CN106125041A - The wideband source localization method of sparse recovery is weighted based on subspace - Google Patents

Abstract

The invention discloses a kind of wideband source localization method weighting sparse recovery based on subspace, including: the broadband signal that multiple dependencys in space are unknown is irradiated to the sensor linear array being made up of multiple isotropic sensors, and obtains observing complex matrix according to sensor linear array；Estimate to be reconstructed to obtain the first signal model to echo signal angle of arrival under compressed sensing framework according to observation complex matrix；After observation complex matrix is carried out truncated singular value decomposition, structure obtains weight matrix；Weight vector is calculated according to weight matrix；Carry out dimensionality reduction according to the first signal model and obtain secondary signal model；Secondary signal model is optimized the 3rd forms of characterization of the echo signal obtained under compressed sensing framework；The 3rd forms of characterization according to the echo signal under compressed sensing framework calculates spectral function and obtains the estimated value of echo signal angle of arrival.Present invention have the advantage that decorrelation LMS ability and the estimated accuracy of MUSIC algorithm with compressed sensing algorithm.

Description

The wideband source localization method of sparse recovery is weighted based on subspace

Technical field

The invention belongs to Array Signal Processing field, a kind of broadband letter weighting sparse recovery based on subspace of specific design Number source location method.

Background technology

The research of angle on target estimation problem has had the history of decades, significant in a lot of fields, wherein The numerous areas such as including radio communication, radar, sonar.

In the case of echo signal form the unknown, what traditional broadband target signal angle estimation first had to carry out is handle Broadband signal is converted into narrow band signal, and the algorithm then utilizing some narrowband target signal angle to estimate carries out angle on target and estimates Meter.Broadband signal being converted into narrow band signal and has two kinds of thinkings, one is noncoherent processing method, is become by Fourier in short-term Change, echo signal is forwarded to frequency domain, then independently carry out angle on target estimation at each frequency, finally each frequency is estimated knot Fruit is merged；Another is relevant processing method, by Short Time Fourier Transform, echo signal is forwarded to frequency domain, then sets Meter one conversion, is mapped to same frequency all frequencies, carries out target finally by narrowband target signal angle algorithm for estimating Angle estimation.No matter which kind of thinking, last stopping over is all that narrowband target signal angle is estimated, and compares the most classical tradition at present Narrowband target signal angle algorithm for estimating have conventional beamformer algorithm, response algorithm that minimum variance is undistorted and classics Subspace algorithm MUSIC algorithm etc..

In contrast, conventional beamformer algorithm is the simplest, but the method has higher secondary lobe and resolution by auspicious The restriction of the profit limit of resolution, the unique way increasing resolution is to increase array aperture.Minimum variance is undistorted algorithm and MUSIC algorithm resolution is not limited by Rayleigh resolution, can realize super-resolution, but the decorrelation LMS ability of two kinds of algorithms is poor, Coherent scene performance can be greatly lowered.

Summary of the invention

It is contemplated that at least solve one of above-mentioned technical problem.

To this end, it is an object of the present invention to propose that a kind of decorrelation LMS ability is strong, estimated accuracy is high based on subspace Weight the wideband source localization method of sparse recovery.

To achieve these goals, embodiment of the invention discloses that a kind of broadband weighting sparse recovery based on subspace Signal source localization method, comprises the following steps: S1: broadband signal unknown for multiple dependencys in space is irradiated to by multiple respectively The sensor linear array constituted to the sensor of the same sex, and array element data in described sensor linear array are carried out segmentation and Fourier change Change, then select the observation data of multiple frequency to obtain observing complex matrix from Fourier's series result；S2: according to described sight Survey complex matrix to estimate to be reconstructed to obtain the first signal model to echo signal angle of arrival under compressed sensing framework, wherein, Described first signal model included the echo signal under the first complete basic matrix, compressed sensing framework the first forms of characterization and First additive noise component；S3: described observation complex matrix carries out truncated singular value decomposition, and to obtain diagonal matrix, each column corresponding Left singular vector and the corresponding right singular vector of each column, the most left unusual according to described diagonal matrix, described each column The corresponding right singular vector of each column described in vector sum structure weight matrix；S4: calculate weight vector according to described weight matrix； S5: carry out dimensionality reduction according to each component in described first signal model and obtain secondary signal model, wherein, described secondary signal Model includes that the second forms of characterization of the echo signal under the second complete basic matrix, compressed sensing framework and the second additive noise divide Amount, the second forms of characterization of the echo signal under described second complete basic matrix and described compressed sensing framework has identical propping up Support collection；S6: described secondary signal model is optimized the 3rd forms of characterization of the echo signal obtained under compressed sensing framework； S7: calculate spectral function according to the 3rd forms of characterization of the echo signal under described compressed sensing framework and obtain echo signal arrival angle The estimated value of degree.

The wideband source localization method weighting sparse recovery based on subspace according to embodiments of the present invention, by subspace Algorithm MUSIC algorithm is combined design and weights the solution phase of sparse recovery algorithms technical ability acquisition compressed sensing algorithm with compressed sensing algorithm Dry ability, has again the estimated accuracy of MUSIC algorithm.

It addition, the wideband source localization side weighting sparse recovery based on subspace according to the above embodiment of the present invention Method, it is also possible to there is following additional technical characteristic:

Further, step S1 farther includes: be irradiated to by M each by broadband signal unknown for Q, space dependency The sensor linear array constituted to the sensor of the same sex, to wide-angle setEach array element of described sensor linear array is adopted Collect to data in every frame data be divided into K section every section and carry out G point quick Fourier conversion；Divide based on to the frequency of echo signal The prior information of cloth, selects the observation data { y of L frequency from Fourier transformation result_k(f_l)}_{K=1 ..., K；L=1 ..., L}, enter And obtain the observation complex matrix Y (f of M × K_l)=[y₁(f_l) ... y_K(f_l)]。

Further, step S2 farther includes: believe target under compressed sensing framework according to described observation complex matrix Number angle of arrival is estimated to be reconstructed to obtain the first signal model by below equation:

Y(f_l)=A (f_l)X(f_l)+N(f_l), l=1 ..., L

Wherein, the complex matrix of M × NFor crossing the first complete basic matrix, N × K square Battle array X (f_l)=[x₁(f_l),...,x_K(f_l)] it is the first forms of characterization of echo signal under compressed sensing framework, M × K matrix N (f_l) it is the first additive noise component,For having of the lattice point set divided in space, N >=K and approximation{x_k(f_l)}_{K=1 ... K；L=1 ..., L}Joint sparse, and there is common support collection Λ.

Further, step S3 farther includes: by below equation, described observation complex matrix is carried out truncated singular value Decompose:

Y(f_l)=Ψ (f_l)∑(f_l)V(f_l)

Wherein, ∑ (f_l) it is diagonal matrix, its diagonal entry is Y (f_l) non-zero singular value, according to descending；Ψ (f_l) the corresponding left singular vector of each column, V (f_l) the corresponding right singular vector of each column；Ψ(f_l) can be written as following Form:

Ψ(f_l)=[Ψ_s(f_l)Ψ_n(f_l)]

Wherein, Ψ_s(f_l) and Ψ_n(f_l) correspond respectively to signal subspace and noise subspace, cross complete basic matrix A (f_l) Can be write as:

A(f_l)=[A_Λ(f_l)A_Λc(f_l)]

Wherein, A_Λ(f_l) and A_Λc(f_l) it is A (f_l) two submatrixs, corresponding column index collection is combined into Λ and Λ^c, and Λ^c =1,2 ..., and N} Λ, by below equation construct weight matrix:

$W\left(f_l\right)=\left[\begin{array}{c}{W}_{\mathrm{\Λ}}\left(f_l\right)\\ W_{{\mathrm{\Λ}}^c}\left(f_l\right)\end{array}\right]=\left[\begin{array}{c}{A}_{\mathrm{\Λ}}^H\left(f_l\right){\mathrm{\Ψ}}_n\left(f_l\right)\\ A_{{\mathrm{\Λ}}^c}^H\left(f_l\right){\mathrm{\Ψ}}_n\left(f_l\right)\end{array}\right]=A^H\left(f_l\right){\mathrm{\Ψ}}_n\left(f_l\right)$

Wherein, H representing matrix conjugate transpose operator.

Further, step S4 farther includes: calculate the power of nth elements in described weight matrix according to below equation Value vector w_n(f_l):

$w_n\left(f_l\right)=\frac{\left|\right|W^n\left(f_l\right)|{|}_2}{\underset{n^{\′}=1}{\overset{N}{\Σ}}\left|\right|W^{n^{\′}}\left(f_l\right)|{|}_2}$

Wherein, Wⁿ(f_l) it is W (f_l) line n.

Further, step S5 farther includes: each component in described first signal model is carried out dimensionality reduction, has M × Q dimensionality reduction matrix Y_SV(f_l)=Y (f_l)V(f_l)D_Q=Ψ (f_l)∑(f_l)D_Q, N × Q dimensionality reduction matrix X_SV(f_l)=X (f_l)V(f_l) D_Q, M × Q dimensionality reduction matrix N_SV(f_l)=N (f_l)V(f_l)D_Q, wherein D_Q=[I_Q；0], I_QFor the unit matrix of Q × Q, 0 is (K-Q) × Q Complete zero unit matrix, and then obtain the secondary signal model after following dimensionality reduction:

Y_SV(f_l)=A (f_l)X_SV(f_l)+N_SV(f_l)

Wherein, X_SV(f_l) and X (f_l) there is identical support collection.

Further, step S6 farther includes: be optimized described secondary signal model by below equation:

minimize||X_SV(f_l)||_w；2,1

$\begin{array}{cc}subjectto& \left|\right|Y_{SV}\left(f_l\right)-A\left(f_l\right)X_{SV}\left(f_l\right)|{|}_F^2\≤{\mathrm{\β}}^2\left(f_l\right)\end{array}$

Wherein, Represent X_SV(f_l) line n, β²(f_l) it is Regularization parameter, under Second-order cone programming framework, utilizes interior point method to try to achieve the 3rd of the echo signal decompressed under perception framework Forms of characterization

Further, step S7 farther includes: calculate spectral function by below equation

$P\left({\widehat{\mathrm{\θ}}}_n\right)=\frac{1}{QL}\underset{l=1}{\overset{L}{\Σ}}\left|\right|{\tilde{X}}_{SV}^n\left(f_l\right)|{|}_2^2$

Wherein,Q peak point be the estimated value of corresponding Q echo signal angle of arrival.

The additional aspect of the present invention and advantage will part be given in the following description, and part will become from the following description Obtain substantially, or recognized by the practice of the present invention.

Accompanying drawing explanation

Above-mentioned and/or the additional aspect of the present invention and advantage are from combining the accompanying drawings below description to embodiment and will become Substantially with easy to understand, wherein:

Fig. 1 is the flow process of the wideband source localization method weighting sparse recovery based on subspace of the embodiment of the present invention Figure；

Fig. 2 be one embodiment of the invention correlated source scene under MUSIC algorithm and Corresponding Sparse Algorithm resolution performance emulation Comparative test result；

Fig. 3 is resolution performance and the resolution performance simulation result comparison diagram of other algorithms of one embodiment of the invention；

Fig. 4 is root-mean-square error performance and the simulation result comparison diagram of other algorithms of one embodiment of the invention.

Detailed description of the invention

Embodiments of the invention are described below in detail, and the example of described embodiment is shown in the drawings, the most from start to finish Same or similar label represents same or similar element or has the element of same or like function.Below with reference to attached The embodiment that figure describes is exemplary, is only used for explaining the present invention, and is not considered as limiting the invention.

In describing the invention, it is to be understood that term " " center ", " longitudinally ", " laterally ", " on ", D score, Orientation or the position relationship of the instruction such as "front", "rear", "left", "right", " vertically ", " level ", " top ", " end ", " interior ", " outward " are Based on orientation shown in the drawings or position relationship, it is for only for ease of the description present invention and simplifies description rather than instruction or dark The device or the element that show indication must have specific orientation, with specific azimuth configuration and operation, therefore it is not intended that right The restriction of the present invention.Additionally, term " first ", " second " are only used for describing purpose, and it is not intended that instruction or hint relatively Importance.

In describing the invention, it should be noted that unless otherwise clearly defined and limited, term " is installed ", " phase Even ", " connection " should be interpreted broadly, for example, it may be fixing connection, it is also possible to be to removably connect, or be integrally connected；Can To be mechanical connection, it is also possible to be electrical connection；Can be to be joined directly together, it is also possible to be indirectly connected to by intermediary, Ke Yishi The connection of two element internals.For the ordinary skill in the art, can understand that above-mentioned term is at this with concrete condition Concrete meaning in invention.

With reference to explained below and accompanying drawing, it will be clear that these and other aspects of embodiments of the invention.Describe at these With in accompanying drawing, specifically disclose some particular implementation in embodiments of the invention, represent the enforcement implementing the present invention Some modes of the principle of example, but it is to be understood that the scope of embodiments of the invention is not limited.On the contrary, the present invention All changes, amendment and equivalent in the range of spirit that embodiment includes falling into attached claims and intension.

Below in conjunction with accompanying drawing, the wideband signal source weighting sparse recovery based on subspace according to embodiments of the present invention is described Localization method.

Fig. 1 is the stream of the wideband source localization method weighting sparse recovery based on subspace of one embodiment of the invention Cheng Tu.

Refer to Fig. 1, a kind of wideband source localization method weighting sparse recovery based on subspace, including following step Rapid:

S1: be irradiated to broadband signal unknown for multiple dependencys in space to be made up of multiple isotropic sensors Sensor linear array, and array element data in sensor linear array are carried out segmentation and Fourier transform, then from Fourier's series result The observation data of the multiple frequency of middle selection are to obtain observing complex matrix.

In one embodiment of the invention, step S1 farther includes:

Broadband signal unknown for Q, space dependency is irradiated to the sensor being made up of M isotropic sensor Linear array, to wide-angle set

Every frame data in the data collect each array element of sensor linear array are divided into K section every section and carry out G point quickly Fourier transformation；

Prior information based on the frequency distribution to echo signal, selects the sight of L frequency from Fourier transformation result Survey data { y_k(f_l)}_{K=1 ..., K；L=1 ..., L}, and then obtain the observation complex matrix Y (f of M × K_l)=[y₁(f_l) … y_K(f_l)]。

S2: estimate to be reconstructed to echo signal angle of arrival according to observation complex matrix under compressed sensing framework and obtain the One signal model, wherein, the first signal model included of the echo signal under the first complete basic matrix, compressed sensing framework One forms of characterization and the first additive noise component.

In one embodiment of the invention, step S2 farther includes:

Estimate to carry out by below equation to echo signal angle of arrival under compressed sensing framework according to observation complex matrix Reconstruct and obtain the first signal model:

Y(f_l)=A (f_l)X(f_l)+N(f_l), l=1 ..., L

Wherein, the complex matrix of M × NFor crossing the first complete basic matrix, N × K square Battle array X (f_l)=[x₁(f_l),...,x_K(f_l)] it is the first forms of characterization of echo signal under compressed sensing framework, M × K matrix N (f_l) it is the first additive noise component,For having of the lattice point set divided in space, N >=K and approximation{x_k(f_l)}_{K=1 ... K；L=1 ..., L}Joint sparse, and there is common support collection Λ.For echo signal Angle estimation problem changes into the estimation problem supporting collection Λ.

Additionally,For signal guide vector, it is written as form:

$a(f_l,{\widehat{\mathrm{\θ}}}_q)=\frac{1}{\sqrt{M}}{\left[\begin{array}{cccc}1& e^{j2{\mathrm{\πf}}_l{\mathrm{\τ}}_1^q}& \mathrm{...}& e^{j2{\mathrm{\πf}}_l{\mathrm{\τ}}_{M-1}^q}\end{array}\right]}^T,$

Wherein,Represent from θ_qThe signal in direction arrives first array element and the time difference of m+1 array element.Assuming that the One array element is positioned at zero, and the coordinate position of m+1 array element isFrom θ_qThe target letter in direction Number direction vector be d^q=-[sin θ_q cosθ_q]^T.As such, it is possible to calculate

${\mathrm{\τ}}_m^q=\frac{-{\left(d^q\right)}^T{r}^m}{c_0}=\frac{r_1^m{\mathrm{sin\θ}}_q+r_2^m{\mathrm{cos\θ}}_q}{c_0},$

Wherein, c₀Represent signal velocity.

S3: observation complex matrix is carried out truncated singular value decomposition and obtains diagonal matrix, the corresponding left singular vector of each column Right singular vector corresponding with each column, the rightest according to diagonal matrix, the corresponding left singular vector of each column and each column Singular vector structure weight matrix.

In one embodiment of the invention, step S3 farther includes:

By below equation, observation complex matrix is carried out truncated singular value decomposition (SVD):

Y(f_l)=Ψ (f_l)∑(f_l)V(f_l)

Wherein, ∑ (f_l) it is diagonal matrix, its diagonal entry is Y (f_l) non-zero singular value, according to descending；Ψ (f_l) the corresponding left singular vector of each column, V (f_l) the corresponding right singular vector of each column；

Ψ(f_l) can be written as following form:

Ψ(f_l)=[Ψ_s(f_l) Ψ_n(f_l)]

Wherein, Ψ_s(f_l) and Ψ_n(f_l) correspond respectively to signal subspace and noise subspace, first crosses complete basic matrix A(f_l) can be write as:

$A\left(f_l\right)=\[\begin{array}{cc}{A}_{\mathrm{\Λ}}\left(f_l\right)& A_{{\mathrm{\Λ}}^c}\left(f_l\right)\end{array}\]$

Wherein, A_Λ(f_l) andFor A (f_l) two submatrixs, corresponding column index collection is combined into Λ and Λ^c, and Λ^c =1,2 ..., and N} Λ, owing to noise subspace is orthogonal to A_Λ(f_l) column space, and not withColumn space just Hand over.Therefore by below equation structure weight matrix:

$W\left(f_l\right)=\left[\begin{array}{c}{W}_{\mathrm{\Λ}}\left(f_l\right)\\ W_{{\mathrm{\Λ}}^c}\left(f_l\right)\end{array}\right]=\left[\begin{array}{c}{A}_{\mathrm{\Λ}}^H\left(f_l\right){\mathrm{\Ψ}}_n\left(f_l\right)\\ A_{{\mathrm{\Λ}}^c}^H\left(f_l\right){\mathrm{\Ψ}}_n\left(f_l\right)\end{array}\right]=A^H\left(f_l\right){\mathrm{\Ψ}}_n\left(f_l\right)$

Wherein, H representing matrix conjugate transpose operator.

S4: calculate weight vector according to weight matrix.

In one embodiment of the invention, step S4 farther includes:

The weight vector w of nth elements in weight matrix is calculated according to below equation_n(f_l):

$w_n\left(f_l\right)=\frac{\left|\right|W^n\left(f_l\right)|{|}_2}{\underset{n^{\′}=1}{\overset{N}{\Σ}}\left|\right|W^{n^{\′}}\left(f_l\right)|{|}_2}$

Wherein, Wⁿ(f_l) it is W (f_l) line n.

S5: carry out dimensionality reduction according to each component in the first signal model and obtain secondary signal model, wherein, secondary signal Model includes that the second forms of characterization of the echo signal under the second complete basic matrix, compressed sensing framework and the second additive noise divide Amount, the second forms of characterization of the echo signal under the second complete basic matrix and compressed sensing framework has identical support collection.

In one embodiment of the invention, step S5 farther includes:

Each component in first signal model is carried out dimensionality reduction, has M × Q dimensionality reduction matrix Y_SV(f_l)=Y (f_l)V(f_l)D_Q =Ψ (f_l)∑(f_l)D_Q, N × Q dimensionality reduction matrix X_SV(f_l)=X (f_l)V(f_l)D_Q, M × Q dimensionality reduction matrix N_SV(f_l)=N (f_l)V(f_l) D_Q, wherein D_Q=[I_Q；0], I_QFor the unit matrix of Q × Q, 0 is complete zero unit matrix of (K-Q) × Q, and then after obtaining following dimensionality reduction Secondary signal model:

Y_SV(f_l)=A (f_l)X_SV(f_l)+N_SV(f_l)

Wherein, X_SV(f_l) and X (f_l) there is identical support collection, and then can be by estimating X_SV(f_l) support the estimation collected Realize the estimation to echo signal angle of arrival.

S6: secondary signal model is optimized the 3rd forms of characterization of the echo signal obtained under compressed sensing framework.

In one embodiment of the invention, step S6 farther includes:

By below equation, secondary signal model is optimized:

minimize||X_SV(f_l)||_w；2,1

$\begin{array}{cc}subjectto& \left|\right|Y_{SV}\left(f_l\right)-A\left(f_l\right)X_{SV}\left(f_l\right)|{|}_F^2\≤{\mathrm{\β}}^2\left(f_l\right)\end{array}$

Wherein, Represent X_SV(f_l) line n, β²(f_l) it is Regularization parameter, under Second-order cone programming framework, utilizes interior point method to try to achieve the 3rd of the echo signal decompressed under perception framework Forms of characterization

S7: obtain echo signal according to the 3rd forms of characterization calculating spectral function of the echo signal under compressed sensing framework and arrive Reach the estimated value of angle.

In one embodiment of the invention, step S7 farther includes:

Spectral function is calculated by below equation

$P\left({\widehat{\mathrm{\θ}}}_n\right)=\frac{1}{QL}\underset{l=1}{\overset{L}{\Σ}}\left|\right|{\tilde{X}}_{SV}^n\left(f_l\right)|{|}_2^2$

Wherein,Q peak point be the estimated value of corresponding Q echo signal angle of arrival.

The wideband source localization method weighting sparse recovery based on subspace of the embodiment of the present invention, employing is blocked unusual Value is decomposed one side and each component of model is carried out dimensionality reduction, reduces computation complexity；Order one side, zygote space arithmetic MUSIC algorithm utilizes the singular value decomposition of observation data matrix to obtain signal space and spatial noise, then utilizes complete square The relation of battle array and spatial noise carries out the structure of weight matrix, it is achieved that supports the element in collection and obtains less weights, dilute Higher priority is obtained when dredging reconstruct；Support the element outside collection and apply big weights, suppress as far as possible when sparse recovery Fall.This invention combines Subspace algorithm MUSIC algorithm and based on the sparse recovery algorithms optimized, and has both had Subspace algorithm High precision performance, has again the decorrelation LMS ability of sparse recovery algorithms.

Below by emulation, the effect of the present invention is described further.

Simulated environment: the emulation of the present invention is to carry out under the software environment of MATLAB R2014a.

Emulation content:

Correlated source scene simulation: purpose is that checking MUSIC algorithm can not effectively be told under correlated source scene Information source and then correct information source angle estimation result can not be given；And possess decorrelation ability based on sparse method, relevant Remain to provide information source angle estimation more accurately under information source scene.Concrete emulation is set to: from θ₁=62 ° and θ₂=67 ° Two coherent signals are irradiated to the even linear array that M=8 spacing is minimum half-wavelength；Additionally, signal to noise ratio (SNR) is set to 10dB, Spatial sampling lattice point number N=180.Simulation result is Fig. 2.

Resolution performance contrast test emulates: from θ₁=62 ° and θ₂Two mid frequencyes of=67 ° are 300Hz, carry a width of The relevant broadband signal of 200Hz is with c₀The speed of=1490m/s is irradiated to be made up of M=8 isotropic array element, spacing Even linear array for minimum half-wavelength.Additionally, signal to noise ratio (SNR) is set to 10dB, spatial sampling lattice point number N=180, frequency domain is fast Umber of beats mesh K=200.Simulation result is Fig. 3.

Root-mean-square error simulation comparison is tested: from θ₁=42.83 ° and θ₂Two uncorrelated broadband information sources of=73.33 ° Being irradiated on even linear array, the parameter of even linear array and other test parameterss are identical with parameter in resolution performance contrast test. Emulation draw root-mean-square error with frequency domain snap number of variations curve, 50 the Monte Carlo experiment results in each some position in curve Meansigma methods.Simulation result is Fig. 4.

Analysis of simulation result: can be seen that in Fig. 2 that MUSIC algorithm could not tell two letters under correlated source scene Source, creates mistake estimation；And algorithm of based on sparse recovery gives the estimation of two correct echo signal angles of comparison Result.Fig. 3 can be seen that, the present invention can well distinguish two echo signals, and MUSIC algorithm fails distinguishes two Echo signal, l₁Although-svd algorithm can distinguish two echo signals, but the estimation to the arrival direction of echo signal produces Bigger error.Thus simulation result is it can be seen that the present invention is in terms of the resolution performance of the estimation of echo signal arrival direction Improve a lot.Although Fig. 4 can be seen that, the root-mean-square error performance of the present invention is poorer than MUSIC algorithm, but than classics Sparse recovery algorithms l₁-svd algorithm improves.

In general, present invention incorporates MUSIC algorithm and l₁-svd algorithm, therefore, in direction of arrival degree is estimated, Higher estimated accuracy can be obtained, also possess higher resolution performance, be provided simultaneously with decorrelation ability.

It addition, other structure of the wideband source localization method weighting sparse recovery based on subspace of the embodiment of the present invention Become and effect is the most all known, in order to reduce redundancy, do not repeat.

In the description of this specification, reference term " embodiment ", " some embodiments ", " example ", " specifically show Example " or the description of " some examples " etc. means to combine this embodiment or example describes specific features, structure, material or spy Point is contained at least one embodiment or the example of the present invention.In this manual, to the schematic representation of above-mentioned term not Necessarily refer to identical embodiment or example.And, the specific features of description, structure, material or feature can be any One or more embodiments or example in combine in an appropriate manner.

Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that: not These embodiments can be carried out multiple change in the case of departing from the principle of the present invention and objective, revise, replace and modification, this The scope of invention is limited by claim and equivalent thereof.

Claims (8)

1. the wideband source localization method weighting sparse recovery based on subspace, it is characterised in that comprise the following steps:

S1: the broadband signal that multiple dependencys in space are unknown is irradiated to the sensing being made up of multiple isotropic sensors Device linear array, and array element data in described sensor linear array are carried out segmentation and Fourier transform, then from Fourier transform results The observation data of the multiple frequency of middle selection are to obtain observing complex matrix；

S2: estimate to be reconstructed to echo signal angle of arrival according to described observation complex matrix under compressed sensing framework and obtain the One signal model, wherein, described first signal model included the echo signal under the first complete basic matrix, compressed sensing framework The first forms of characterization and the first additive noise component；

S3: described observation complex matrix is carried out truncated singular value decomposition and obtains diagonal matrix, the corresponding left singular vector of each column Right singular vector corresponding with each column, according to described diagonal matrix, the corresponding left singular vector of described each column and described respectively Column corresponding right singular vector structure weight matrix；

S4: calculate weight vector according to described weight matrix；

S5: carry out dimensionality reduction according to each component in described first signal model and obtain secondary signal model, wherein, described second Signal model includes that the second forms of characterization of the echo signal under the second complete basic matrix, compressed sensing framework and the second additivity are made an uproar Sound component, the second forms of characterization of the echo signal under described second complete basic matrix and described compressed sensing framework has identical Support collection；

S6: described secondary signal model is optimized the 3rd forms of characterization of the echo signal obtained under compressed sensing framework；

S7: obtain echo signal according to the 3rd forms of characterization calculating spectral function of the echo signal under described compressed sensing framework and arrive Reach the estimated value of angle.

The wideband source localization method weighting sparse recovery based on subspace the most according to claim 1, its feature exists In, step S1 farther includes:

Broadband signal unknown for Q, space dependency is irradiated to the sensor linear array being made up of M isotropic sensor, Angle of arrival set

Every frame data in the data collect each array element of described sensor linear array are divided into K section every section and carry out G point quickly Fourier transformation；

Prior information based on the frequency distribution to echo signal, selects the observation number of L frequency from Fourier transformation result According to { y_k(f_l)}_{K=1 ..., K；L=1 ..., L}, and then obtain the observation complex matrix Y (f of M × K_l)=[y₁(f_l) ... y_K(f_l)]。

The wideband source localization method weighting sparse recovery based on subspace the most according to claim 2, its feature exists In, step S2 farther includes:

Estimate to carry out by below equation to echo signal angle of arrival under compressed sensing framework according to described observation complex matrix Reconstruct and obtain the first signal model:

Y(f_l)=A (f_l)X(f_l)+N(f_l), l=1 ..., L

Wherein, the complex matrix of M × NFor crossing the first complete basic matrix, N × K matrix X (f_l)=[x₁(f_l),...,x_K(f_l)] it is the first forms of characterization of echo signal under compressed sensing framework, M × K matrix N (f_l) It is the first additive noise component,For having of the lattice point set divided in space, N >=K and approximation {x_k(f_l)}_{K=1 ... K；L=1 ..., L}Joint sparse, and there is common support collection Λ.

The wideband source localization method weighting sparse recovery based on subspace the most according to claim 3, its feature exists In, step S3 farther includes:

By below equation described observation complex matrix carried out truncated singular value decomposition:

Y(f_l)=Ψ (f_l)∑(f_l)V(f_l)

Wherein, ∑ (f_l) it is diagonal matrix, its diagonal entry is Y (f_l) non-zero singular value, according to descending；Ψ(f_l) The corresponding left singular vector of each column, V (f_l) the corresponding right singular vector of each column；

Ψ(f_l) can be written as following form:

Ψ(f_l)=[Ψ_s(f_l) Ψ_n(f_l)]

Wherein, Ψ_s(f_l) and Ψ_n(f_l) correspond respectively to signal subspace and noise subspace, cross complete basic matrix A (f_l) writeable Become:

$A\left(f_l\right)=\[\begin{array}{cc}{A}_{\mathrm{\Λ}}\left(f_l\right)& A_{{\mathrm{\Λ}}^c}\left(f_l\right)\end{array}\]$

Wherein, A_Λ(f_l) andFor A (f_l) two submatrixs, corresponding column index collection is combined into Λ and Λ^c, and Λ^c= 1,2 ..., and N} Λ, by below equation construct weight matrix:

$W\left(f_l\right)=\left[\begin{array}{c}{W}_{\mathrm{\Λ}}\left(f_l\right)\\ W_{{\mathrm{\Λ}}^c}\left(f_l\right)\end{array}\right]=\left[\begin{array}{c}{A}_{\mathrm{\Λ}}^H\left(f_l\right){\mathrm{\Ψ}}_n\left(f_l\right)\\ A_{{\mathrm{\Λ}}^c}^H\left(f_l\right){\mathrm{\Ψ}}_n\left(f_l\right)\end{array}\right]=A^H\left(f_l\right){\mathrm{\Ψ}}_n\left(f_l\right)$

Wherein, H is Matrix Conjugate transposition operator.

The wideband source localization method weighting sparse recovery based on subspace the most according to claim 4, its feature exists In, step S4 farther includes:

The weight vector w of nth elements in described weight matrix is calculated according to below equation_n(f_l).:

$w_n\left(f_l\right)=\frac{\left|\right|W^n\left(f_l\right)|{|}_2}{\underset{n^{\′}=1}{\overset{N}{\Σ}}\left|\right|W^{n^{\′}}\left(f_l\right)|{|}_2}$

Wherein, Wⁿ(f_l) it is W (f_l) line n.

The wideband source localization method weighting sparse recovery based on subspace the most according to claim 5, its feature exists In, step S5 farther includes:

Each component in described first signal model is carried out dimensionality reduction, has M × Q dimensionality reduction matrix Y_SV(f_l)=Y (f_l)V(f_l)D_Q =Ψ (f_l)∑(f_l)D_Q, N × Q dimensionality reduction matrix X_SV(f_l)=X (f_l)V(f_l)D_Q, M × Q dimensionality reduction matrix N_SV(f_l)=N (f_l)V(f_l) D_Q, wherein D_Q=[I_Q；0], I_QFor the unit matrix of Q × Q, 0 is complete zero unit matrix of (K-Q) × Q, and then after obtaining following dimensionality reduction Secondary signal model:

Y_SV(f_l)=A (f_l)X_SV(f_l)+N_SV(f_l)

Wherein, X_SV(f_l) and X (f_l) there is identical support collection.

The wideband source localization method weighting sparse recovery based on subspace the most according to claim 6, its feature exists In, step S6 farther includes:

By below equation, described secondary signal model is optimized:

minimize||X_SV(f_l)||_w；2,1

$\begin{array}{cc}subjectto& \left|\right|Y_{SV}\left(f_l\right)-A\left(f_l\right)X_{SV}\left(f_l\right)|{|}_F^2\≤{\mathrm{\β}}^2\left(f_l\right)\end{array}$

Wherein, Represent X_SV(f_l) line n, β²(f_l) it is canonical Change parameter, under Second-order cone programming framework, utilize interior point method to try to achieve the 3rd sign of the echo signal decompressed under perception framework Form

The wideband source localization method weighting sparse recovery based on subspace the most according to claim 7, its feature exists In, step S7 farther includes:

Spectral function is calculated by below equation

$P\left({\widehat{\mathrm{\θ}}}_n\right)=\frac{1}{QL}\underset{l=1}{\overset{L}{\Σ}}\left|\right|{\tilde{X}}_{SV}^n\left(f_l\right)|{|}_2^2$

Wherein,Q peak point be the estimated value of corresponding Q echo signal angle of arrival.