CN109870669A - How soon a kind of two dimension claps mesh free compression Wave beam forming identification of sound source method - Google Patents
How soon a kind of two dimension claps mesh free compression Wave beam forming identification of sound source method Download PDFInfo
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Abstract
The invention discloses a kind of two dimensions how soon to clap mesh free compression Wave beam forming identification of sound source method, comprising the following steps: step 1 obtains measurement acoustic pressure matrix P★；Step 2, iteration are sought acoustic pressure P:1, are solved using the SDPT3 solver in the tool box CVX of MATLAB:2, the l+1 times rule of iteration parameter κ is determinedl+1；3, the weight matrix W that the l+1 times iteration determinesl+1；When iteration twice in successionBetween relative variation be less than or equal to 10‑3Or maximum number of iterations is when being completed, iteration ends；Step 3, estimation sound source DOA；Step 4, estimation strength of sound source.The present invention can accurately estimate the lesser DOA of sound source distance, and can quantitatively obtain the intensity of sound source, improve resolution ratio, denoising ability and identification of sound source precision.
Description
Technical field
The invention belongs to sound field identification technology fields.
Background technique
Compression Wave beam forming based on plane Microphone array measurement is to realize sound source 2-d direction finding (Direction-
Of-arrival, DOA) estimation and strength quantifies effective way.Conventional compression Wave beam forming assume sound source be distributed in one group it is pre-
On the discrete grid block point being first arranged, each mesh point represents an observed direction, applies sparse constraint and is presented as minimum sound source
Distribution vectorNorm.When above-mentioned hypothesis is invalid, reconstruction result inaccuracy, the problem is referred to as base mismatch, in reality
Often occur in.
Fundamentally to solve the problems, such as this, two-dimentional single snap is successively developed and how soon has clapped mesh free compression Wave beam forming plan
Slightly, compared to single snap, how soon shooting method is more steady, but existing based on atom norm minimum (Atomic Norm
Minimization, ANM) two dimension how soon clap mesh free compression Wave beam forming identification of sound source exist it is smaller to sound source distance
Generate the defect of failure.
Summary of the invention
In view of the problems of the existing technology, the technical problem to be solved by the invention is to provide a kind of two dimensions how soon to clap
Mesh free compresses Wave beam forming identification of sound source method, it can be improved resolution ratio, be gone using iteration weight weighted atom norm minimum
Noise immune and identification of sound source precision.
The technical problem to be solved by the present invention is in this way technical solution realize, it comprising steps of
Step 1 obtains measurement acoustic pressure matrix P★；
Measure acoustic pressure matrixAre as follows:
P★=P+N
Measure acoustic pressure matrix P★It is obtained by Microphone array measurement,For noise jamming,For set of complex numbers, A
For the line number of rectangle microphone array, B is the columns of rectangle microphone array, and L is snap number；
The acoustic pressure P that step 2, reconstruct sound source generate at array microphone；
Step 1), the mathematical model for establishing reconstruct P
In formula,It is the formula calculated result, | | | |FIndicating Frobenius norm, P is acoustic pressure matrix to be asked,
Define Tb() is double Toeplitz operator, and the block Toeplitz type of A × A dimension is mapped as to any given vector u
Hermitian matrix:
Tb(u) in, each piece of Ta(0≤a≤A-1) is all the Toeplitz matrix of B × B dimension:
It is all auxiliary quantity, κ > 0 is regularisation parameter,For unit matrix, " tr () " indicates to seek the mark of matrix, and subscript " H " indicates conjugate transposition, and " >=0 " indicates partly just
It is fixed；
Step 2) solves P
Initializationκ0=1, then W0=I, the result based on the l times iterationκl, the step of the l+1 times iteration
Are as follows:
1. being solved using the SDPT3 solver in the tool box CVX of MATLAB:
2. determining regularisation parameter κl+1:
ForMaximum eigenvalue；
3. the weight matrix W that the l+1 times iteration determinesl+1:WhenLess than or equal to 10-3Or maximum number of iterations is when being completed, iteration ends；
Step 3, estimation sound source DOA；
Step 4, estimation strength of sound source.
The solution have the advantages that:
The present invention can accurately estimate the lesser DOA of sound source distance, and can quantitatively obtain the intensity of sound source, overcome existing
Have how soon the two dimension of ANM claps the defect of mesh free compression Wave beam forming, improves resolution ratio, denoising ability and identification of sound source essence
Degree.
Detailed description of the invention
Detailed description of the invention of the invention is as follows:
Fig. 1 is Microphone array measurement layout；
The emulation reconstruction result comparison diagram that Fig. 2 is frequency of source when being 2000Hz, 3000Hz, 4000Hz and 4900Hz；
Fig. 2 (a), (c), (e), (g) are ANM；Fig. 2 (b), (d), (f), (h) are the present invention；
Fig. 3 is the reconstruction accuracy of acoustic pressure P, the estimated accuracy of sound source DOA and strength of sound source of the present invention and existing ANM
Quantified precision curve comparison figure；
Fig. 3 (a)With ΔminChange curve；
Fig. 3 (b)With ΔminChange curve；
Fig. 3 (c)With ΔminChange curve；
Fig. 4 is test layout；
The experiment Reconstruction of Sound Field Comparative result that Fig. 5 is frequency of source when being 2000Hz, 3000Hz, 4000Hz and 4900Hz
Figure；
Fig. 5 (a), (c), (e), (g) are ANM；Fig. 5 (b), (d), (f), (h) are the present invention.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples:
The present invention the following steps are included:
Step 1 obtains measurement acoustic pressure matrix P★
Two-dimentional mesh free compression Wave beam forming identification of sound source is to utilize rectangle Microphone array measurement acoustical signal.Such as Fig. 1 institute
Show Microphone array measurement layout, symbol "●" indicate microphone, a=0,1 ..., A-1, b=0,1 ..., B-1 be respectively x,
The microphone index of y dimension, Δ x, Δ y are respectively the microphone interval of x, y dimension, θi、φiRespectively the elevation angle of i bugle call source DOA and
Azimuth (0 °≤θ≤90 °, 0 °≤φ≤360 °).NoteI bugle call source is taken fastly to be each
Intensity (acoustic pressure that sound source generates at (0,0) number microphone) composition row vector, l=1,2 ..., L be snap index, si,l
Take the intensity in i bugle call source fastly for l,For set of complex numbers.
Assuming that sound source radiation plane sound wave, wavelength λ, t1i≡sinθi cosφiΔ x/ λ, t2i≡sinθi sinφiΔ
Y/ λ, then each sound source that takes fastly generates the row vector that acoustic pressure forms at (a, b) number microphoneIt may be expressed as:
In formula (1), k is sound source sum,For imaginary unit.
Construct matrix:
Column vectorScalarRow vectorWherein, subscript " T " indicates transposition, symbolIndicate Kronecker
Product, " | | | |2" indicateNorm,Be positive set of real numbers, | | ψi||2=1, it is corresponding with formula (1), have:
There are noise jammingsWhen, measure acoustic pressure matrixIt may be expressed as:
P★=P+N (3)
In l-G simulation test, addition noise is independent same distribution white Gaussian noise, signal-to-noise ratio (Signal-to-noise
Ratio, SNR) it is defined as SNR=20log10(||P||F/||N||F), thus can determine | | N | |F=| | P | |F10-SNR/20,
In, " | | | |F" indicate Frobenius norm.
When experimental test,It is obtained by Microphone array measurement.
The acoustic pressure P that step 2, reconstruct sound source generate at array microphone
Step 1), the mathematical model for establishing reconstruct P
The first step how soon two dimension claps mesh free compression Wave beam forming post-processing is to filter out measurement acoustic pressure P★In noise, again
The acoustic pressure P that structure sound source generates at array microphone, the step are realized by applying sparse constraint to sound source.It is sparse to establish source
The measurement of property:
In formula (4),It is the function about P,All it is
Auxiliary quantity, κ > 0 are regularisation parameter,For unit matrix, " tr () " indicates to ask the mark of matrix, subscript " H " table
Show conjugate transposition, " >=0 " indicates positive semidefinite.
Define Tb() is double Toeplitz operator, and the block Toeplitz of A × A dimension is mapped as to any given vector u
Type Hermitian matrix:
In formula (5), each piece of Ta(0≤a≤A-1) is all the Toeplitz matrix of B × B dimension:
The reconstruction of P is writeable are as follows:
In formula (7), ε is noise control parameter, is usually taken to be | | N | |F。
Joint type (4), (7) can obtain:
In formula (8),Indicate calculated result, P is acoustic pressure matrix to be asked.
How soon existing ANM two dimension claps the atom norm that mesh free compression Wave beam forming identification of sound source method uses P
Sound source sparsity is measured, the reconstruction of P is writeable are as follows:
For convex function, which is convex optimization problem, can be converted into after following semi definite programming using in the tool box CVX
SDPT3 solver solve:
When separating smaller between sound source, how soon existing ANM two dimension, which claps mesh free compression Wave beam forming, to obtain because of above formula
'sIt is unable to high probability accurately and includes sound source DOA information or reliably fail to the prediction of sound source number is unstable.
Step 2) solves P using present method invention
NoteκlThe optimal solution and regularisation parameter determined for the l times iteration,The weight matrix that the l times iteration determines, the alternative functions formula of the l+1 times iteration are as follows:
In formula (9),It isThe tangent plane at place, cl
For the constant unrelated with variable.Ignore cl, the minimization problem of the l+1 times iteration is writeable are as follows:
Formula (10) is convex optimization problem, can be solved with the SDPT3 solver in the tool box CVX.
Initializationκ0=1, then W0=I, it is sparse to enhance, it enables κ be gradually reduced in an iterative process, becomes as the following formula
Change:
In formula (11),ForMaximum eigenvalue, l is the number of iterations.
Therefore, it initializesκ0=1, then W0=I, the result based on the l times iterationκl, the l+1 times iteration
Step are as follows:
1. being solved using the SDPT3 solver in the tool box CVX of MATLAB:
2. determining regularisation parameter κl+1:
ForMaximum eigenvalue；
3. the weight matrix W that the l+1 times iteration determinesl+1:When changing twice in succession
GenerationRelative variation, i.e.,Less than or equal to 10-3Or maximum number of iterations is when being completed, iteration
It terminates, maximum number of iterations is selected as 20.
Step 3, estimation sound source DOA；
How soon the operation of the step claps mesh free compression Wave beam forming identification of sound source method phase with prior art ANM two dimension
Together.Bibliography Z.Yang, L.Xie, P.Stoica.Vandermonde decomposition of multilevel
Toeplitz matrices with application to multidimensional super-resolution[J]
.IEEE Transactions on Information Theory, 2016,62 (6): 3685-3701. (" multiple Toeplitz
The Vandermonde of matrix decomposes and its application [J] ", Yang, Xie Lihua, P.Stoica, " IEEE in multidimensional super-resolution
Information Theory ", 2016,62 (6): 3685-3701).
Obtain sound source numberAnd sound source
Step 4, estimation strength of sound source；
NoteFor the perception calculated according to the sound source DOA of estimation
Matrix,For the matrix that each intensity for taking each sound source fastly of quantization is constituted, obtained according to formula (2)
The calculating formula of strength of sound source:
In formula, A is perception matrix, and subscript "+" indicates pseudoinverse,To use present invention iterative solution gained acoustic pressure.
Analogue simulation test
Accuracy and the raising for comparing its performance of the invention are established to verify, carries out identification of sound source analogue simulation.
Emulation be provided that specific position assume have certain strength radiation specific frequency sound wave point sound source (assuming that
Six sound sources, the elevation angle are followed successively by 60 °, 60 °, 50 °, 40 °, 30 °, 70 °, azimuth be followed successively by 180 °, 190 °, 90 °, 90 °,
200 °, 300 °, intensity (root mean square:) be followed successively by 100dB, 97dB, 97dB, 94dB, 94dB, 90dB (with reference to 2 ×
10-5Pa))。
Emulate detailed process are as follows:
1, each microphone is calculated according to formula (2) and formula (3) and receives sound pressure signal (with A=B=8, Δ x=Δ y=0.035m
Microphone array measurement acoustical signal, Signal to Noise Ratio (SNR) takes 20dB, 10) snap sum is set as；
2, acoustic pressure is iteratively solved according to the present method invention of step 2
3, sound source DOA is estimated according to step 3；
4, strength of sound source is estimated according to step 4.
Present method invention is compared with the result of ANM method, as shown in Fig. 2, the frequency of sound source radiation sound wave: Fig. 2
(a) and Fig. 2 (b) is 2000Hz, and it is 4000Hz that Fig. 2 (c), which is 3000Hz, Fig. 2 (e) and Fig. 2 (f) with figure (d),；Fig. 2 (g) and Fig. 2
It (h) is 4900Hz；In every width figure, " * " indicates reconstruct sound source distribution, and "○" indicates real sources distribution, and is convenient for comparison, respectively
DB scaling is carried out with reference to maximum output value in figure, display dynamic range is 0~-20dB, meanwhile, the top of every width figure also arranges
Go out with standard sound pressure size 2.0 × 10-5Pa is the maximum output value of reference.Under 2000Hz, 3000Hz, 4000Hz, 4900Hz,
Minimum separation between sound sourceBe followed successively by 0.025,0.038,0.050,
0.062。
As seen from Figure 2: how soon clapping mesh free compression Wave beam forming (Fig. 2 (a), Fig. 2 (c), Fig. 2 using the two dimension of ANM
(e), Fig. 2 (g)) only accurate reconstruction 4900Hz when sound source distribution, and compressed using how soon two dimension of the invention claps mesh free
The reconstruction result of Wave beam forming (Fig. 2 (b), Fig. 2 (d), Fig. 2 (f), Fig. 2 (h)) under four frequencies is accurate, so proving: this
Invention overcomes the defect of ANM, has higher resolution.
Definition standard Frobenius norm errorAverage Frobenius norm errorAnd standardNorm errorCome measure the reconstruction accuracy of P, sound source DOA estimates
Count the quantified precision of precision and strength of sound source, whereinIt is constituted for estimation the and true sound source elevation angle
Column vector,For estimation and true sound bearing angle constitute column vector,For
The column vector that the root mean square of quantization and true strength of sound source is constituted.Error amount is smaller, and precision is higher, and calculated result is more accurate
As seen from Figure 3: compared with using the two dimension of ANM how soon to clap mesh free compression Wave beam forming, the present invention has
Stronger denoising ability and better resolution ratio can more accurately reconstruct acoustic pressure that sound source generates at array microphone, more
Accurately estimate the DOA for separating lesser sound source to each other and quantifies its intensity.
Verification experimental verification
To examine the correctness of emulation conclusion and being formed in reality using how soon two dimension of the invention claps mesh free compression wave beam
Validity and superiority in the application of border, carry out verification test.
Fig. 4 is test layout, and measurement array is64 4958 type microphones of company are equally distributed
Rectangular array (A=B=8, Δ x=Δ y=0.035m), sound source are 3 loudspeakers of stationary white noise signal excitation, Cong Zuozhi
The right side, cartesian coordinate are followed successively by (2.24,0,5) m, (- 1.24,0,5) m, (- 2.24,0,5) m, the elevation angle be followed successively by 24.13 °,
13.93 °, 24.13 °, azimuth are followed successively by 0 °, 180 °, 180 °, carry out in semianechoic room due to testing, and ground has reflection,
For loudspeaker about ground there is also 3 mirror image sound sources, cartesian coordinate is followed successively by (2.24, -2.2,5) m, (- 1.24, -2.2,5)
M, (- 2.24, -2.2,5) m, the elevation angle are followed successively by 32.13 °, 26.80 °, 32.13 °, azimuth be followed successively by 315.52 °, 240.59 °,
224.48°.The acoustic pressure that each microphone measures is through PULSE 3560D type data collection system while acquiring and being transferred to PULSE
Fast Fourier Transform (FFT) is carried out in LABSHOP, obtains acoustic pressure frequency spectrum, the long 1s of each snap, sample frequency 16384Hz includes 214
A sampled point, 10 snaps are used.Further, using ANM (based on pencil of matrix and pairing) and present invention post-processing acoustic pressure frequency
Spectrum is distributed to reconstruct sound source, remaining setting is consistent with emulation.
It is 2000Hz, 3000Hz, 4000Hz and 4900Hz as a result, in every width figure that Fig. 5, which gives frequency of source, and " * " refers to
Show reconstruct sound source distribution, carry out dB scaling with reference to maximum output value, "○" indicates real sources DOA, does not include strength information.Four
Under a frequency, the minimum separation between sound source is followed successively by 0.032,0.048,0.065,0.079.
As seen from Figure 5: ANM is used, in the sound source distribution that 2000Hz (Fig. 5 (a)) and 3000Hz (Fig. 5 (c)) is reconstructed
The distribution of substantial deviation real sources, has only accurately estimated six main sound in 4000Hz (Fig. 5 (e)) and 4900Hz (Fig. 5 (g))
The DOA in source.Using the present invention, the sound source DOA estimated result of Fig. 5 (b), 5 (d), 5 (f), 5 (h) under four frequencies is accurate.
Conclusion (of pressure testing) is consistent with emulation conclusion, it was demonstrated that emulation conclusion is correct, how soon claps mesh free using two dimension of the invention
Compression wave beam is formed in practical application more effectively.
Claims (2)
1. how soon a kind of two dimension claps mesh free compression Wave beam forming identification of sound source method, characterized in that the following steps are included:
Step 1 obtains measurement acoustic pressure matrix P★；
Measure acoustic pressure matrix P★∈CAB×LAre as follows:
P★=P+N
Measure acoustic pressure matrix P★It is obtained by Microphone array measurement, N ∈ CAB×LFor noise jamming, C is set of complex numbers, and A is rectangle
The line number of microphone array, B are the columns of rectangle microphone array, and L is snap number；
The acoustic pressure P that step 2, reconstruct sound source generate at array microphone；
Step 1), the mathematical model for establishing reconstruct P
In formula,It is the formula calculated result, | | | |FIndicate Frobenius norm, P is acoustic pressure matrix to be asked, definition
Tb() is double Toeplitz operator, and the block Toeplitz type Hermitian square of A × A dimension is mapped as to any given vector u
Battle array:
Tb(u) in, each piece of Ta(0≤a≤A-1) is all the Toeplitz matrix of B × B dimension:
It is all auxiliary quantity, κ > 0 is regularisation parameter, I ∈ ΡAB×AB
For unit matrix, " tr () " indicates to ask the mark of matrix, subscript "H" indicate conjugate transposition,Indicate positive semidefinite；
Step 2) solves P
Initializationκ0=1, then W0=I, the result based on the l times iterationκl, Wl, the step of the l+1 times iteration
Are as follows:
1. being solved using the SDPT3 solver in the tool box CVX of MATLAB:
2. determining regularisation parameter κl+1: ForMaximum eigenvalue；
3. the weight matrix W that the l+1 times iteration determinesl+1:WhenLess than or equal to 10-3Or maximum number of iterations is when being completed, iteration ends；
Step 3, estimation sound source DOA；
Step 4, estimation strength of sound source.
2. how soon a kind of two dimension according to claim 1 claps mesh free compression Wave beam forming identification of sound source method, feature
It is that the maximum number of iterations is 20.
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