and data required by the arbitrary data processing apparatus, and may also be used for temporarily storing data that has been output or is to be output.
Example 4
As shown in fig. 5, the present embodiment relates to a beamforming system for calculating a covariance matrix based on singular value decomposition, comprising:
the covariance matrix calculation module is used for calculating a covariance matrix of the observation signal based on the observation signal acquired by the sensor array and an exponential smoothing method;
the noise power calculation module is used for carrying out singular value decomposition on the covariance matrix of the observation signal and calculating noise power by utilizing the singular value;
the inverse matrix calculation module of the observed signal covariance matrix calculates an inverse matrix of the observed signal covariance matrix by using the left singular vector matrix, the right singular vector matrix and the singular values;
the interference noise covariance matrix calculation module calculates an interference noise covariance matrix according to the definition of the covariance matrix by utilizing an inverse matrix of the observed signal covariance matrix and a theoretical steering vector of an interference signal;
an interference noise covariance matrix recalculation module that recalculates an interference noise covariance matrix by adding the spherical spread noise covariance matrix and the diagonal load to the calculated interference noise covariance matrix;
the beam enhanced target signal acquisition module calculates a wave beam formed filter coefficient matrix by using the recalculated interference noise covariance matrix and the theoretical steering vector of the target signal and adopting an MVDR method; and obtaining a beam enhanced target signal based on the signal vector received by the sensor array and the filter coefficient matrix.
The embodiments of the present invention are described in a progressive manner, and the same and similar parts of the embodiments are all referred to each other, and each embodiment is mainly described in the differences from the other embodiments. In particular, for system embodiments, since they are substantially similar to method embodiments, the description is relatively simple, as relevant to see a section of the description of method embodiments.
The foregoing is merely exemplary of the present invention and is not intended to limit the present invention. Various modifications and variations of the present invention will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are to be included in the scope of the claims of the present invention.
Claims (10)
1. A beamforming method for calculating a covariance matrix based on singular value decomposition, the method comprising the steps of:
s1, calculating a covariance matrix of an observation signal based on the observation signal acquired by a sensor array and an exponential smoothing method;
s2, singular value decomposition is carried out on a covariance matrix of the observed signal, and noise power is calculated by utilizing the singular value;
s3, calculating an inverse matrix of the covariance matrix of the observation signal by using the left singular vector matrix, the right singular vector matrix and the singular values;
s4, calculating an interference noise covariance matrix according to the definition of the covariance matrix by utilizing an inverse matrix of an observed signal covariance matrix and a theoretical steering vector of an interference signal;
s5, recalculating the interference noise covariance matrix by using the calculated interference noise covariance matrix and adding the spherical expansion noise covariance matrix and the diagonal loading capacity;
s6, calculating a wave beam forming filter coefficient matrix by using the recalculated interference noise covariance matrix and a theoretical steering vector of the target signal and adopting an MVDR method; and obtaining a beam enhanced target signal based on the signal vector received by the sensor array and the filter coefficient matrix.
2. The beamforming method according to claim 1, wherein the formula for calculating the covariance matrix of the observed signal based on the observed signal collected by the sensor array and the exponential smoothing method in step S1 comprises:
Φ y (n,f)＝α 1 Φ y (n-1,f)+(1-α 1 )y(n,f)y H (n,f) (1)
wherein n represents a time frame; f represents frequency; alpha 1 The value range is (0, 1) for the exponential smoothing factor, the larger the value is, the larger the effect of the historical prediction data is, and the smaller the effect of the current actual data is;
y(n,f)＝[Y 1 (n,f) Y 2 (n,f)…Y M (n,f)] T (2)
is an Mx1-dimensional acoustic signal vector; y is Y m (n, f) is the signal observed by the mth sensor; [] T Transpose the conventional matrix; and when n=1, Φ y (0, f) is
Φ y (0,f)＝Γ 0,π (f)+εI M (3)
Wherein I is M Is an M-order identity matrix; epsilon is regularization parameter which changes along with frequency, the value range is (0, 1), and the larger the frequency is, the smaller the value is; Γ -shaped structure 0,π (f) A covariance matrix of spherical diffusion noise, wherein the (i, j) element is:
[Γ 0,π (f)] ij ＝sinc(2πf(j-i)τ 0 ) (4)
wherein τ 0 ＝δ/c 0 Is the time delay of adjacent sensor array elements,delta is the distance between adjacent sensor array elements, c 0 The propagation speed of a physical quantity, sinc (·) is the sampling function.
3. The beamforming method according to claim 1, wherein the step S2 of performing singular value decomposition on the covariance matrix of the observed signal, and estimating the noise power using the singular values comprises:
observed signal covariance matrix Φ for current time frame y (n, f) singular value decomposition:
Φ y (n,f)＝USV H (5)
wherein U and V are respectively a left singular vector matrix and a right singular vector matrix, which are M multiplied by M unitary matrices; s is a diagonal matrix, and diagonal elements of the diagonal matrix are singular values arranged from large to small; [] H Is the conjugate transpose of the matrix;
calculating the power of noise Is the average of the smallest (M- (j+d)) singular values, where J is the total number of interfering signals and D is the number of target signals.
4. The beamforming method according to claim 1, wherein the calculating the inverse matrix of the covariance matrix of the observed signal using the left singular vector matrix, the right singular vector matrix, and the singular values in step S3 comprises:
wherein S is -1 Is obtained by inverting the diagonal element of S.
5. The beamforming method according to claim 1, wherein the calculating the interference noise covariance matrix according to the definition of the covariance matrix by using the inverse matrix of the observed signal covariance matrix and the theoretical steering vector of the interference signal in step S4 comprises:
calculating the power of the jth interfering signalThe formula of (2) is as follows:
wherein d is H (Θ j F) is the theoretical steering vector of the j-th interference signal, Θ j The incoming wave direction vector of the j-th interference signal; in the three-dimensional spherical coordinate system of the system,θ j and phi j Pitch angle and azimuth angle respectively;
calculating interference noise covariance matrix phi according to the definition of covariance matrix ξ The formula of (2) is as follows:
6. the beamforming method according to claim 1, wherein the formula for recalculating the interference noise covariance matrix using the calculated interference noise covariance matrix in step S5, adding the spherical spread noise covariance matrix and the diagonal load is as follows:
Φ ε (n,f)＝α 2 Φ ξ (n,f)+(1-α 2 )Φ y (0,f) (9)
wherein alpha is 2 For diagonally loading the weight factor, the value range is (0, 1), and the larger the value is, the more sensitive the value is to the change of the signal.
7. The beamforming method according to claim 1, wherein the process of calculating a filter coefficient matrix for beamforming by using the interference noise covariance matrix and the theoretical steering vector of the target signal in step S6 and using the MVDR method, and obtaining the target signal for beam enhancement based on the signal vector and the filter coefficient matrix received by the sensor array comprises:
the formula for calculating the beamforming filter coefficients is as follows:
wherein d (Θ) s F) is the theoretical steering vector of the target signal, Θ s The incoming wave direction of the target signal;
the formula for performing beam enhancement filtering calculation on the signals received by the sensor is as follows:
z(n,f)＝w H (n,f)y(n,f) (11)
and multiplying the frequency domain signal z (n, f) after beam enhancement of each frame by a self-defined window function, and performing inverse Fourier transform to obtain a time domain target signal after beam enhancement.
8. A beamforming system for calculating a covariance matrix based on singular value decomposition, comprising:
the covariance matrix calculation module is used for calculating a covariance matrix of the observation signal based on the observation signal acquired by the sensor array and an exponential smoothing method;
the noise power calculation module is used for carrying out singular value decomposition on the covariance matrix of the observation signal and calculating noise power by utilizing the singular value;
the inverse matrix calculation module of the observed signal covariance matrix calculates an inverse matrix of the observed signal covariance matrix by using the left singular vector matrix, the right singular vector matrix and the singular values;
the interference noise covariance matrix calculation module calculates an interference noise covariance matrix according to the definition of the covariance matrix by utilizing an inverse matrix of the observed signal covariance matrix and a theoretical steering vector of an interference signal;
an interference noise covariance matrix recalculation module that recalculates an interference noise covariance matrix by adding the spherical spread noise covariance matrix and the diagonal load to the calculated interference noise covariance matrix;
the beam enhanced target signal acquisition module calculates a wave beam formed filter coefficient matrix by using the recalculated interference noise covariance matrix and the theoretical steering vector of the target signal and adopting an MVDR method; and obtaining a beam enhanced target signal based on the signal vector received by the sensor array and the filter coefficient matrix.
9. Beamforming apparatus for calculating a covariance matrix based on singular value decomposition, comprising one or more processors configured to implement the beamforming method of any of claims 1-7 based on singular value decomposition.
10. A computer readable storage medium, having stored thereon a program which, when executed by a processor, is adapted to carry out the beamforming method of any one of claims 1-7 for calculating a covariance matrix based on singular value decomposition.
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