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

Broadband signal source positioning method based on subspace weighting sparse recovery

Technical Field

The invention belongs to the field of array signal processing, and particularly relates to a broadband signal source positioning method based on subspace weighting sparse recovery.

Background

The research on the target angle estimation problem has been in history for decades and has great significance in many fields, including wireless communication, radar, sonar and the like.

In the case of unknown target signal form, the conventional wideband target signal angle estimation firstly converts the wideband signal into a narrowband signal, and then performs target angle estimation by using some narrowband target signal angle estimation algorithm. Two ideas exist for converting a broadband signal into a narrow-band signal, one is an incoherent processing method, a target signal is converted into a frequency domain through short-time Fourier transform, then target angle estimation is independently carried out at each frequency point, and finally estimation results of each frequency point are fused; in the other coherent processing method, the target signal is converted into a frequency domain through short-time Fourier transform, then a transform is designed, all frequency points are mapped to the same frequency point, and finally the target angle is estimated through a narrow-band target signal angle estimation algorithm. In any way, the final foot-fall is the estimation of the narrow-band target signal angle, and the traditional narrow-band target signal angle estimation algorithm compared with the classical method at present comprises a conventional beam forming algorithm, a minimum variance distortionless response algorithm, a classical subspace algorithm MUSIC algorithm and the like.

In contrast, the conventional beamforming algorithm is the simplest, but this method has higher sidelobes and resolution is limited by the rayleigh resolution limit, and the only way to increase the resolution is to increase the array aperture. The resolution of the minimum variance distortionless algorithm and the MUSIC algorithm is not limited by Rayleigh resolution, super resolution can be realized, but the decorrelation capability of the two algorithms is poor, and the performance of the algorithms in a coherent information source scene can be greatly reduced.

Disclosure of Invention

The present invention is directed to solving at least one of the above problems.

Therefore, one purpose of the present invention is to provide a broadband signal source positioning method based on subspace weighted sparse recovery, which has strong coherent solution capability and high estimation accuracy.

In order to achieve the above object, an embodiment of the present invention discloses a broadband signal source positioning method based on subspace weighted sparse recovery, including the following steps: s1: irradiating a plurality of broadband signals with unknown correlation in space to a sensor linear array formed by a plurality of isotropic sensors, segmenting and Fourier transforming array element data in the sensor linear array, and selecting observation data of a plurality of frequency points from Fourier transformation results to obtain an observation complex matrix; s2: reconstructing the estimation of the target signal arrival angle under a compressed sensing frame according to the observation complex matrix to obtain a first signal model, wherein the first signal model comprises a first complete basis matrix, a first representation form of the target signal under the compressed sensing frame and a first additive noise component; s3: performing truncated singular value decomposition on the observation complex matrix to obtain a diagonal matrix, left singular vectors corresponding to each column and right singular vectors corresponding to each column, and constructing a weight matrix according to the diagonal matrix, the left singular vectors corresponding to each column and the right singular vectors corresponding to each column; s4: calculating a weight vector according to the weight matrix; s5: performing dimensionality reduction according to each component in the first signal model to obtain a second signal model, wherein the second signal model comprises a second complete basis matrix, a second characterization form of the target signal under a compressed sensing frame and a second additive noise component, and the second complete basis matrix and the second characterization form of the target signal under the compressed sensing frame have the same support set; s6: optimizing the second signal model to obtain a third representation form of the target signal under a compressed sensing framework; s7: and calculating a spectrum function according to a third representation form of the target signal under the compressed sensing framework to obtain an estimated value of the arrival angle of the target signal.

According to the broadband signal source positioning method based on subspace weighting sparse recovery, the subspace algorithm MUSIC algorithm and the compressed sensing algorithm are combined to design the weighting sparse recovery algorithm skill to obtain the decorrelation capability of the compressed sensing algorithm, and the estimation accuracy of the MUSIC algorithm is achieved.

In addition, the broadband signal source positioning method based on subspace weighted sparse recovery according to the above embodiment of the present invention may further have the following additional technical features:

further, step S1 further includes: irradiating the spatial Q broadband signals with unknown correlation to a sensor linear array consisting of M isotropic sensors to a large-angle setDividing each frame of data in the data acquired by each array element of the sensor linear array into K sections and performing G-point fast Fourier transform on each section; based on a priori information on the frequency distribution of the target signal,selecting observation data { y of L frequency points from Fourier transform results_k(f_l)}_{k＝1,...,K；l＝1,...,L}Further, an observation complex matrix Y (f) of M × K is obtained_l)＝[y₁(f_l) ... y_K(f_l)]。

Further, step S2 further includes: and according to the observation complex matrix, reconstructing the arrival angle of the target signal under a compressed sensing frame by the following formula estimation to obtain a first signal model:

Y(f_l)＝A(f_l)X(f_l)+N(f_l),l＝1,...,L

wherein, M × N complex matrixIs a first complete basis matrix, N × K matrix X (f)_l)＝[x₁(f_l),...,x_K(f_l)]For the first representation of the target signal in the compressive sensing framework, M × K matrix N (f)_l) For the first additive noise component is a first additive noise component,for the set of grid points divided in space, N is more than or equal to K and is similar to{x_k(f_l)}_{k＝1,...K；l＝1,...,L}The union is sparse and has a common set of supports Λ.

Further, step S3 further includes: performing truncated singular value decomposition on the observation complex matrix by the following formula:

Y(f_l)＝Ψ(f_l)∑(f_l)V(f_l)

wherein, ∑ (f)_l) Is a diagonal matrix with diagonal elements of Y (f)_l) The non-zero singular values of (a) are arranged in descending order; Ψ (f)_l) Respective lines of left singular vectors, V (f)_l) Each column of right singular vectors; Ψ (f)_l) The following can be written:

Ψ(f_l)＝[Ψ_s(f_l)Ψ_n(f_l)]

therein, Ψ_s(f_l) And Ψ_n(f_l) Overcomplete basis matrices A (f) corresponding to signal subspace and noise subspace, respectively_l) Can be written as:

A(f_l)＝[A_Λ(f_l)A_Λc(f_l)]

wherein A is_Λ(f_l) And A_Λc(f_l) Is A (f)_l) The corresponding column index sets are Λ and Λ^cAnd Λ^c1, 2., N } \\ Λ, a weight matrix is constructed by the following formula:

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

where H denotes the matrix conjugate transpose operator.

Further, step S4 further includes: calculating the weight vector w of the nth element in the weight matrix according to the following formula_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) Is W (f)_l) Row n.

Further, step S5 further includes performing dimensionality reduction on each component in the first signal model by using an M × Q dimensionality reduction matrix Y_SV(f_l)＝Y(f_l)V(f_l)D_Q＝Ψ(f_l)∑(f_l)D_QN × Q dimension-reducing matrix X_SV(f_l)＝X(f_l)V(f_l)D_QM × Q dimension reduction matrix N_SV(f_l)＝N(f_l)V(f_l)D_QWherein D is_Q＝[I_Q；0]，I_QIs a unit array of Q × Q, 0 is an all-zero unit array of (K-Q) × Q, and a second reduced dimension is obtainedAnd (3) 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) With the same support set.

Further, step S6 further includes: optimizing the second signal model by:

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, represents X_SV(f_l) Line n of (8), β²(f_l) For regularizing the parameters, under the second-order cone programming frame, the third representation form of the target signal under the decompression sensing frame is obtained by using an interior point method

Further, step S7 further includes: calculating a spectral function by the following formula

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

Wherein,the Q peak points are the estimated values of the corresponding Q target signal arrival angles.

Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.

Drawings

The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1 is a flow chart of a method for broadband signal source localization based on subspace weighted sparse recovery according to an embodiment of the present invention;

FIG. 2 shows the results of a simulation comparison test of the resolution performance of the MUSIC algorithm and the sparse algorithm in a relevant information source scenario according to an embodiment of the present invention;

FIG. 3 is a graph comparing the resolution performance of one embodiment of the present invention with the results of resolution performance simulation of other algorithms;

FIG. 4 is a graph comparing root mean square error performance with simulation results of other algorithms in accordance with one embodiment of the present invention.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.

In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are used only for convenience in describing the present invention and for simplicity in description, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.

These and other aspects of embodiments of the invention will be apparent with reference to the following description and attached drawings. In the description and drawings, particular embodiments of the invention have been disclosed in detail as being indicative of some of the ways in which the principles of the embodiments of the invention may be practiced, but it is understood that the scope of the embodiments of the invention is not limited correspondingly. On the contrary, the embodiments of the invention include all changes, modifications and equivalents coming within the spirit and terms of the claims appended hereto.

The following describes a broadband signal source positioning method based on subspace weighted sparse recovery according to an embodiment of the present invention with reference to the accompanying drawings.

Fig. 1 is a flowchart of a method for broadband signal source localization based on subspace weighted sparse recovery according to an embodiment of the present invention.

Referring to fig. 1, a method for positioning a wideband signal source based on subspace weighted sparse recovery includes the following steps:

s1: a plurality of broadband signals with unknown correlation in space are irradiated to a sensor linear array formed by a plurality of isotropic sensors, the array element data in the sensor linear array are segmented and subjected to Fourier transformation, and then observation data of a plurality of frequency points are selected from Fourier transformation results to obtain an observation complex matrix.

In one embodiment of the present invention, step S1 further includes:

irradiating the spatial Q broadband signals with unknown correlation to a sensor linear array consisting of M isotropic sensors to a large-angle set

Dividing each frame of data in the data acquired by each array element of the sensor linear array into K sections and performing G-point fast Fourier transform on each section;

selecting observation data { y of L frequency points from Fourier transform results based on prior information of frequency distribution of target signals_k(f_l)}_{k＝1,...,K；l＝1,...,L}Further, an observation complex matrix Y (f) of M × K is obtained_l)＝[y₁(f_l) … y_K(f_l)]。

S2: and reconstructing the estimation of the target signal arrival angle under a compressed sensing frame according to the observation complex matrix to obtain a first signal model, wherein the first signal model comprises a first complete base matrix, a first representation form of the target signal under the compressed sensing frame and a first additive noise component.

In one embodiment of the present invention, step S2 further includes:

according to the observation complex matrix, the arrival angle of a target signal is estimated and reconstructed under a compressed sensing frame through the following formula to obtain a first signal model:

Y(f_l)＝A(f_l)X(f_l)+N(f_l),l＝1,...,L

wherein, M × N complex matrixIs a first complete basis matrix, N × K matrix X (f)_l)＝[x₁(f_l),...,x_K(f_l)]For the first representation of the target signal in the compressive sensing framework, M × K matrix N (f)_l) For the first additive noise component is a first additive noise component,for the set of grid points divided in space, N is more than or equal to K and is similar to{x_k(f_l)}_{k＝1,...K；l＝1,...,L}The joint is sparse and has a common support set Λ the problem of estimating the target signal angle translates to an estimation problem for the support set Λ.

In addition to this, the present invention is,for signal steering vectors, the following is written:

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

wherein,is expressed from theta_qThe time difference of arrival of the signals in the direction of the first array element and the m +1 array element. Assuming that the first array element is located at the origin of coordinates, the (m + 1) th array element has a coordinate position ofFrom theta_qThe direction vector of the directional target signal is d^q＝-[sinθ_qcosθ_q]^T. Thus, it can 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, c₀Representing the signal propagation speed.

S3: and performing truncated singular value decomposition on the observation complex matrix to obtain a diagonal matrix, left singular vectors corresponding to the lines and right singular vectors corresponding to the lines, and constructing a weight matrix according to the diagonal matrix, the left singular vectors corresponding to the lines and the right singular vectors corresponding to the lines.

In one embodiment of the present invention, step S3 further includes:

truncated Singular Value Decomposition (SVD) of the observed complex matrix is performed by the following formula:

Y(f_l)＝Ψ(f_l)∑(f_l)V(f_l)

wherein, ∑ (f)_l) Is a diagonal matrix with diagonal elements of Y (f)_l) The non-zero singular values of (a) are arranged in descending order; Ψ (f)_l) Respective lines of left singular vectors, V (f)_l) Each column of right singular vectors;

Ψ(f_l) The following can be written:

Ψ(f_l)＝[Ψ_s(f_l) Ψ_n(f_l)]

therein, Ψ_s(f_l) And Ψ_n(f_l) A first overcomplete basis matrix A (f) corresponding to a signal subspace and a noise subspace, respectively_l) Can be written 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 is_Λ(f_l) Andis A (f)_l) The corresponding column index sets are Λ and Λ^cAnd Λ^cN } Λ, since the noise subspace is orthogonal to a_Λ(f_l) Is not in contact withAre orthogonal. The weight matrix is thus constructed by the following formula:

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

where H denotes the matrix conjugate transpose operator.

S4: and calculating a weight vector according to the weight matrix.

In one embodiment of the present invention, step S4 further includes:

calculating the weight vector w of the nth element in the weight matrix according to the following formula_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) Is W (f)_l) Row n.

S5: and performing dimensionality reduction according to each component in the first signal model to obtain a second signal model, wherein the second signal model comprises a second complete basis matrix, a second characterization form of the target signal under the compressed sensing framework and a second additive noise component, and the second complete basis matrix and the second characterization form of the target signal under the compressed sensing framework have the same support set.

In one embodiment of the present invention, step S5 further includes:

reducing dimensions of each component in the first signal model by using an M × Q dimension reduction matrix Y_SV(f_l)＝Y(f_l)V(f_l)D_Q＝Ψ(f_l)∑(f_l)D_QN × Q dimension-reducing matrix X_SV(f_l)＝X(f_l)V(f_l)D_QM × Q dimension reduction matrix N_SV(f_l)＝N(f_l)V(f_l)D_QWherein D is_Q＝[I_Q；0]，I_QThe signal is a unit array of Q × Q, 0 is an all-zero unit array of (K-Q) × Q, and then a second signal model after dimension reduction is obtained as follows:

Y_SV(f_l)＝A(f_l)X_SV(f_l)+N_SV(f_l)

wherein, X_SV(f_l) And X (f)_l) Have the same support set and thus can be estimated by estimating X_SV(f_l) The estimation of the support set enables estimation of the angle of arrival of the target signal.

S6: and optimizing the second signal model to obtain a third representation form of the target signal under the compressed sensing framework.

In one embodiment of the present invention, step S6 further includes:

the second signal model is optimized by the following formula:

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, represents X_SV(f_l) Line n of，β²(f_l) For regularizing the parameters, under the second-order cone programming frame, the third representation form of the target signal under the decompression sensing frame is obtained by using an interior point method

S7: and calculating a spectrum function according to a third representation form of the target signal under a compressed sensing framework to obtain an estimated value of the arrival angle of the target signal.

In one embodiment of the present invention, step S7 further includes:

calculating a spectral function by the following formula

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

Wherein,the Q peak points are the estimated values of the corresponding Q target signal arrival angles.

According to the broadband signal source positioning method based on subspace weighting sparse recovery, the truncated singular value decomposition is adopted to reduce the dimension of each component of the model, and the calculation complexity is reduced; on one hand, a signal space and a noise space are obtained by utilizing singular value decomposition of an observation data matrix in combination with a subspace algorithm MUSIC algorithm, and then a weight matrix is constructed by utilizing the relation between an over-complete matrix and the noise space, so that elements in a support set can obtain smaller weights, and higher priority can be obtained during sparse reconstruction; and (4) applying a large weight to elements outside the support set, and inhibiting the elements as much as possible during sparse recovery. The invention combines the subspace algorithm MUSIC algorithm and the optimization-based sparse recovery algorithm, and has the high-precision performance of the subspace algorithm and the coherent resolving capability of the sparse recovery algorithm.

The effect of the present invention will be further explained by simulation.

Simulation environment: the simulation of the present invention was performed in the software environment of MATLAB R2014 a.

Simulation content:

simulation of related information source scenes: the method aims to verify that the MUSIC algorithm cannot effectively distinguish the information source in a related information source scene so as not to give a correct information source angle estimation result; the sparse-based method has decorrelation capability, and can still provide more accurate information source angle estimation in a related information source scene. The specific simulation is as follows: from theta₁62 ° and θ₂Two related signals of 67 degrees are irradiated to 8 uniform linear arrays with the minimum half wavelength distance; further, the signal-to-noise ratio (SNR) is set to 10dB, and the number N of spatial sampling grid points is 180. The simulation result is shown in fig. 2.

Simulation of a resolution performance contrast test: from theta₁62 ° and θ₂Two related wideband signals with center frequency of 300Hz and bandwidth of 200Hz at 67 DEG c₀＝1490mThe speed of/s is irradiated to the uniform linear array which is composed of 8 isotropic array elements and has the minimum half wavelength of the pitch. Further, the signal-to-noise ratio (SNR) is set to 10dB, the number N of spatial sampling grid points is 180, and the number K of frequency domain snapshots is 200. The simulation result is shown in fig. 3.

Root mean square error simulation comparison test: from theta₁42.83 ° and θ₂Two irrelevant broadband source lights to the uniform linear array at 73.33 degrees, and the parameters of the uniform linear array are the same with the parameters in the contrast test of the resolution performance and other test parameters. And (4) simulating and drawing a curve of the variation of the root mean square error along with the frequency domain snapshot number, wherein the average value of the results of 50 Monte Carlo tests of each point position in the curve is shown. The simulation result is shown in fig. 4.

And (3) simulation result analysis: it can be seen in fig. 2 that the MUSIC algorithm fails to distinguish between two sources in the context of related sources, resulting in an erroneous estimate; and sparse recovery based algorithms give a more correct estimation result of the two target signal angles. It can be seen from fig. 3 that the present invention can distinguish two target signals well, while the MUSIC algorithm cannot distinguish two target signals, i₁The SVD algorithm, although able to distinguish between two target signals, produces a large error in the estimation of the direction of arrival of the target signals. From the simulation results, the method has the advantage that the resolution performance of the estimation of the arrival direction of the target signal is greatly improved. In FIG. 4, it can be seen that the RMS error performance of the present invention is slightly worse than that of the MUSIC algorithm, but is still better than that of the classical sparse recovery algorithm₁There is a certain improvement in the SVD algorithm.

In combination, the present invention combines the MUSIC algorithm with l₁SVD algorithm, therefore, in the signal arrival angle estimation, it can obtain higher estimation precision, and has higher resolution performance, and at the same time has decorrelation capability.

In addition, other configurations and functions of the broadband signal source positioning method based on subspace weighted sparse recovery according to the embodiment of the present invention are known to those skilled in the art, and are not described in detail for reducing redundancy.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (8)

1. A broadband signal source positioning method based on subspace weighting sparse recovery is characterized by comprising the following steps:

s1: irradiating a plurality of broadband signals with unknown correlation in space to a sensor linear array formed by a plurality of isotropic sensors, segmenting and Fourier transforming array element data in the sensor linear array, and selecting observation data of a plurality of frequency points from Fourier transformation results to obtain an observation complex matrix;

s2: reconstructing the estimation of the target signal arrival angle under a compressed sensing frame according to the observation complex matrix to obtain a first signal model, wherein the first signal model comprises a first complete basis matrix, a first representation form of the target signal under the compressed sensing frame and a first additive noise component;

s3: performing truncated singular value decomposition on the observation complex matrix to obtain a diagonal matrix, left singular vectors corresponding to each column and right singular vectors corresponding to each column, and constructing a weight matrix according to the diagonal matrix, the left singular vectors corresponding to each column and the right singular vectors corresponding to each column;

s4: calculating a weight vector according to the weight matrix;

s5: performing dimensionality reduction according to each component in the first signal model to obtain a second signal model, wherein the second signal model comprises a second complete basis matrix, a second characterization form of the target signal under a compressed sensing frame and a second additive noise component, and the second complete basis matrix and the second characterization form of the target signal under the compressed sensing frame have the same support set;

s6: optimizing the second signal model to obtain a third representation form of the target signal under a compressed sensing framework;

s7: and calculating a spectrum function according to a third representation form of the target signal under the compressed sensing framework to obtain an estimated value of the arrival angle of the target signal.

2. The subspace-weighted sparse recovery-based wideband signal source localization method according to claim 1, wherein the step S1 further comprises:

irradiating Q broadband signals with unknown spatial correlation to a sensor linear array consisting of M isotropic sensors to obtain an angle set

Dividing each frame of data in the data acquired by each array element of the sensor linear array into K sections and performing G-point fast Fourier transform on each section;

based on aiming atPriori information of frequency distribution of the target signal, and observation data { y) of L frequency points is selected from Fourier transform results_k(f_l)}_{k＝1,...,K；l＝1,...,L}Further, an observation complex matrix Y (f) of M × K is obtained_l)＝[y₁(f_l) ... y_K(f_l)]。

3. The subspace-weighted sparse recovery-based wideband signal source localization method according to claim 2, wherein the step S2 further comprises:

and according to the observation complex matrix, reconstructing the arrival angle of the target signal under a compressed sensing frame by the following formula estimation to obtain a first signal model:

Y(f_l)＝A(f_l)X(f_l)+N(f_l),l＝1,...,L

wherein, M × N complex matrixIs a first complete basis matrix, N × K matrix X (f)_l)＝[x₁(f_l),...,x_K(f_l)]For the first representation of the target signal in the compressive sensing framework, M × K matrix N (f)_l) For the first additive noise component is a first additive noise component,for the set of grid points divided in space, N is more than or equal to K and is similar to{x_k(f_l)}_{k＝1,...K；l＝1,...,L}The union is sparse and has a common set of supports Λ.

4. The subspace-weighted sparse recovery-based wideband signal source localization method according to claim 3, wherein the step S3 further comprises:

performing truncated singular value decomposition on the observation complex matrix by the following formula:

Y(f_l)＝Ψ(f_l)∑(f_l)V(f_l)

wherein, ∑ (f)_l) Is a diagonal matrix with diagonal elements of Y (f)_l) The non-zero singular values of (a) are arranged in descending order; Ψ (f)_l) Respective lines of left singular vectors, V (f)_l) Each column of right singular vectors;

Ψ(f_l) The following can be written:

Ψ(f_l)＝[Ψ_s(f_l) Ψ_n(f_l)]

therein, Ψ_s(f_l) And Ψ_n(f_l) Overcomplete basis matrices A (f) corresponding to signal subspace and noise subspace, respectively_l) Can be written 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 is_Λ(f_l) Andis A (f)_l) The corresponding column index sets are Λ and Λ^cAnd Λ^c1, 2., N } \\ Λ, a weight matrix is constructed by the following formula:

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

where H is the matrix conjugate transpose operator.

5. The subspace-weighted sparse recovery-based wideband signal source localization method according to claim 4, wherein the step S4 further comprises:

calculating the weight vector w of the nth element in the weight matrix according to the following formula_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) Is W (f)_l) Row n.

6. The subspace-weighted sparse recovery-based wideband signal source localization method according to claim 5, wherein the step S5 further comprises:

reducing dimensions of each component in the first signal model by using an M × Q dimension reduction matrix Y_SV(f_l)＝Y(f_l)V(f_l)D_Q＝Ψ(f_l)∑(f_l)D_QN × Q dimension-reducing matrix X_SV(f_l)＝X(f_l)V(f_l)D_QM × Q dimension reduction matrix N_SV(f_l)＝N(f_l)V(f_l)D_QWherein D is_Q＝[I_Q；0]，I_QThe signal is a unit array of Q × Q, 0 is an all-zero unit array of (K-Q) × Q, and then a second signal model after dimension reduction is obtained as follows:

Y_SV(f_l)＝A(f_l)X_SV(f_l)+N_SV(f_l)

wherein, X_SV(f_l) And X (f)_l) With the same support set.

7. The subspace-weighted sparse recovery-based wideband signal source localization method according to claim 6, wherein the step S6 further comprises:

optimizing the second signal model by:

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, represents X_SV(f_l) Line n of (8), β²(f_l) For regularizing the parameters, under the second-order cone programming frame, the third representation form of the target signal under the decompression sensing frame is obtained by using an interior point method

8. The subspace-weighted sparse recovery-based wideband signal source localization method according to claim 7, wherein the step S7 further comprises:

calculating a spectral function by the following formula

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

Wherein,the Q peak points are the estimated values of the corresponding Q target signal arrival angles.