CN108931776A - A kind of high-precision Matched Field localization method - Google Patents
A kind of high-precision Matched Field localization method Download PDFInfo
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- 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
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Abstract
The present invention discloses the purpose of the present invention, is to provide a kind of high-precision Matched Field localization method, can extract the most essential feature of sound-source signal, achievees the effect that remove noise, improves the accuracy of positioning.In order to achieve the above objectives, solution of the invention is：A kind of high-precision Matched Field localization method, includes the following steps：Step 1, the search range of sound source is determined；Step 2, according to array received to underwater sound signal and sound field propagation model measuring and calculating grid point on sound field function gi(rq), Matched Field positioning is implemented to target；Step 3, sparse reconstruct is carried out to signal is received according to space sparse theory；Step 4, signal is reconstructed using management loading method；Step 5, the signal of reconstruct is optimized, obtains the reconstruction signal for most approaching original signal.
Description
Technical field
The invention belongs to Underwater Acoustics Engineering technical fields, are related to a kind of sound localization method, in particular to a kind of to be based on space
The sparse localization method for carrying out matching field source.
Background technique
Propagation attenuation is small in the seawater and is influenced by suspended material in water small for sound wave, and remote information is suitble to transmit,
Therefore sound wave is the main carriers of underwater information, and ocean be then be limited on one sea, under be limited to the complicated sound in seabed
Waveguide.Underwater interested target source radiation/reflected sound signals, the signal are propagated in the channel of ocean, hydrophone receiving array
Sampled signal.Submarine target source positioning, i.e., by analyze, handle signal and the ocean channel knowledge that sensor array receives come
Estimate target source position.Auditory localization is one of research emphasis of array signal processing, is led in hydroacoustic electronic warfare and ocean engineering etc.
Domain is widely used.
Matched-field processing combines the propagation characteristic of array signal processing and sound wave in Oceanic waveguide, takes full advantage of underwater sound letter
Road physical model, compared with the signal processing technology of other desalination channel models, positioning performance can be substantially improved.At Matched Field
Mainly comprising two aspect of the positioning of submarine target source and ocean environment parameter inverting, the latter is known as Matched Field chromatography for the application of reason
(Matched Field Tomography, abbreviation MFT).Essentially, the positioning of matching field source is one according to reception letter
Number and channel knowledge solve the inverse problem of sound source position, Matched Field chromatography is according to receiving signal and sound source information inverting ocean ring
The inverse problem of border parameter.At present there are many high resolution Matched-field processing, but when they all rely on greatly more independent
Between sample and sensitive to environment mismatch.But for scenes such as time varying channel, motion target trackings, stable observation time compared with
It is short, it is difficult to obtain more independent time sample number, therefore the high resolution Matched-field processing under snap deletion condition is worth grinding
Study carefully.
Signal by vector obtained after Basis Function transformation be it is sparse or compressible, here it is the sparse tables of signal
Show.It can exist in fields such as image, communication and radars and be widely applied from the cost of essentially decreased signal processing.
In fact, sparsity equally exists in Acoustic Object detection.The target source of radiation signal is logical simultaneously in complicated marine environment
It is often less, if regarding the target element spatial distribution in certain area as piece image (by the target strength table of all coordinate positions
Show), then the diagram is only brighter in several strong target positions, therefore this is that a width has rarefaction representation under area of space coordinate
Image.Current existing Matched-field processing device mainly utilizes ocean channel knowledge and acoustic pressure data, they do not utilize water
The sparsity of lower object space spectrum.
Summary of the invention
The purpose of the present invention is to provide a kind of high-precision Matched Field localization method, can extract sound-source signal most
The feature of essence achievees the effect that remove noise, improves the accuracy of positioning.
In order to achieve the above objectives, solution of the invention is：
A kind of high-precision Matched Field localization method, includes the following steps：
Step 1, the search range of sound source is determined；
Step 2, according to array received to underwater sound signal and sound field propagation model measuring and calculating grid point on sound field function gi(rq),
Matched Field positioning is implemented to target；
Step 3, sparse reconstruct is carried out to signal is received according to space sparse theory；
Step 4, signal is reconstructed using management loading method；
Step 5, the signal of reconstruct is optimized, obtains the reconstruction signal for most approaching original signal.
In above-mentioned steps 1, receiving array is vertically put, sound source is located at the right side of receiving array, selects normal mode calculation using models
Sound field.
In above-mentioned steps 1, in observation scope, Q mesh point turned to observation scope discrete region, obtain net region (R,
Z), wherein R indicates the distance range on search grid region, and Z indicates the depth bounds on search grid region, by these
Mesh point number consecutively is：1,2 ..., Q-1, Q.
The detailed content of above-mentioned steps 2 is：
Normal wave pattern is used to the net region (R, Z) divided, it is dilute according to positional relationship construction between array element and mesh point
Base G is dredged, then i-th of array element receives signal rarefaction representation under following base：
G=[g (r1),g(r2),...,g(rQ)]
Wherein, g (rQ)=[g1(rq),g2(rq),...,gM(rq)]T, q=1,2 ... Q, Q indicate the grid of search space partition
Number；gi(rq) indicate from position rqGreen's function between i-th of array element, wherein each rqA corresponding possible sound
Source position, i=1,2 ..., M, M are element number of array；
Reception sparse signal representation at i-th of array element is：
Y=GX+N
Wherein, Y ∈ CM×LFor array received data matrix；G∈CM×QFor calculation matrix；N∈CM×LFor noise matrix；Sound source is X
∈CQ×L, it is to show that corresponding position does not have sound source when the element on X row is 0, because sound source K≤Q, K are much smaller than Q, so letter
Number can sparsity indicate.
In above-mentioned steps 3, sparse reconstruct is carried out to signal is received using following formula：
Wherein,Indicate l0Norm；Indicate l2Norm；S.t. it indicates so that the condition met；β indicates preset noise
In the presence of optimize convergent threshold value.
The detailed content of above-mentioned steps 4 is：
The algorithm of X reconstruct is solved using management loading algorithm, mathematics is carried out by first-order autoregression AR model
Description, concrete principle are as follows：
Wherein β ∈ (- 1,1) is the coefficient of AR, if β=0, the signal of above-mentioned MMV model (mostly measurement vector) description is
For independent same distribution signal source；If β=± 1, above-mentioned MMV model is converted into SMV (single measurement vector).Q is expressed as
The divided spatial position number of Acoustic Object, L indicate number of snapshots.
The Joint Distribution signal X for being obtained vector hydrophone according to AR modeli.=[Xi1,Xi2,...,XiL] multidimensional Gauss point
Cloth probability density function is expressed as：
ρ(Xi.；γi,Bi)~N (0, γiBi), i=1 ..., Q
Wherein γiIt is the vector of positive hyper parameter, the sparse unknown prior variance of row of signal source X distribution is by its control, X and solution
Sparse degree it is closely related, work as γiValue be 0 when, corresponding XiRowElement is all
When 0, then γiWith sparsity, and γiLearning rules be algorithm core part.BiEstimate from sample data for one
Positive definite matrix out, BiGood modeled signal source XiBetween time-dependent behavior；γiBiFor the density covariance matrix of X.
Then the prior probability of X is：
Wherein Σ0It is defined as：
If designing a different B to each signal source X, over-fitting state will lead to, it is right in order to avoid over-fitting
In sequential organization signal, it is contemplated that describing the dependency structure of all signal sources using an identical B.Institute's above formula can
To be expressed as：Wherein Γ=diag [γ1,...,γQ]。
As it is assumed that noise is the Stationary Gauss Random process of zero-mean, the noise in different array elements is uncorrelated, and noise and letter
It is number uncorrelated, so noise vector meets following Gaussian Profile：
ρ (N)=N (0, λ)
Wherein λ is noise variance.
It can derive that signal source X obeys mean value and is according to bayesian criterionVariance isPosteriority Gaussian Profile, expression formula
It is as follows：
Equal value expression is：
Covariance matrix is expressed as：
That is the solution procedure of mean value and variance is converted into hyper parameter λ, γi,Bi,Solution, when all hyper parameters are estimated
Meter come out after, so that it may obtain signal source X maximum a posteriori probability (Maximum a posterior probability,
MAP) it is：
X*=uX=(λ Σ0 -1+GTG)-1GTY
=Σ0GT(λI+GΣ0GT)-1Y
The learning rules of sparse spike γ, positive definite matrix B and real noise variance λ can be obtained by minimizing cost function formula：
Wherein
It is solved using EM (Evidence maximization) algorithm, show that hyper parameter γ, the learning rules of B, λ are as follows respectively
It is shown：
Sparse Bayesian algorithm is utilized again, can be derived from as drawn a conclusion：
X=Γ GT(λI+GΓGT)-1Y
Expression formula is carried out transformation to be shown below：
Newest learning rules then can be derived according to above formula, expression formula is as follows：
In order to improve stability, will update B is：
Learning rules are simplified simultaneously, expression formula is as follows：
The detailed content of above-mentioned steps 5 is：
(51) hyper parameter λ is initialized, the value of γ, B enable λ=10 herein-3, γ=1, B are the M rank unit that leading diagonal is all 1
Matrix, M are the number of signal source；
(52) hyper parameter λ is updated, the learning rules of γ, B, and the iteration step converges on one until each hyper parameter always
More stable value；
(53) it calculatesWherein Θ includes three super parameter λ, γ, B.According toValue it can be concluded that X*Value,
Further according to the maximum a posteriori probability X of underwater sound signal source X*Acoustic Object source signal can be recovered, according to sparse principle, is completed
The Matched Field of underwater sound source positions.
After adopting the above scheme, the present invention utilizes echo signal in the sparse characteristic of spatial domain, in Signal acquiring and processing process
It is middle by space sparse theory be applied to Matched Field sound source positioning, specific method be by using by sound-source signal in Matched Field to
The mode of low-dimensional calculation matrix projection obtains measurement data more less than measurement data amount needed for nyquist sampling theorem, knot
Chorus source signal is finally asked with the sparse reconstructing method optimization of signal after the sparse form of spatial domain constructs restructuring matrix
Solve target sound source signal parameter.Rarefaction representation is carried out to sound-source signal in Matched Field, it is most essential sound-source signal can be extracted
Feature can achieve the effect of removal noise, improve the accuracy of positioning.
Detailed description of the invention
Fig. 1 is simulated environment schematic diagram of the invention；
Fig. 2 is the positioning schematic diagram of matching field source used in the present invention；
Fig. 3 is the space sparse table diagram of source signal proposed by the present invention；
Fig. 4 is flow chart of the invention.
Specific embodiment
Below with reference to attached drawing, technical solution of the present invention is described in detail.
As shown in figure 4, the present invention provides a kind of high-precision Matched Field localization method, include the following steps：
Step 1, the search range of sound source is determined.
It is simulated environment schematic diagram shown in Fig. 1, the position of receiving array as shown in Figure 2 is vertically put, sound source, which is located at, receives battle array
The right side of column.Propagation characteristic of the sound wave in ocean is very complicated, but its communication process can be explained by wave equation, at this
In embodiment, normal mode calculation using models sound field is selected.
In observation scope, Q mesh point is turned to observation scope discrete region, is obtained net region (R, Z), wherein R is indicated
Distance range on search grid region, Z indicates the depth bounds on search grid region, by these mesh point number consecutivelies
For：1,2 ..., Q-1, Q；
Step 2, according to array received to underwater sound signal and sound field propagation model measuring and calculating grid point on sound field function gi(rq),
Matched Field positioning is implemented to target.Specific step is as follows：
Underwater Acoustic Propagation model is established to the net region (R, Z) divided, by Underwater Acoustic Propagation calculation using models, obtains each grid regions
Sound source on the domain generated sound field function g in each array elementi(rq) (i=1,2 ..., M), wherein each rqIt is one corresponding
Possible sound source position, q=1,2 ... Q.
Normal wave pattern is used to the net region (R, Z) divided, it is dilute according to positional relationship construction between array element and mesh point
Dredge base G, then i-th array element receive signal can under following base rarefaction representation：
G=[g (r1),g(r2),...,g(rQ)]
Wherein, g (rQ)=[g1(rq),g2(rq),...,gM(rq)]T, q=1,2 ... Q, Q indicate the grid of search space partition
Number, in general Q >=sound source number K.gi(rq) (i=1,2 ..., M) it indicates from position rqTo between i-th of array element
Green's function, wherein each rqA corresponding possible sound source position.
Array received signal can rarefaction representation be：
Y=GX+N
Wherein：Y∈CM×LFor array received data matrix；G∈CM×QFor the calculation matrix of array；N∈CM×LFor noise matrix；X
∈CQ×LFor the signal of source emission, row element corresponding with sound source position is not 0 in X, and the corresponding element of other rows is all
0, due to number K≤Q of sound source, so X has sparsity.
Step 3, sparse reconstruct is carried out to signal is received according to space sparse theory.As shown in figure 3, being described as follows：
Then next the measuring signal Y of acquisition is exactly to carry out sparse reconstruct to signal：
Wherein,Indicate l0Norm；Indicate l2Norm；S.t. it indicates so that the condition met；β indicates preset noise
In the presence of optimize convergent threshold value.
What auditory localization problem to be solved is exactly by realizing the estimation to sound source position to the solution of following formula.
For the sake of simplicity, in the analysis of later orientation problem, it is assumed that noise is not present, i.e., idealizes problem：
min||X||0, s.t.Y=GX
In Underwater Acoustic Environment, since sound source number K is far smaller than the number Q of grid point, when the array number for receiving battle array is more than or equal to
2 times of sound source number, i.e. when Q >=2K, the equidistant constant δ of the beam of G2K(G) with very big probability less than 1, institute's above formula has unique solution X
=X*.Submarine target positioning problem to be solved is to solve for out the supported collection of X, determines corresponding to the element in the supported collection of X
Sound source position, to realize the positioning of underwater sound source.
Step 4, signal is reconstructed using management loading method, is described as follows：
The algorithm of X reconstruct is solved using management loading algorithm, mathematics is carried out by first-order autoregression AR model
Description, concrete principle are as follows：
Wherein β ∈ (- 1,1) is the coefficient of AR, if β=0, the signal of above-mentioned MMV model (mostly measurement vector) description is
For independent same distribution signal source；If β=± 1, above-mentioned MMV model is converted into SMV (single measurement vector).Q is expressed as
The divided spatial position number of Acoustic Object, L indicate number of snapshots.
The Joint Distribution signal X for being obtained vector hydrophone according to AR modeli.=[Xi1,Xi2,...,XiL] multidimensional Gauss point
Cloth probability density function is expressed as：
ρ(Xi.；γi,Bi)~N (0, γiBi), i=1 ..., Q
Wherein γiIt is the vector of positive hyper parameter, the sparse unknown prior variance of row of signal source X distribution is by its control, X and solution
Sparse degree it is closely related, work as γiValue be 0 when, corresponding XiRowElement is all
When 0, then γiWith sparsity, and γiLearning rules be algorithm core part.BiEstimate from sample data for one
Positive definite matrix out, BiGood modeled signal source XiBetween time-dependent behavior；γiBiFor the density covariance matrix of X.
Then the prior probability of X is：
Wherein Σ0It is defined as：
If designing a different B to each signal source X, over-fitting state will lead to, it is right in order to avoid over-fitting
In sequential organization signal, it is contemplated that describing the dependency structure of all signal sources using an identical B.Institute's above formula can
To be expressed as：Wherein Γ=diag [γ1,...,γQ]。
As it is assumed that noise is the Stationary Gauss Random process of zero-mean, the noise in different array elements is uncorrelated, and noise and letter
It is number uncorrelated, so noise vector meets following Gaussian Profile：
ρ (N)=N (0, λ)
Wherein λ is noise variance.
It can derive that signal source X obeys mean value and is according to bayesian criterionVariance isPosteriority Gaussian Profile, expression formula
It is as follows：
Equal value expression is：
Covariance matrix is expressed as：
That is the solution procedure of mean value and variance is converted into hyper parameter λ, γi,Bi,Solution, when all hyper parameters are estimated
Meter come out after, so that it may obtain signal source X maximum a posteriori probability (Maximum a posterior probability,
MAP) it is：
X*=uX=(λ Σ0 -1+GTG)-1GTY
=Σ0GT(λI+GΣ0GT)-1Y
The learning rules of sparse spike γ, positive definite matrix B and real noise variance λ can be obtained by minimizing cost function formula：
Wherein
It is solved using EM (Evidence maximization) algorithm, show that hyper parameter γ, the learning rules of B, λ are as follows respectively
It is shown：
Sparse Bayesian algorithm is utilized again, can be derived from as drawn a conclusion：
X=Γ GT(λI+GΓGT)-1Y
Expression formula is carried out transformation to be shown below：
Newest learning rules then can be derived according to above formula, expression formula is as follows：
In order to improve stability, will update B is：
Learning rules are simplified simultaneously, expression formula is as follows：
Step 5, the signal of reconstruct is optimized, obtains the reconstruction signal for most approaching original signal.Illustrate as
Under：
1, hyper parameter λ is initialized, the value of γ, B enable λ=10 herein-3, γ=1, B are the M rank unit square that leading diagonal is all 1
Battle array, M are the number of signal source；
2, hyper parameter λ, the learning rules of γ, B are updated, and the iteration step compares until each hyper parameter converges on one always
More stable value；
3, it calculatesWherein Θ includes three super parameter λ, γ, B.According toValue it can be concluded that X*Value, then
According to the maximum a posteriori probability X of underwater sound signal source X*Acoustic Object source signal can be recovered, according to sparse principle, completes water
The Matched Field of lower sound source positions.
The above examples only illustrate the technical idea of the present invention, and this does not limit the scope of protection of the present invention, it is all according to
Technical idea proposed by the present invention, any changes made on the basis of the technical scheme are fallen within the scope of the present invention.
Claims (7)
1. a kind of high-precision Matched Field localization method, it is characterised in that include the following steps：
Step 1, the search range of sound source is determined；
Step 2, according to array received to underwater sound signal and sound field propagation model measuring and calculating grid point on sound field function gi(rq),
Matched Field positioning is implemented to target；
Step 3, sparse reconstruct is carried out to signal is received according to space sparse theory；
Step 4, signal is reconstructed using sparse Bayesian algorithm；
Step 5, the signal of reconstruct is optimized, obtains the reconstruction signal for most approaching original signal.
2. a kind of high-precision Matched Field localization method as described in claim 1, it is characterised in that：In the step 1, it will connect
It receives array vertically to put, sound source is located at the right side of receiving array, selects normal mode calculation using models sound field.
3. a kind of high-precision Matched Field localization method as described in claim 1, it is characterised in that：In the step 1, seeing
It surveys in range, Q mesh point is turned to observation scope discrete region, is obtained net region (R, Z), wherein R is indicated in dragnet
Distance range on lattice region, Z indicate the depth bounds on search grid region, are by these mesh point number consecutivelies：1,
2 ..., Q-1, Q.
4. a kind of high-precision Matched Field localization method as claimed in claim 3, it is characterised in that：The step 2 it is detailed
Content is：
Normal wave pattern is used to the net region (R, Z) divided, it is dilute according to positional relationship construction between array element and mesh point
Base G is dredged, then i-th of array element receives signal rarefaction representation under following base：
G=[g (r1),g(r2),...,g(rQ)]
Wherein, g (rQ)=[g1(rq),g2(rq),...,gM(rq)]T, q=1,2 ... Q, Q indicate the grid number of search space partition
Mesh；gi(rq) indicate from position rqGreen's function between i-th of array element, wherein each rqA corresponding possible sound source
Position, i=1,2 ..., M, M indicate element number of array；
Reception sparse signal representation at i-th of array element is：
Y=GX+N
Wherein, Y ∈ CM×LFor array received data matrix；G∈CM×QFor calculation matrix；N∈CM×LFor noise matrix；Sound source is X
∈CQ×L, then show that corresponding position does not have sound source when the element on X row is 0, because sound source K≤Q, K are much smaller than Q, so letter
Number can sparsity indicate.
5. a kind of high-precision Matched Field localization method as claimed in claim 4, it is characterised in that：In the step 3, utilize
Following formula carries out sparse reconstruct to signal is received：
Wherein,Indicate l0Norm；Indicate l2Norm；S.t. it indicates so that the condition met；β indicates that preset noise is deposited
When optimize convergent threshold value.
6. a kind of high-precision Matched Field localization method as claimed in claim 5, it is characterised in that：The step 4 it is detailed
Content is：
The algorithm of X reconstruct is solved using management loading algorithm, mathematics is carried out by first-order autoregression AR model
Description, concrete principle are as follows：
Wherein β ∈ (- 1,1) is the coefficient of AR, if β=0, the signal of above-mentioned MMV model (mostly measurement vector) description is
For independent same distribution signal source；If β=± 1, above-mentioned MMV model is converted into SMV (single measurement vector).Q is expressed as
The divided spatial position number of Acoustic Object, L indicate number of snapshots.
The Joint Distribution signal X for being obtained vector hydrophone according to AR modeli.=[Xi1,Xi2,...,XiL] Multi-dimensional Gaussian distribution
Probability density function is expressed as：
ρ(Xi.；γi,Bi)~N (0, γiBi), i=1 ..., Q
Wherein γiIt is the vector of positive hyper parameter, the sparse unknown prior variance of row of signal source X distribution is by its control, X and solution
Sparse degree it is closely related, work as γiValue be 0 when, corresponding XiRowElement is all
When 0, then γiWith sparsity, and γiLearning rules be algorithm core part.BiEstimate from sample data for one
Positive definite matrix out, BiGood modeled signal source XiBetween time-dependent behavior；γiBiFor the density covariance matrix of X.
Then the prior probability of X is：
Wherein Σ0It is defined as：
If designing a different B to each signal source X, over-fitting state will lead to, it is right in order to avoid over-fitting
In sequential organization signal, it is contemplated that describing the dependency structure of all signal sources using an identical B.Institute's above formula can
To be expressed as：Wherein Γ=diag [γ1,...,γQ]。
As it is assumed that noise is the Stationary Gauss Random process of zero-mean, the noise in different array elements is uncorrelated, and noise and letter
It is number uncorrelated, so noise vector meets following Gaussian Profile：
ρ (N)=N (0, λ)
Wherein λ is noise variance.
It can derive that signal source X obeys mean value and is according to bayesian criterionVariance isPosteriority Gaussian Profile, expression formula
It is as follows：
Equal value expression is：
Covariance matrix is expressed as：
That is the solution procedure of mean value and variance is converted into hyper parameter λ, γ i, Bi,Solution, when all hyper parameters are estimated
After out, so that it may obtain the maximum a posteriori probability (Maximum a posterior probability, MAP) of signal source X
For：
X*=uX=(λ Σ0 -1+GTG)-1GTY
=Σ0GT(λI+GΣ0GT)-1Y
The learning rules of sparse spike γ, positive definite matrix B and real noise variance λ can be obtained by minimizing cost function formula：
L|γ,B,λ|@log|λI+GΣ0GT|+
YT|λI+GΣ0GT|Y
=log | Σy|+YTΣy -1Y
Wherein Σy@λI+GΣ0GT。
It is solved using EM (Evidence maximization) algorithm, show that hyper parameter γ, the learning rules of B, λ are as follows respectively
It is shown：
Sparse Bayesian algorithm is utilized again, can be derived from as drawn a conclusion：
X=Γ GT(λI+GΓGT)-1Y
Expression formula is carried out transformation to be shown below：
Newest learning rules then can be derived according to above formula, expression formula is as follows：
In order to improve stability, will update B is：
Learning rules are simplified simultaneously, expression formula is as follows：
7. a kind of high-precision Matched Field localization method as claimed in claim 6, it is characterised in that：The step 5 it is detailed
Content is：
(51) hyper parameter λ is initialized, the value of γ, B enable λ=10 herein-3, γ=1, B are the M rank unit square that leading diagonal is all 1
Battle array, M are the number of signal source；
(52) hyper parameter λ is updated, the learning rules of γ, B, and the iteration step converges on one until each hyper parameter always
More stable value；
(53) it calculatesWherein Θ includes three super parameter λ, γ, B.According toValue it can be concluded that X*Value,
Further according to the maximum a posteriori probability X of underwater sound signal source X*Acoustic Object source signal can be recovered, according to sparse principle, is completed
The Matched Field of underwater sound source positions.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110398716A (en) * | 2019-08-23 | 2019-11-01 | 北京工业大学 | A kind of more sound localization methods using balanced composition sparse between sound source |
| CN111664932A (en) * | 2020-05-22 | 2020-09-15 | 重庆大学 | Sound source identification method based on Bayesian compressed sensing |
| CN112255590A (en) * | 2020-10-26 | 2021-01-22 | 中国电子科技集团公司第三研究所 | Low-altitude sound source inversion positioning method and device based on fuzzy function matching |
| CN113419218A (en) * | 2021-07-27 | 2021-09-21 | 中山大学 | Underwater sound source matching field positioning method based on image signal processing |
| CN115825870A (en) * | 2023-02-17 | 2023-03-21 | 北京理工大学 | Off-grid compression matching field processing sound source positioning method based on group sparsity |
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|---|---|---|---|---|
| CN110398716A (en) * | 2019-08-23 | 2019-11-01 | 北京工业大学 | A kind of more sound localization methods using balanced composition sparse between sound source |
| CN110398716B (en) * | 2019-08-23 | 2021-05-28 | 北京工业大学 | Multi-sound-source positioning method utilizing sparse component equalization among sound sources |
| CN111664932A (en) * | 2020-05-22 | 2020-09-15 | 重庆大学 | Sound source identification method based on Bayesian compressed sensing |
| CN112255590A (en) * | 2020-10-26 | 2021-01-22 | 中国电子科技集团公司第三研究所 | Low-altitude sound source inversion positioning method and device based on fuzzy function matching |
| CN112255590B (en) * | 2020-10-26 | 2024-03-01 | 中国电子科技集团公司第三研究所 | Low-altitude sound source inversion positioning method and device based on fuzzy function matching |
| CN113419218A (en) * | 2021-07-27 | 2021-09-21 | 中山大学 | Underwater sound source matching field positioning method based on image signal processing |
| CN115825870A (en) * | 2023-02-17 | 2023-03-21 | 北京理工大学 | Off-grid compression matching field processing sound source positioning method based on group sparsity |
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