CN106646376A - P-norm noise source positioning identification method based on weight correction parameter - Google Patents

Abstract

The invention discloses a P-norm noise source positioning identification method based on a weight correction parameter, relating to the technical field of noise source positioning. The positioning identification method includes step 1 eigenvalue decomposition sound source positioning recognition method; step 2 P-norm noise source signal reconstruction method; and step 3 selection of algorithm for weight correction parameter Epsilon. The characteristic subspace of each order and the subspace response function are obtained by characteristic decomposition, a subspace sound source vector reconstruction model is established for the characteristic subspace of each order, the reconstruction model is solved by the P-norm sparsity constraint of the weight correction parameter, the subspace sound source vector is forced to converge faster and more efficiently to the location of the real sparse source, and the more concentrated sparse solution of energy can be obtained; the effects of signal-to-noise ratio, measurement distance, array aperture and analysis frequency on the algorithm positioning performance are analyzed, the simulation result shows that the method can achieve the accurate estimation of the position and amplitude of different types of sound sources, and the stability is good.

Description

P norm noise source positioning identifying methods based on weighting corrected parameter

Technical field

The present invention relates to a kind of P norm High Resolution noise sources fixation and recognition side based on weighting corrected parameter Method, belongs to noise source field of locating technology.

Background technology

Conventional beamformer (conventional beamforming, CBF) is used as topmost noise source array signal Treatment technology is widely used to aircraft because of its excellent tolerance and ease for operation, the detection of automobile radiated noise with it is fixed In position.But conventional beamformer its spatial resolution is limited by array physical pore size, that is, there is " Rayleigh limit (Rayleigh) ", in the detection of many sound sources, it is serious that problem " is obscured " in space.

In order to break through " Rayleigh limit ", numerous High-Resolution Spectral Estimation methods are arisen at the historic moment, wherein with subspace multiple signal point Class (MUSIC) algorithm is representative, and the algorithm is same so as to obtain by carrying out feature decomposition to basic matrix receiving data covariance matrix The corresponding signal subspace of component of signal and noise subspace, using its orthogonal property " needle-like " space spectral peak, phase are constructed Positioning precision and spatial resolution are greatly improved compared with conventional various methods.But the method is only capable of obtaining sound bearing Estimated result, it is impossible to the relative size of true reflection sound source contribution, it is impossible to reach the purpose of identification of sound source.

The content of the invention

For the problems referred to above, the technical problem to be solved in the present invention is to provide a kind of P norms based on weighting corrected parameter High Resolution noise source positioning identifying method.

The P norm noise source positioning identifying methods based on weighting corrected parameter of the present invention, its positioning identifying method is：

Step one, Eigenvalues Decomposition auditory localization recognition methods：

Spectrum matrix by M units omnidirectional acoustic microphones array received data configuration is：

Wherein：P (ω)=[P₁(ω) P₂(ω)L P_M(ω)]^TCarry out after discrete Fourier transform for array received signal Frequency domain snap vector, subscript H represents conjugate transposition；Due toFor Hermite matrixes, its Eigenvalues Decomposition can be represented Into：

Wherein Λ is a diagonal matrix, by the eigenvalue cluster for sorting into：

Λ=diag [λ₁,λ₂,L,λ_M] (3)

U is that M × M ties up matrix, is made up of orthogonal characteristic vector：

U=[φ₁ Mφ₂ ML Mφ_M] (4)

One proper subspace of each orthogonal characteristic vector definition, represents what array was responded to signal in the subspace Direction vector, its characteristic value is subspace response intensity；Array is defined from there through characteristic value and characteristic vector to exist sound source Receptance function in the subspace is：

By u_iBringing the spectrum matrix that formula (2) obtains being characterized by subspace receptance function into is：

Because proper subspace and characteristic vector have identical orthogonal property, above formula can be write as：

Comparison expression (1) and formula (7) find that response of the array to spatial sound source can be expressed as each rank proper subspace response letter Several superpositions；If S_iFor the corresponding i ranks sound source vector of the i-th rank proper subspace, H is the transmission between sound source vector and reception array element Jacobian matrix, then can regard a network system as per rank proper subspace, it is output as subspace receptance function u_i：

HS_i=u_i (8)

Because sound wave is micro- amplitude wave, principle of stacking is met, when input isWhen principle of stacking confirm network output ForThat is response of the array to spatial sound source, then from network system transmission characteristic, now input signalWith regard to table Show target sound source to be identified in scanning space；

Step 2, P norm noise source signal Reconstruction Methods：

N number of lattice point region being turned to by scanning field is discrete, being beam scanning point at node, it is pre- that each scanning element has one first If sound source, in addition to target sound source, remaining is imaginary sound source, and all default sound source amplitudes constitute (TN) × 1 in subspace and tie up Sound source vector S_i, T represents default sound source number of types；

Think subspace receptance function u_iIt is to be produced by the sound field superposition of these default source radiations, the default sound source class of difference Type combines M × (TN) the dimension transfer function matrix H constituted between scanning element and array element, can be calculated by solution formula (8) and be spoken Source vector S_i, i.e., beam scanning output in the subspace；Consideration formula (8) is acoustics inverse problem, is generally obtained using Regularization Technique The approximate solution of the problem of obtaining；

Wherein α is referred to as regularization parameter；Its value is relevant with the signal to noise ratio of input, usually matrix H H^-1(or H^-1H) most The 0.1%～10% of big characteristic value；

Due to imaginary sound source not necessary being, its amplitude is in vectorial S_iShow as zero or be approximately zero, using based on plus The P norm iterative algorithms of power corrected parameter, by formula (8) following optimization problem with linear constraints is converted into；

Wherein the span of p is between 0 to 1, different norm constraints to be represented respectively；E_(p)(S_i) less explanation S_iIn Information more localizes, more sparse；Above formula is solved using the method for Lagrange multipliers, the cost function to be minimized is：

Wherein λ is Lagrange multipliers vector, to S_iComplex gradient is sought respectively with λ and is solved, obtain：

By (12) Shi Ke get：

And then can solve with regard to sound source vector S_iIt is as follows with the formal solution of Lagrange multipliers λ：

Wherein W=diag (| S_i(n)|^P-2)；Because formula (14) is a nonlinear equation, it is therefore desirable to using iteration side Method solves S_i；Using W as iteration weighting matrix, its value is the diagonal matrix that a front iteration result is constituted, and substitutes into formula (14) Obtain the S of a new generation_i, the W being made up of it as weighting matrix of future generation, so repeatedly till solution is optimal；Consider To matrix H W^-1H^HUsually ill, needing to introduce regularization parameter in each iterative process reduces reconstructed error；To sum up To solution sound source vector S_iIterative formula it is as follows：

Wherein (k) represents iterations, and the cost function that each iteration can be obtained in the same manner is：

Due to sound source vector S_iThe characteristics of information localizes, can all have the Partial Elements value to be in each iterative process Zero, corresponding weighted value is similarly zero when these elements are substituted into weighting matrix W, so thatIn be zero unit Element existsIn be still zero；And corrected weighting matrix W：

W=diag (| S_i(n)|^P-2+ε) (17)

The selection of step 3, weighting corrected parameter ε to algorithm：

25 monopole sound sources of random distribution in scanning space, meet N/ κ=100/25=4>3 sparse condition, sends out Radio frequency rate f=2kHz, discusses respectively shadow of parameter ε to sound source vector reconstruction precision when strength of sound source average is 0.1,1,10 Ring, the excursion 0.001～5 of ε carries out altogether 25 iteration, 50 Monte-carlo l-G simulation tests；

The size for finally weighting corrected parameter is relevant with sound field information：

WhereinRepresent the result directly calculated by (9) formula before weighted iteration.

Compared with prior art, beneficial effects of the present invention are：Each rank proper subspace and son are obtained by feature decomposition Roomage response function, sets up subspace sound source vector reconstruction model, profit to each rank proper subspace using the method for default sound source The reconstruction model is solved with the P norm sparsity constraints of weighting corrected parameter, forces the subspace sound source vector can faster, more effectively Restrain to true sparse source position, obtain the sparse solution that energy is more concentrated；Analyze signal to noise ratio, measurement distance, basic matrix hole Footpath and analysis impact of the frequency to algorithm positioning performance, simulation result show the method be capable of achieving to different type sound source position and The accurate estimation of amplitude, stability is preferable.

Description of the drawings

For ease of explanation, the present invention is embodied as and accompanying drawing is described in detail by following.

Fig. 1 is the flow chart of the present invention；

Fig. 2 is P-EVD performances in the present invention and ε and signal mean value relationship curve map；

Fig. 3 is impact schematic diagrames of the ε new in the present invention to P-EVD performances；Wherein a is ε and strength of sound source relation curve Figure；B is strength of sound source average and reconstruction precision graph of relation；

Fig. 4 is incoherent monopole auditory localization schematic diagram in embodiment, and wherein a is CBF；B is MUSIC；C is P-EVD；

Fig. 5 is the monopole auditory localization schematic diagram that is concerned with embodiment；Wherein a is CBF；B is MUSIC；C is P-EVD；

Fig. 6 is distributed auditory localization schematic diagram in embodiment；Wherein a is CBF；B is MUSIC；C is P-EVD；

Fig. 7 is mixed type auditory localization schematic diagram in embodiment；Wherein a is CBF monopoles；B is CBF dipoles；C is MUSIC monopoles；D is MUSIC- dipoles；E is P-EVD monopoles；F is P-EVD dipoles；

Fig. 8 is impact schematic diagram of the embodiment medium frequency to auditory localization performance；Wherein a is amplitude Estimation error；B is side Position evaluated error；

Fig. 9 is impact schematic diagram of the aperture ratio to auditory localization performance of finding range in embodiment；Wherein a is amplitude Estimation mistake Difference；B is orientation evaluated error；

Figure 10 is impact schematic diagram of the noise to auditory localization performance in embodiment；Wherein a is amplitude Estimation error；B is Orientation evaluated error.

Specific embodiment

It is concrete below by what is illustrated in accompanying drawing to make the object, technical solutions and advantages of the present invention of greater clarity Embodiment is describing the present invention.However, it should be understood that these descriptions are simply exemplary, and it is not intended to limit the model of the present invention Enclose.Additionally, in the following description, the description to known features and technology is eliminated, to avoid unnecessarily obscuring the present invention's Concept.

As shown in figure 1, this specific embodiment is employed the following technical solutions：Its positioning identifying method is：

First, Eigenvalues Decomposition auditory localization recognition methods：

Consider be by the spectrum matrix of M units omnidirectional acoustic microphones array received data configuration：

Wherein：P (ω)=[P₁(ω) P₂(ω)L P_M(ω)]^TCarry out after discrete Fourier transform for array received signal Frequency domain snap vector, subscript H represents conjugate transposition.Due toFor Hermite matrixes, its Eigenvalues Decomposition (EVD) Can be expressed as：

Wherein Λ is a diagonal matrix, by the eigenvalue cluster for sorting into：

Λ=diag [λ₁,λ₂,L,λ_M] (3)

U is that M × M ties up matrix, is made up of orthogonal characteristic vector：

U=[φ₁ Mφ₂ ML Mφ_M] (4)

One proper subspace of each orthogonal characteristic vector definition, represents what array was responded to signal in the subspace Direction vector, its characteristic value is subspace response intensity；It is possible thereby to define array to sound by characteristic value and characteristic vector Receptance function of the source in the subspace be：

By u_iBringing the spectrum matrix that formula (2) obtains being characterized by subspace receptance function into is：

Because proper subspace and characteristic vector have identical orthogonal property, above formula can be write as：

Comparison expression (1) and formula (7) find that response of the array to spatial sound source can be expressed as each rank proper subspace response letter Several superpositions.If S_iFor the corresponding i ranks sound source vector of the i-th rank proper subspace, H is the transmission between sound source vector and reception array element Jacobian matrix, then can regard a network system as per rank proper subspace, it is output as subspace receptance function u_i：

HS_i=u_i (8)

Because sound wave is micro- amplitude wave, principle of stacking is met, when input isWhen principle of stacking confirm network output ForThat is response of the array to spatial sound source, then from network system transmission characteristic, now input signalWith regard to table Show target sound source to be identified in scanning space.So far, each rank of solution is converted into the Detection location of extraterrestrial target sound source special Levy the sound source Vector Problem in subspace.

2nd, P norms noise source signal Reconstruction Method (P-EVD)：

It is identical with conventional beamformer auditory localization recognition methods, for arbitrary order proper subspace, first by scanning field It is discrete to turn to N number of lattice point region, it is beam scanning point at node, there is a default sound source in each scanning element, the default sound source can To be point sound source, sound source of the dipole, multipole source etc., the alternatively combining form of different type sound source.In addition to target sound source, Remaining is imaginary sound source, and all default sound source amplitudes constitute the dimension of (TN) × 1 sound source vector S in subspace_i, T represents default Sound source number of types.Think subspace receptance function u_iIt is to be produced by the sound field superposition of these default source radiations, the default sound of difference Source Type combines M × (TN) the dimension transfer function matrix H constituted between scanning element and array element, can be calculated by solving formula (8) Speak source vector S_i, i.e., beam scanning output in the subspace；Consideration formula (8) is acoustics inverse problem, generally adopts regularization skill Art obtains the approximate solution of problem.

Wherein α is referred to as regularization parameter；Its value is relevant with the signal to noise ratio of input, usually matrix H H^-1(or H^-1H) most The 0.1%～10% of big characteristic value.

Due to imaginary sound source not necessary being, its amplitude is in vectorial S_iShow as zero or be approximately zero, and target sound source Generally there is larger amplitude, this explanation S_iThe characteristics of localizing with information, can be regarded as one group of sparse signal.Canonical Although change technology solves the ill-posedness of inverse problem, but can not obtain the sparse solution of optimum.In order to obtain energy concentration Sparse solution, using the P norm iterative algorithms based on weighting corrected parameter, by formula (8) following optimization problem with linear constraints is converted into.

Wherein the span of p is between 0 to 1, different norm constraints to be represented respectively.E_(p)(S_i) less explanation S_iIn Information more localizes, more sparse.Above formula is solved using the method for Lagrange multipliers, the cost function to be minimized is：

Wherein λ is Lagrange multipliers vector, to S_iComplex gradient is sought respectively with λ and is solved, obtain：

By (12) Shi Ke get：

And then can solve with regard to sound source vector S_iIt is as follows with the formal solution of Lagrange multipliers λ：

Wherein W=diag (| S_i(n)|^P-2).Because formula (14) is a nonlinear equation, it is therefore desirable to using iteration side Method solves S_i.Using W as iteration weighting matrix, its value is the diagonal matrix that a front iteration result is constituted, and substitutes into formula (14) Obtain the S of a new generation_i, the W being made up of it as weighting matrix of future generation, so repeatedly till solution is optimal.Consider To matrix H W^-1H^HUsually ill, needing to introduce regularization parameter in each iterative process reduces reconstructed error.To sum up To solution sound source vector S_iIterative formula it is as follows：

Wherein (k) represents iterations, and the cost function that each iteration can be obtained in the same manner is：

Due to sound source vector S_iThe characteristics of information localizes, can all have the Partial Elements value to be in each iterative process Zero, it may be noted that corresponding weighted value is similarly zero when these elements are substituted into weighting matrix W, so that In be that zero element existsIn be still zero.Sound source vector S can so be caused_iPartial information is lacked, in consideration of it, square will be weighted Battle array W is corrected：

W=diag (| S_i(n)|^P-2+ε) (17)

3rd, selections of the corrected parameter ε to algorithm is weighted：

From analysis above, the information being introduced in avoiding sound source vectorial for weighting corrected parameter is lost, really Protect the robustness of iterative process.Therefore the participation of parameter ε will certainly affect the performance of algorithm in calculating process.Weighting corrected parameter Impact of the selection to sound source vector reconstruction precision it is very big, select appropriate corrected parameter to improve reconstruction precision and may be used also Discernible sound source number in increase space.Impact of parameter ε to algorithm is discussed below.

25 monopole sound sources of random distribution in scanning space, meet N/ κ=100/25=4>3 sparse condition, sends out Radio frequency rate f=2kHz, discusses respectively shadow of parameter ε to sound source vector reconstruction precision when strength of sound source average is 0.1,1,10 Ring, the excursion 0.001～5 of ε carries out altogether 25 iteration, 50 Monte-carlo l-G simulation tests.

When showing that strength of sound source average is different in Fig. 2, impacts of the corrected parameter ε to P-EVD performances is weighted, it can be found that Impacts of the corrected parameter ε to sound source vector reconstruction precision is relevant with strength of sound source average, and for identical corrected parameter, signal is strong Degree average is less, and reconstruction precision is higher；When the timing of signal strength signal intensity average one, as the increase reconstruction precision of parameter ε is reduced, P- The hydraulic performance decline of EVD algorithms.In order that the selection of parameter has more versatility, the condition of strong signal correspondence small parameter is met, will Weighting corrected parameter does following change, is no longer the fixed value empirically chosen, and its size is relevant with sound field information：

WhereinRepresent the result directly calculated by (9) formula before weighted iteration.In order to verify the validity of above formula parameter, Using same Fig. 1 identicals simulated conditions, analyze under new weighting corrected parameter, the relation of strength of sound source average and reconstruction precision And the corresponding ε values of difference strength of sound source average.

Fig. 3 shows impacts of the weighting corrected parameter ε new in formula (18) to P-EVD positioning performances.From Fig. 3 (a), With the increase of strength of sound source, parameter ε value is less and less, and this is identical with the result shown in Fig. 2, again demonstrates sound-source signal Stronger, required weighting corrected parameter value is less.Fig. 3 (b) using parameter ε in figure (a) it is shown that be weighted superposition meter Calculate the relation of strength of sound source and sound source vector reconstruction precision.Curve in figure is compared with the result in Fig. 3, it is seen that new Under weighting corrected parameter ε, no matter why strength of sound source is worth, and sound source vector reconstruction success rate reaches more than 99%, illustrates such as formula (18) the weighting corrected parameter ε for showing has adaptivity.In actually measurement, superposition can be weighted using parameter ε Calculate to improve the performance of algorithm.

Embodiment：

Simulation analysis：

In order to be based on the validity of P norms noise source location algorithm (P-EVD) of weighting corrected parameter, by it to inhomogeneity The fixation and recognition result of type sound source and the conventional beamformer technology (CBF) and subspace MUSIC algorithms of classics are compared point Analysis；Using 7 × 7 uniform grid battle arrays being made up of acoustic microphones, array element distance 0.3m；Target sound source is located in x-y plane, is swept Domain 8m × 8m；Sweep spacing 0.25m；Basic matrix face is with scanning plane at a distance of z=5m；Ambient noise is white Gaussian noise, except special Illustrate, signal to noise ratio snr=20dB；Monte-Carlo experiment numbers are 50；Take P=1；Regularization parameter takes eigenvalue of maximum 1%.

The distributed sound source being made up of monopole or dipole can be regarded as mostly in view of noise source, therefore default sound source is adopted With monopole sound source and the sound source of the dipole of any direction, its frequency-domain expression is as follows：

Wherein,The direction vector between sound source and array element is represented, θ is the angle that dipole direction is axis of doublet and x-axis, Because the dipole of any direction in x-y plane by the dipole subrepresentation positioned at θ=0 ° and θ=90 °, therefore can preset sound source class Type may be set to the sound source of the dipole of x directions θ=0 °, and the sound source of the dipole and monopole point sound source of y directions θ=90 ° divide below The other sound source to multi-form carries out simulation analysis.

Example one：Two incoherent monopole sound source As and B be located at respectively (- 1,0,0) and (1,0,0), tranmitting frequency is 1.5kHz amplitudes are a_A=a_B=2 simple signal.

It is positioning result of three kinds of algorithms to incoherent monopole sound source shown in Fig. 4, due to conventional beamformer algorithm Spatial resolution is low, and secondary lobe big rise and fall (Fig. 4 (a)), and the locus of two sound sources can not be told from scanning figure； MUSIC algorithms in Fig. 4 (b) are a kind of high resolution space Power estimation algorithms, and its spatial resolution has apparently higher than CBF Sharp focusing peak and low sidelobe level, two sound source locus are high-visible in figure, and the method is capable of achieving to incoherent sound source It is accurately positioned；But preferable not to the utmost to the estimation of sound source amplitude (two sound source amplitudes are a in figure_A=a_B=0.055), this be due to MUSIC spatial spectral estimation algorithms are to estimate target sound source orientation with the orthogonality of noise subspace using signal subspace；Not The amplitude of target sound source can be obtained；Understand that P-EVD algorithms are to obtain signal energy high concentration by constraint of P norms by upper elaboration Sparse solution, therefore estimation to sound source amplitude is also capable of achieving on the basis of completing to be accurately positioned sound source, make this problem It is addressed；Fig. 4 (c) is shown the spatial spectrum using the output of P-EVD algorithms, without secondary lobe in figure, with more sharp focusing Peak yardstick, sound source position is high-visible, can obtain high-accuracy high-resolution auditory localization result. show that two sound source amplitudes are in figure a_A=a_B=2.08, evaluated error is 4%, and estimated accuracy is good；In error allowed band, the method can be obtained to sound source side Position and the estimated result of amplitude satisfaction.

Example two：Consider the two relevant sub- sound source As of single-stage and B, its sound source parameter is with example one.

The result shown from Fig. 5 can be seen that：(1) it is similar to the simulation result of example one, the low resolution of CBF make its according to Number and the locus of sound source, positioning failure cannot so be told.(2) although MUSIC algorithms are in incoherent auditory localization High-resolution superiority is shown, but for coherent sound sources, it is due to cannot accurately estimate sound source number therefore difficult to realize right The detection (Fig. 5 (b)) of coherent sound sources, its positioning result equally fails.(3) P-EVD algorithms still have excellent spatial discrimination Rate and accurate amplitude Estimation ability, a_A=a_B=1.99, its amplitude Estimation error is 1%, and overcoming additive method can not be processed The deficiency of coherent sound sources.Example together the explanation of example two P-EVD methods be capable of achieving the accurate estimation to sound source position and amplitude and Its coherence need not be considered.

Example three：Target sound source is that two Sound Source Centers have respectively positioned at (- 1,1.5,0) and the incoherent of (1, -0.8,0) Limit for length line source A and B, with x-axis angle 45 ° and 90 ° are respectively, and its length is 1.4m, and tranmitting frequency is 1.5kHz sound source amplitudes a_A=a_B=1 simple signal, is regarded as the distributed sound source being made up of multiple monopole sound sources.Scanning result such as Fig. 6 institutes Show, distributed sound source is marked by * in figure.

As a result show：(1) it is two concentration sound sources that scanning outputs of the CBF and MUSIC to distributed sound source is appeared more like, MUSIC algorithms are only a cancellation most secondary lobe interference in CBF, improve spatial resolution, still can not obtain precisely Positioning result and amplitude Estimation.(2) scanning result of P-EVD is fine with what the distributed sound source of demarcation in figure was coincide, output Sound source amplitude is a_A=a_B=0.99, evaluated error 1%.By the emulation, the method is capable of achieving to distributed sound source shape State, direction, effective identification of position and its accurate estimation of amplitude.

Example four：Sound source of the dipole A is located at (1,1,0), and its axis of doublet is 45 ° ± 180 ° with x angular separations, (- 2, -1,0) there is the monopole sound source B being concerned with sound source A in place simultaneously, and the equal tranmitting frequency of two sound sources is 1.5kHz, amplitude a_A=a_B =1 simple signal.

When space has monopole and sound source of the dipole simultaneously, according to default sound source type, after array scanning terminates The output result of monopole Source Model and sound source of the dipole model can be simultaneously obtained, as shown in fig. 7, arrow mark shows in figure For sound field gradients, to judge dipole direction.Scannings of the CBF to one pole submodel and dipole model in Fig. 7 (a) exports phase Seemingly, scanning result shows two peak values of presence, although the direction phase of sound field gradients and sound source A in dipole scanning result Together, but only cannot judge sound source number and type from this two scanning figures, and then identification of sound source cannot be realized.Although MUSIC is calculated Method has preferable dipole scanning result, but the coherence of target source causes scanning result of the MUSIC algorithms to one pole submodel Occurs peak value (Fig. 5 (b)) at sound source of the dipole A, the output result for positioning ultimate failure .P-EVD algorithms shows its monopole Model only exists unique scanning spike with the output result of dipole model, the sound source type and orientation phase with emulation setting Together, output amplitude is respectively a_B=0.97, a_A=1.048, evaluated error 3% and 4.8%；The scanning result of dipole from figure Output dipole direction can also be observed to there is 2.2% evaluated error between θ=43.982, with sound source A. P- described above EVD algorithms can judge sound source type by scanning result, realize to sound source locus, amplitude and direction (sound source of the dipole) Satisfactory estimation.

The P norm noise sources positioning performance analysis of weighting corrected parameter：

Simulation result shows superiority of the P-EVD algorithms in different type auditory localization identification, in order to further beg for By the robustness of the algorithm, from analysis frequency, measurement distance and array aperture when these parameters pair of signal to noise ratio tripartite surface analysis The impact of auditory localization error and amplitude Estimation error.

Fig. 8-10 give P-EVD auditory localizations performance by analysis frequency, range finding space when ambient interferences to sound source shadow Loud curve；Can be obtained as drawn a conclusion by comparative analysis：(1) P-EVD algorithms overcome conventional beamformer low frequency and are limited Shortcoming, may be implemented in it is low, in, auditory localization in high full frequency band is not constrained by measurement distance and array aperture, and positioning is accurate Truly have effect；(2) tolerance estimated sound bearing relative to P-EVD algorithms, its sound source amplitude Estimation is only in medium-high frequency section Effectively, and find range aperture ratio need to can obtain satisfied amplitude Estimation result less than 15 sides；(3) antijamming capability of P-EVD and CBF Quite, when ambient interferences are too strong, all there is huge deviation in estimation of the two methods to sound bearing and amplitude, as a result completely Failure, signal to noise ratio is to can just obtain preferable fixation and recognition result during more than 0dB.

From the point of view of above simulation result, P-EVD algorithms are relative higher to the applicability of measurement parameter with conventional method, Satisfied auditory localization recognition effect can be obtained in the case of major part measurement.

The general principle and principal character and advantages of the present invention of the present invention has been shown and described above.The technology of the industry Personnel it should be appreciated that the present invention is not restricted to the described embodiments, the simply explanation described in above-described embodiment and specification this The principle of invention, without departing from the spirit and scope of the present invention, the present invention also has various changes and modifications, these changes Change and improvement is both fallen within scope of the claimed invention.The claimed scope of the invention by appending claims and its Equivalent thereof.

Claims (1)

1. based on the P norm noise source positioning identifying methods for weighting corrected parameter, it is characterised in that：Its positioning identifying method For：

Step one, Eigenvalues Decomposition auditory localization recognition methods：

Spectrum matrix by M units omnidirectional acoustic microphones array received data configuration is：

$R=\stackrel{\‾}{P\left(\mathrm{\ω}\right)P{\left(\mathrm{\ω}\right)}^H}---\left(1\right)$

Wherein：P (ω)=[P₁(ω) P₂(ω) L P_M(ω)]^TThe frequency after discrete Fourier transform is carried out for array received signal Domain snap vector, subscript H represents conjugate transposition；Due toFor Hermite matrixes, its Eigenvalues Decomposition can be expressed as：

$R={\mathrm{U\ΛU}}^H=\underset{i=1}{\overset{r}{\Σ}}{\mathrm{\λ}}_i{\mathrm{\φ}}_i{\mathrm{\φ}}_i^H---\left(2\right)$

Wherein Λ is a diagonal matrix, by the eigenvalue cluster for sorting into：

Λ=diag [λ₁,λ₂,L,λ_M] (3)

U is that M × M ties up matrix, is made up of orthogonal characteristic vector：

U=[φ₁ Mφ₂ ML Mφ_M] (4)

One proper subspace of each orthogonal characteristic vector definition, represents the direction that array is responded to signal in the subspace Vector, its characteristic value is subspace response intensity；Array is defined from there through characteristic value and characteristic vector to sound source in the son Receptance function in space is：

$u_i=\sqrt{{\mathrm{\λ}}_i}{\mathrm{\φ}}_i---\left(5\right)$

By u_iBringing the spectrum matrix that formula (2) obtains being characterized by subspace receptance function into is：

$R=\underset{i=1}{\overset{r}{\Σ}}{u}_i{u}_i^H---\left(6\right)$

Because proper subspace and characteristic vector have identical orthogonal property, above formula can be write as：

$R=\left(\underset{i=1}{\overset{r}{\mathrm{\Σ}}}{u}_i\right)\left(\underset{i=1}{\overset{r}{\mathrm{\Σ}}}{u}_i^H\right)---\left(7\right)$

Comparison expression (1) and formula (7) find that response of the array to spatial sound source can be expressed as each rank proper subspace receptance function Superposition；If S_iFor the corresponding i ranks sound source vector of the i-th rank proper subspace, H is the transmission function between sound source vector and reception array element Matrix, then can regard a network system as per rank proper subspace, it is output as subspace receptance function u_i：

HS_i=u_i (8)

Because sound wave is micro- amplitude wave, principle of stacking is met, when input isWhen principle of stacking confirm network be output asThat is response of the array to spatial sound source, then from network system transmission characteristic, now input signalMean that Target sound source to be identified in scanning space；

Step 2, P norm noise source signal Reconstruction Methods：

N number of lattice point region being turned to by scanning field is discrete, being beam scanning point at node, each scanning element has a default sound first Source, in addition to target sound source, remaining is imaginary sound source, and all default sound source amplitudes constitute the dimension of (TN) × 1 sound source in subspace Vectorial S_i, T represents default sound source number of types；Think subspace receptance function u_iIt is to be superimposed by the sound field of these default source radiations Produce, the default sound source type of difference combines M × (TN) the dimension transfer function matrix H constituted between scanning element and array element, passes through Solution formula (8) can calculate sound source vector S_i, i.e., beam scanning output in the subspace；Consideration formula (8) is acoustics inverse problem, is led to The approximate solution of problem is obtained frequently with Regularization Technique；

$\left\{\begin{array}{cc}{s}_i=H^{-1}{({\mathrm{HH}}^{-1}+\mathrm{\&alpha;}I)}^{-1}{u}_i& M<N\\ s_i={(H^{-1}H+\mathrm{\&alpha;}I)}^{-1}{H}^{-1}{u}_i& M<N\end{array}\right.---\left(9\right)$

Wherein α is referred to as regularization parameter；Its value is relevant with the signal to noise ratio of input, usually matrix H H^-1(or H^-1H) maximum feature The 0.1%～10% of value；

Due to imaginary sound source not necessary being, its amplitude is in vectorial S_iShow as zero or be approximately zero, using based on weighting amendment The P norm iterative algorithms of parameter, by formula (8) following optimization problem with linear constraints is converted into；

$\left\{\begin{array}{ccc}min:& E_{\left(P\right)}\left(S_i\right)=\underset{l=1}{\overset{T\&CenterDot;L}{\&Sigma;}}|S_i{|}^P& 0\&le;P\&le;1\\ s.t:& {\mathrm{HS}}_i=u_i& \end{array}\right.---\left(10\right)$

Wherein the span of p is between 0 to 1, different norm constraints to be represented respectively；E_(p)(S_i) less explanation S_iIn information More localize, it is more sparse；Above formula is solved using the method for Lagrange multipliers, the cost function to be minimized is：

$\min F\stackrel{\mathrm{\&Delta;}}{=}\underset{l=1}{\overset{T\&CenterDot;L}{\&Sigma;}}|S_i\left(l\right){|}^P+{\mathrm{\&lambda;}}^H({\mathrm{HS}}_i-u_i)---\left(11\right)$

Wherein λ is Lagrange multipliers vector, to S_iComplex gradient is sought respectively with λ and is solved, obtain：

$\left\{\begin{array}{c}{F}_{S_i}=Pdiag\left(\right|S_i\left(n\right){|}^{P-2})S_i+H^H\mathrm{\&lambda;}=0\\ F_{\mathrm{\&lambda;}}={\mathrm{HS}}_i-u_i=0\end{array}\right.---\left(12\right)$

By (12) Shi Ke get：

$\left\{\begin{array}{c}{S}_i=-\frac{1}{P}{\left(diag\left(|S_i\left(n\right){|}^{p-2}\right)\right)}^{-1}{H}^H\mathrm{\&lambda;}\\ u_i=-\frac{1}{p}H{\left(diag\left(|S_i\left(n\right){|}^{p-2}\right)\right)}^{-1}{H}^H\mathrm{\&lambda;}\end{array}\right.---\left(13\right)$

And then can solve with regard to sound source vector S_iIt is as follows with the formal solution of Lagrange multipliers λ：

$\left\{\begin{array}{c}{S}_i=W^{-1}{H}^H{\left({\mathrm{HW}}^{-1}{H}^H\right)}^{-1}{u}_i\\ \mathrm{\&lambda;}=-P{\left({\mathrm{HW}}^{-1}{H}^H\right)}^{-1}{u}_i\end{array}\right.---\left(14\right)$

Wherein W=diag (| S_i(n)|^P-2)；Because formula (14) is a nonlinear equation, it is therefore desirable to solved using alternative manner S_i；Using W as iteration weighting matrix, its value is the diagonal matrix that a front iteration result is constituted, and substitutes into formula (14) and obtains new The S of a generation_i, the W being made up of it as weighting matrix of future generation, so repeatedly till solution is optimal；In view of matrix HW^-1H^HUsually ill, needing to introduce regularization parameter in each iterative process reduces reconstructed error；To sum up solved Sound source vector S_iIterative formula it is as follows：

$\left\{\begin{array}{c}{S}_i^{\left(k+1\right)}={\left(W^{\left(k\right)}\right)}^{-1}{H}^H{\left(H{\left(W^{\left(k\right)}\right)}^{-1}{H}^H+\mathrm{\&alpha;}I\right)}^{-1}{u}_i\\ {\mathrm{\&lambda;}}^{\left(k+1\right)}=-P{\left(H{\left(W^{\left(k+1\right)}\right)}^{-1}{H}^H+\mathrm{\&alpha;}I\right)}^{-1}{u}_i\end{array}\right.---\left(15\right)$

Wherein (k) represents iterations, and the cost function that each iteration can be obtained in the same manner is：

$\min F^{\left(k\right)}=\underset{l=1}{\overset{T\&CenterDot;L}{\&Sigma;}}|S_i^{\left(k\right)}\left(n\right){|}^P+{\left({\mathrm{\&lambda;}}^{\left(k\right)}\right)}^H({\mathrm{HS}}_i^{\left(k\right)}-u_i)---\left(16\right)$

Due to sound source vector S_iThe characteristics of information localizes, can all have Partial Elements value to be zero, by this in each iterative process A little elements weighted value corresponding when substituting into weighting matrix W is similarly zero, so thatIn be that zero element exists In be still zero；And corrected weighting matrix W：

W=diag (| S_i(n)|^P-2+ε) (17)

The selection of step 3, weighting corrected parameter ε to algorithm：

25 monopole sound sources of random distribution in scanning space, meet N/ κ=100/25=4>3 sparse condition, transmitting frequency Rate f=2kHz, discusses respectively impact of parameter ε to sound source vector reconstruction precision when strength of sound source average is 0.1,1,10, ε's Excursion 0.001～5, carries out altogether 25 iteration, 50 Monte-carlo l-G simulation tests；

The size for finally weighting corrected parameter is relevant with sound field information：

$\mathrm{\&epsiv;}=\frac{min\left|S_2^{\left(0\right)}\right|}{\left|\right|S_i^{\left(0\right)}|{|}_{l\mathrm{\&infin;}}}---\left(18\right)$

WhereinRepresent the result directly calculated by (9) formula before weighted iteration.