CN110109058B - Planar array deconvolution sound source identification method - Google Patents

Planar array deconvolution sound source identification method Download PDF

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CN110109058B
CN110109058B CN201910366448.8A CN201910366448A CN110109058B CN 110109058 B CN110109058 B CN 110109058B CN 201910366448 A CN201910366448 A CN 201910366448A CN 110109058 B CN110109058 B CN 110109058B
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sound source
vector
distribution
planar array
matrix
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CN110109058A (en
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吴桂娇
李智
余立超
徐福健
王平
褚志刚
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Chongqing University
Hunan Aviation Powerplant Research Institute AECC
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Hunan Aviation Powerplant Research Institute AECC
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
    • G01S5/20—Position of source determined by a plurality of spaced direction-finders

Abstract

The invention discloses a method for identifying a planar array deconvolution sound source, which comprises the following steps: 1. calculating a traditional beam forming output result; 2. establishing an equation set between a beam forming output result and sound source distribution; 3. and (3) iteratively solving the sound source distribution, wherein in the step, a source intensity distribution solving method suitable for the planar array is constructed by combining a sound source identification problem on the basis of generalized sparsity adaptive matching pursuit gSAMP. The invention has the technical effects that: the invention has high spatial resolution, can effectively remove side lobes, accurately positions each sound source, has positioning precision superior to that of the prior OMP-DAMAS method, and does not need prior knowledge of the sparsity of sound source signals.

Description

Planar array deconvolution sound source identification method
Technical Field
The invention belongs to the technical field of sound field identification, and particularly relates to a sound source identification method of a planar array.
Background
A sound source identification method based on beam forming of a microphone array can reliably identify a sound source, and has been widely used, among which The deconvolution imaging method for The mapping of acoustic sources (DAMAS) is The most classic. The documents "Orthogonal matching pursuit to the decoding of the acoustic source inverse [ J ]", Padois T, Berry a, Journal of the acoustic source of America,2015,138(6) ("Orthogonal matching pursuit is applied to the deconvolution acoustic source imaging inverse problem [ J ]", Padois T, Berry a, american acoustics, 2015,138(6): 3678.) propose the OMP-dam method, applying an Orthogonal matching pursuit algorithm (Orthogonal matching pursuit, OMP) to the solution of the inverse problem of deconvolution acoustic source imaging, improving the recognition performance of the deconvolution method, OMP selecting only one column of the most correlated residuals, i.e. the true columns of the acoustic source, to reconstruct the original signal to the mas. However, the existing OMP-DAMAS method requires a priori knowledge of the sparsity of the sound source (the a priori knowledge means that the number of noise sources needs to be determined in advance, and the number of iterations is determined according to the number, but the number is not easy to be determined in practical application), and when a multi-sound source is identified, a target column is easy to be mistakenly selected as a column adjacent to the target column, so that the identification accuracy is deteriorated, and the positioning is deviated.
Disclosure of Invention
Aiming at the problems in the prior art, the technical problem to be solved by the invention is to provide a planar array deconvolution sound source identification method, which does not use the prior knowledge of the sparsity of sound source signals and can improve the positioning accuracy of the sound source.
The technical problem to be solved by the invention is realized by the technical scheme that the technical scheme comprises
Step 1, calculating the output result of the traditional beam forming
The calculation of the beamforming output is:
Figure BDA0002048362570000011
wherein C ═ Σr′C(r′)＝∑r′q(r′)v*(r′)vT(r') is a full cross-spectrum matrix in the frequency domain;
r ' is a sound source position vector, q (r ') is the source intensity at r ', and superscripts T and x respectively represent transposition and conjugation; v ═ vm(r)]A steering column vector, v, representing the focus point rm(r) denotes a steering vector of the mth microphone; l is a matrix with all elements 1, w [ | v [ ]m|]2；
Step 2, establishing an equation set between a beam forming output result and sound source distribution
b＝Aq
Where b ═ b (r) is an N-dimensional beamforming output column vector, and N is the number of grid points; a ═ psf (r | r') ] is a point spread function matrix of dimension N × N; q is an N-dimensional sound source distribution column vector;
step 3, iterative solution of sound source distribution
1) 1, the initialization t, and the residual rt-1B, supporting set
Figure BDA0002048362570000021
Matrix Λt-1＝0；
2) Calculating the correlation coefficient h ═ AHrt-1The superscript H denotes the transpose conjugate, and the indices corresponding to the first S elements of the absolute value in H are chosen as { λ }i}i＝1,2…S；
3) Let gamma bet＝Γt-1∪{λi}i＝1,2…S(ii) a Calculating a least squares solution:
Figure BDA0002048362570000022
θtis an N-dimensional source intensity distribution estimation vector to be solved,
Figure BDA0002048362570000023
according to gammatThe included indexes select an intermediate matrix constructed by corresponding columns in the propagation function matrix A;
4) find index
Figure BDA0002048362570000024
An index of a sound source distribution vector;
5) let Jt＝Jt-1∪μ，Λt＝Λt-1∪aμ，aμThe μ th column vector of A; updating the source intensity distribution estimation again:
Figure BDA0002048362570000025
6) updating residual error vector
Figure BDA0002048362570000026
7) If | rt‖2>E, enabling t to be t +1, returning to the step 2), and otherwise, outputting a result;
8) obtaining the estimated value q of the sound source distribution vector at JtHas a non-zero value of JtIs the final index set with a value of
Figure BDA0002048362570000027
Preferably, in step 3, 2), the parameter S is S < D and S < M/D, D is the number of sound sources, and M is the number of microphones.
Preferably, in step 3, 7), ε is selected to be 10-3To 10-6A value within the range.
The invention has the technical effects that:
the invention constructs a deconvolution sound source identification method suitable for a planar array on the basis of generalized sparsity adaptive matching pursuit. According to simulation and experimental verification: the invention has high spatial resolution, can effectively remove side lobes, accurately positions each sound source, has positioning precision superior to that of the prior OMP-DAMAS method, does not need prior knowledge of the sparsity of sound source signals, and has overall performance superior to that of the OMP-DAMAS method.
Drawings
The drawings of the invention are illustrated as follows:
FIG. 1 is a planar array sampling model of the present invention;
FIG. 2 is a flow chart of an iterative solution algorithm of the present invention;
FIG. 3 is a diagram of the sound source identification effect of the simulation of the present invention and OMP-DAMAS;
FIG. 4 is a graph of experimental identification imaging of the invention and OMP-DAMAS.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
the invention comprises the following steps:
step 1, calculating the output result of the traditional beam forming
As shown in fig. 1, assuming that sound sources to be measured all fall on a known sound source plane, a microphone plane array is located right in front of the sound source plane, and a sound pressure signal received by a microphone is changed into a full cross-spectrum matrix C in a frequency domain after being subjected to inverse fourier transform, which is expressed by the following formula:
C＝∑r′C(r′)＝∑r′q(r′)v*(r′)vT(r′) (1)
in the formula (1), r ' is a sound source position vector, q (r ') is the source intensity at the position of r ', and superscripts T and x respectively represent transposition and conjugation; v ═ vm(r)]A steering column vector, v, representing the focus point rm(r) denotes a steering vector of the mth microphone, which is expressed as follows:
Figure BDA0002048362570000031
in the formula (2), the reaction mixture is,
Figure BDA0002048362570000032
denotes a complex unit, k ═ 2 π f/c denotes a wave number, f denotes an acoustic frequency, and c denotes a wave velocity. r denotes the location vector from the center of the array to the focal point, rmRepresenting the location vector from the center of the array to the mth microphone.
According to the document "four typical beam forming sound source identification and clarification methods [ J ]", Yangye, Church, data collection and processing, 2014,29(2): 316-:
Figure BDA0002048362570000033
in formula (3), l is a matrix in which all elements are 1, and w [ | v [ ]m|]2。
Step 2, establishing an equation set between a beam forming output result and sound source distribution
Substituting formula (1) for formula (3) to obtain:
Figure BDA0002048362570000041
in equation (4), psf (r | r ') is called an array point propagation function, and indicates a contribution amount of a point sound source having unit source intensity to beam-forming sound pressure generated at the r position when only the point sound source exists at the r' position, and when r 'is r', psf is 1. It can be seen that the output quantity of the beam forming at the r position can be expressed as the sum of the beam forming sound pressure contribution of each sound source point at the point multiplied by the corresponding source intensity, and a linear equation set among the beam forming output result, the array point propagation function and the sound source distribution is constructed according to the deconvolution algorithm:
b＝Aq (5)
in formula (5), b ═ b (r) is an N-dimensional beamforming output column vector, and N is the number of mesh points; a ═ psf (r | r') ] is a point spread function matrix of dimension N × N; q is an N-dimensional sound source distribution column vector; where A, b is known and q is unknown.
For equation (5), the existing DAMAS method adopts the gaussian seidel iteration method to solve the sound source intensity distribution, and OMP-DAMAS reconstructs q by an orthogonal matching pursuit algorithm by using the sparse characteristic of the sound source distribution vector.
Step 3, iterative solution of sound source distribution
In the literature, "generalized sparsity adaptive matching pursuit algorithm for CS [ J/OL]"Mayushuang, Liu Cui Xiang, Guo Shitao, Wangbaozhu, computer engineering and application (first network thesis, release address ishttp://kns.cnki.net/kcms/ detail/11.2127.TP.20181115.1637.006.htmlAnd the network initial date is 2018-11-19), on the basis of the generalized sparsity adaptive matching pursuit gSAMP, in combination with the sound source identification problem, the iterative solving process of the invention is shown in FIG. 2, and the steps are as follows:
1) 1, the initialization t, and the residual rt-1B, supporting set
Figure BDA0002048362570000042
Matrix Λt-1＝0；Λt-1Is a matrix with elements of 0, and Γ and J are both empty sets/matrices, which are intermediate quantities in the iterative process.
2) Calculating the correlation coefficient h ═ AHrt-1The superscript H denotes the transpose conjugate, and the indices corresponding to the first S elements of the absolute value in H are chosen as { λ }i}i＝1,2…S；
3) Let gamma bet＝Γt-1∪{λi}i＝1,2…S(ii) a Calculating a least squares solution:
Figure BDA0002048362570000043
θtis an N-dimensional source intensity distribution estimation vector to be solved,
Figure BDA0002048362570000044
according to gammatThe included indexes select an intermediate matrix constructed by corresponding columns in the propagation function matrix A;
this equation represents solving for a vector θtSo that
Figure BDA0002048362570000051
To a minimum (b and
Figure BDA0002048362570000052
known), the calculation result is
Figure BDA0002048362570000053
θtIt is in fact an unknown in the equation.
Figure BDA0002048362570000054
Is calculated as a pair oftAn estimate of (d).
4) Find index
Figure BDA0002048362570000055
An index of a sound source distribution vector;
5) let Jt＝Jt-1∪μ，Λt＝Λt-1∪aμ，aμThe μ th column vector of A; updating the source intensity distribution estimation again:
Figure BDA0002048362570000056
6) updating residual error vector
Figure BDA0002048362570000057
7) If | rt‖2>E, enabling t to be t +1, returning to the step 2), and otherwise, outputting a result;
8) obtaining the estimated value q of the sound source distribution vector at JtHas a non-zero value of JtIs the final index set with a value of
Figure BDA0002048362570000058
Each iteration is at JtThis set is added with a new index, which can be regarded as the sound source coordinates, i.e. JtIs the set of coordinates that ultimately identifies all sound sources.
The above-mentioned iterative formula involves the selection of two parameters S and epsilon; wherein S is the number of atoms selected in each iteration, and compared with the selection of OMP-DAMAS single atoms (the atoms refer to columns in a point spread function matrix, namely S is always 1), the probability of successfully recovering the original signal can be effectively improved by increasing the number of the atoms selected in each iteration. A recommended formula (S < D and S < M/D) is given for the selection of the parameter S in the method, D is the number of sound sources, and M is the number of microphones. In practical application, S only needs to be a small integer (e.g. 2) greater than 1 to achieve the effect of improving the sound source positioning accuracy.
Epsilon is a threshold value for stopping iteration when residual error rtWhen the 2 norm is attenuated to a certain value, the original signal can be approximated by the selected atomsLike a sparse representation. When epsilon is selected to be a large value, iteration can be quickly stopped after a main sound source is found; when epsilon is selected to be smaller, iteration can be stopped after finding a secondary sound source, and 10 is generally selected-3To 10-6A value within the range.
Simulation test
In order to verify the accuracy of the method, the method is compared with OMP-DAMAS, the performance improvement of the method is explored, and sound source identification simulation is carried out.
At a specific position, a point sound source of radiation intensity and frequency sound wave is set, a plane area 2m × 2m in front is identified by an array, the sound source plane is 1m away from the array, and the sound source plane is discretized into 21 × 21 grid points. The simulation assumes that the sound source is 6 incoherent monopole point sound sources, the coordinates of which are (-0.6,0,1), (0.6,0,1), (-0.2,0.5,1), (0.2,0.5,1), (-0.2, -0.5,1), (0.2, -0.5,1) m, the imaging results of the sound source under the conditions of 2000Hz, 4000Hz and 6000Hz are respectively calculated, the effective sound pressure is 0.02Pa, the corresponding sound pressure level is 60dB, the cross-spectrum matrix of the sound pressure signals received by each microphone is calculated according to the formula (1) in the forward direction, and Gaussian white noise with the signal-to-noise ratio of 10dB is added; and setting a focusing sound source plane, reconstructing sound source intensity distribution and imaging respectively based on the OMP-DAMAS and the method. Wherein OMP-DAMAS sets the iteration number to be 6 according to the prior knowledge. The method sets the maximum iteration times to be 20 times, takes S to be 4 and epsilon to be 10-6. The imaging result is converted in decibels with reference to the reference sound pressure, and the display dynamic range is set to be 10 dB.
The effect of the simulation is shown in fig. 3, where the position of the real sound source is marked by a white cross in fig. 3, and the position of the sound source is indicated by a high-amplitude black dot as the "main lobe".
As can be seen from FIG. 3, OMP-DAMAS has two sources whose locations deviate at a source frequency of 2000Hz, and at a source frequency of 6000Hz, OMP-DAMAS loses one source and reconstructs a virtual pseudolobe at a non-source location. The method accurately positions the sound source position under three frequencies, and obtains a clear sound source imaging image.
Verification test
For testing artificial junctionsAnd if the result is correct, taking the loudspeaker excited by the steady-state signal as a sound source to carry out experimental verification. By using
Figure BDA0002048362570000061
A 36 channel Combo array of company, 0.65m array diameter, integrated 4958 microphone samples the sound pressure signal. Sound pressure signals received by the microphones are simultaneously acquired by a PULSE 3560D type data acquisition system and transmitted to a PULSE LABSHOP for spectrum analysis to obtain a cross-spectrum matrix of the sound pressure signals, the sampling frequency is set to be 16384Hz, a Hanning window is added to the signals, an average of 64 sections and a 66.7% overlapping rate are adopted, the time length of each section is 0.25s, and the corresponding frequency resolution is 4 Hz.
The sound pressure signals are sampled by the array, frequency domain signals with the frequency of 2000Hz are extracted and are led into a post-processing program written by MATLAB for imaging, and FIG. 4 is an identification imaging graph of a sound source of a test loudspeaker.
As seen from FIG. 4, the position of a sound source in the OMP-DAMAS imaging graph deviates from a grid point, the method accurately identifies the positions of four loudspeakers, and the method improves the positioning accuracy of the sound source.

Claims (3)

1. A planar array deconvolution sound source identification method comprises the following steps,
step 1, calculating the output result of the traditional beam forming
The calculation of the beamforming output is:
Figure FDA0002048362560000011
wherein C ═ Σr′C(r′)＝∑r′q(r′)v*(r′)vT(r') is a full cross-spectrum matrix in the frequency domain;
r ' is a sound source position vector, q (r ') is the source intensity at r ', and superscripts T and x respectively represent transposition and conjugation; v ═ vm(r)]A steering column vector, v, representing the focus point rm(r) denotes a steering vector of the mth microphone; l is a matrix with all elements 1，w＝[|vm|]2；
Step 2, establishing an equation set between a beam forming output result and sound source distribution
b＝Aq
Where b ═ b (r) is an N-dimensional beamforming output column vector, and N is the number of grid points; a ═ psf (r | r') ] is a point spread function matrix of dimension N × N; q is an N-dimensional sound source distribution column vector;
the method is characterized in that:
step 3, iterative solution of sound source distribution
1) 1, the initialization t, and the residual rt-1B, supporting set
Figure FDA0002048362560000016
Matrix At-1＝0；
2) Calculating the correlation coefficient h ═ AHrt-1The superscript H denotes the transpose conjugate, and the indices corresponding to the first S elements of the absolute value in H are chosen as { λ }i}i＝1，2...S；
3) Let gamma bet＝Γt-1∪{λi}i＝1，2...S(ii) a Calculating a least squares solution:
Figure FDA0002048362560000012
θtis an N-dimensional source intensity distribution estimation vector to be solved,
Figure FDA0002048362560000013
according to gammatThe included indexes select an intermediate matrix constructed by corresponding columns in the propagation function matrix A;
4) find index
Figure FDA0002048362560000014
An index of a sound source distribution vector;
5) let Jt＝Jt-1∪μ，At＝At-1∪aμ，aμThe μ th column vector of A; updating the source intensity distribution estimation again:
Figure FDA0002048362560000015
6) updating residual error vector
Figure FDA0002048362560000021
7) If rt||2If the value is more than epsilon, making t equal to t +1 return to the step 2), otherwise, outputting the result;
8) obtaining the estimated value q of the sound source distribution vector at JtHas a non-zero value of JtIs the final index set with a value of θt。
2. The planar array deconvolution sound source identification method of claim 1, wherein: in step 3, 2), the parameters S are S < D and S < M/D, D is the number of sound sources, and M is the number of microphones.
3. The planar array deconvolution sound source identification method of claim 1 or 2, characterized by: in step 3 7) above, ε is selected to be 10-3To 10-6A value within the range.
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