CN104407319A - Method and system for finding direction of target source of array signal - Google Patents

Abstract

The invention provides a method and a system for finding a direction of a target source of an array signal. The method comprises the following steps: performing signal sampling on the array signal to be detected to obtain a sampling matrix of the array signal, and acquiring a preset base matrix and a regularization parameter; performing singular value decomposition on the sampling matrix to obtain observation data, transferring the observation data into a signal subspace to obtain a target matrix; determining a target source direction of the array signal according to the target matrix, the base matrix, the regularization parameter and a preset direction finding equation set. According to the scheme, the target source direction finding of a high-dimensional signal can be abstracted into solution of underdetermined system of equations, so that effects of lower reconstruction error and higher success rate can be achieved within a larger signal-to-noise ratio range, and signals with higher correlation can be identified.

Description

The target source direction-finding method of array signal and system

Technical field

The present invention relates to signal processing technology field, particularly relate to a kind of target source direction-finding method and system of array signal.

Background technology

In signal transacting field, Array Signal Processing is a very important branch.Array Signal Processing utilizes multiple sensors of being placed on diverse location to the signal extracting array signal and accept and useful information thereof.Facing to increasing higher-dimension signal processing problems, compressive sensing theory grows up gradually, and therefore compressive sensing theory is widely used in higher-dimension signal processing problems.Compressive sensing theory is the sampling and the theory of reconstruct that propose based on this class signal of sparse signal, and its core technology is sparse signal.Rarefaction representation is the architectural feature according to signal, given signal is decomposed on redundancy base, transform domain is selected adaptively a small amount of base represent original signal exactly, it can extract the essential characteristic of signal effectively, be conducive to the subsequent treatment to signal, can reduce signal transacting cost, therefore, the rarefaction representation pattern that further investigation is used for Array Signal Processing is necessary.

At present, topmost two research directions of Array Signal Processing are adaptive spatial filtering and Estimation of Spatial Spectrum.Adaptive spatial filtering is familiar beam forming technique, is used widely in engineering, and the shortcoming of these class methods is that its evaluated error is relevant to target direction and signal to noise ratio (S/N ratio).And Estimation of Spatial Spectrum is an emerging technology combined with the former, it can improve the angle estimation precision, angular resolution and other parameters precisions that process spacing wave greatly in theory, very wide application prospect is had in various fields such as radar, communication, sonars, the shortcoming of these class methods is that its algorithm is complicated, thus bring a large amount of resource overheads, and computing time is longer.Therefore, the research emphasis of the target source direction finding of present stage how the target source direction finding problem of a high dimensional signal is abstracted into solving equations problem, to realize the effect obtaining lower reconstructed error and the higher probability of success in larger SNR ranges, thus the signal larger to correlativity identifies.

Summary of the invention

The object of the present invention is to provide a kind of target source direction-finding method and system of array signal, the target source direction finding problem of a high dimensional signal can be abstracted into underdetermined system of equations Solve problems, to realize the effect obtaining lower reconstructed error and the higher probability of success in larger SNR ranges, thus the signal larger to correlativity identifies.

Object of the present invention can be achieved through the following technical solutions:

A target source direction-finding method for array signal, comprises the steps:

The sampling matrix that signal sampling obtains described array signal is carried out to array signal to be measured, and obtains the basis matrix and regularization parameter preset;

Svd is carried out to described sampling matrix and obtains observation data, forward described observation data to signal subspace, obtain objective matrix;

Solve according to described objective matrix, described basis matrix, described regularization parameter and default second order cone the target source direction that formula determines described array signal, described second order cone solves formula and is:

$\begin{array}{c}\min (s+{\mathrm{\λ}1}^{T}t)\\ s.t.z=Y_{\mathrm{SVD}}-A{\hat{X}}_{\mathrm{SVD}},\\ {\left|\right|z\left|\right|}_2\≤s,\\ {\left|\right|\mathrm{Re}\left({\hat{X}}_{\mathrm{SVDi}}\right),\mathrm{Im}\left({\hat{X}}_{\mathrm{SVDi}}\right)\left|\right|}_2\≤t_i,i\∈\{\mathrm{1,2},...,N\}\end{array}$

Wherein, Y _sVDrepresent described objective matrix, represent the expression matrix of coefficients of described array signal, t represents evaluated error, and A represents described basis matrix, and λ represents described regularization parameter.

A target source direction-finding system for array signal, comprising:

Acquisition module, for carrying out to array signal to be measured the sampling matrix that signal sampling obtains described array signal, and obtains the basis matrix and regularization parameter preset;

Decomposing module, obtaining observation data for carrying out svd to described sampling matrix, forwarding described observation data to signal subspace, obtaining objective matrix;

Direction finding module, for solving according to described objective matrix, described basis matrix, described regularization parameter and default second order cone the target source direction that formula determines described array signal, described second order cone solves formula and is:

$\begin{array}{c}\min (s+{\mathrm{\λ}1}^{T}t)\\ s.t.z=Y_{\mathrm{SVD}}-A{\hat{X}}_{\mathrm{SVD}},\\ {\left|\right|z\left|\right|}_2\≤s,\\ {\left|\right|\mathrm{Re}\left({\hat{X}}_{\mathrm{SVDi}}\right),\mathrm{Im}\left({\hat{X}}_{\mathrm{SVDi}}\right)\left|\right|}_2\≤t_i,i\∈\{\mathrm{1,2},...,N\}\end{array}$

Wherein, Y _sVDrepresent described objective matrix, represent the expression matrix of coefficients of described array signal, t represents evaluated error, and A represents described basis matrix, and λ represents described regularization parameter.

According to the scheme of the invention described above, it carries out to array signal to be measured the sampling matrix that signal sampling obtains described array signal, and obtain the basis matrix and regularization parameter preset, svd is carried out to described sampling matrix and obtains observation data, forward described observation data to signal subspace, obtain objective matrix, according to described objective matrix, described basis matrix, described regularization parameter and default second order cone solve the target source direction that formula determines described array signal, because the present invention program solves based on second order cone the target source direction that formula determines described array signal, and second order cone solves formula is the target source direction finding problem of high dimensional signal is converted to underdetermined system of equations Solve problems, and and then underdetermined system of equations Solve problems is converted to Second-order cone programming problem obtains, achieve the effect obtaining lower reconstructed error and the higher probability of success in larger SNR ranges, thus the signal larger to correlativity identifies, effectively can extract the essential characteristic of array signal, be conducive to the subsequent treatment of pair array signal, signal transacting cost can be reduced.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of the target source direction-finding method embodiment of array signal of the present invention;

Fig. 2 is the structural representation of the target source direction-finding system embodiment of array signal of the present invention;

Fig. 3 is based on l ₁the normalization space puppet that the Second-order cone programming algorithm of-SVD obtains is composed;

Fig. 4 is the relation curve of root-mean-square error and fast umber of beats;

Fig. 5 is the relation curve in root-mean-square error and target element direction;

Fig. 6 is the relation curve of root-mean-square error and array number.

Embodiment

For making object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is described in further detail.Should be appreciated that embodiment described herein only in order to explain the present invention, do not limit protection scope of the present invention.

In the following description, the embodiment first for the target source direction-finding method of array signal of the present invention is described, then is described each embodiment of the target source direction-finding system of array signal of the present invention.

Shown in Figure 1, be the schematic flow sheet of the target source direction-finding method embodiment of array signal of the present invention.As shown in Figure 1, the target source direction-finding method of the array signal in the present embodiment comprises the steps:

Step S101: the sampling matrix that signal sampling obtains described array signal is carried out to array signal to be measured, and obtain the basis matrix and regularization parameter preset;

The signal that can realize arbitrarily can be adopted to adopt mode to carry out signal sampling, adopt the sampled data obtained to generate described sampling matrix according to signal;

Step S102: svd is carried out to described sampling matrix and obtains observation data, forward described observation data to signal subspace, obtain objective matrix;

The observation space of signal transacting can be decomposed into signal subspace and noise subspace, these two spaces are orthogonal, signal subspace forms with signal characteristic of correspondence vector by the data covariance matrix of the array signal received, and noise subspace is then made up of minimal eigenvalue (noise variance) characteristic of correspondence vectors all in covariance matrix;

Step S103: solve according to described objective matrix, described basis matrix, described regularization parameter and default second order cone the target source direction that formula determines described array signal, described second order cone solves formula and is:

$\begin{array}{c}\min (s+{\mathrm{\λ}1}^{T}t)\\ s.t.z=Y_{\mathrm{SVD}}-A{\hat{X}}_{\mathrm{SVD}},\\ {\left|\right|z\left|\right|}_2\≤s,\\ {\left|\right|\mathrm{Re}\left({\hat{X}}_{\mathrm{SVDi}}\right),\mathrm{Im}\left({\hat{X}}_{\mathrm{SVDi}}\right)\left|\right|}_2\≤t_i,i\∈\{\mathrm{1,2},...,N\}\end{array}---\left(1\right)$

Wherein, Y _sVDrepresent described objective matrix, represent the expression matrix of coefficients of described array signal, t represents evaluated error, and A represents described basis matrix, and λ represents described regularization parameter, and this regularization parameter is used for allowed error range;

That is solve by solving second order cone the target source direction that formula obtains described array signal, the mode of solving can be the mode that can realize arbitrarily, wherein in an embodiment, using minimize (s+Param*t) as the objective function solved, call the convex optimization tool of CVX to solve described second order cone and solve formula, obtain the target source direction of described array signal, this considers that minimize (s+Param*t) and described second order cone solve min (the s+ λ 1 in formula ^tt) be form one to one, directly can call CVX kit and calculate, greatly can improve counting yield.

In addition, solve formula according to described objective matrix, described basis matrix, described regularization parameter and default second order cone and determine that the target source direction of described array signal also may further include: describedly solve formula according to described objective matrix, described basis matrix, described regularization parameter and default second order cone and determine that the step in the target source direction of described array signal comprises the steps: that solving formula according to described objective matrix, described basis matrix, described regularization parameter and described second order cone obtains the pseudo-spectrogram in space corresponding to described array signal; The target source direction of described array signal is determined according to the pseudo-spectrogram in described space, wherein, the horizontal ordinate of the pseudo-spectrogram in space represents angle domain, the mould of ordinate corresponding to the every a line (each angle) of the expression matrix of coefficients X finally tried to achieve characterizes, and the possibility that forms of signal is larger thus for larger then this target source of the corresponding modulus value of a certain angle.

Accordingly, according to the scheme of above-mentioned the present embodiment, according to the scheme of the invention described above, it carries out to array signal to be measured the sampling matrix that signal sampling obtains described array signal, and obtain the basis matrix and regularization parameter preset, svd is carried out to described sampling matrix and obtains observation data, forward described observation data to signal subspace, obtain objective matrix, according to described objective matrix, described basis matrix, described regularization parameter and default second order cone solve the target source direction that formula determines described array signal, because the present invention program solves based on second order cone the target source direction that formula determines described array signal, and second order cone solves formula is the target source direction finding problem of high dimensional signal is converted to underdetermined system of equations Solve problems, and and then underdetermined system of equations Solve problems is converted to Second-order cone programming problem obtains, achieve the effect obtaining lower reconstructed error and the higher probability of success in larger SNR ranges, thus the signal larger to correlativity identifies, effectively can extract the essential characteristic of array signal, be conducive to the subsequent treatment of pair array signal, signal transacting cost can be reduced.

For the ease of understanding the solution of the present invention, introduce principle of the present invention in detail below.

Found by research, the following formula of muting thinned array signal (1) represents, because the unknown number number in this model is more than equation number, the Solve problems of sparse solution can be defined as a mathematical problem---solving of the underdetermined system of equations.In order to solve this underdetermined system of equations, the application's scheme proposes based on l ₁the second order cone naturalization algorithm of norm.First this algorithm carries out joint sparse expression to high dimensional signal, then signal source direction finding problem is abstracted into second order cone naturalization problem, finally solves.Joint sparse represents the problem that can solve higher-dimension signal transacting complexity while not affecting signal self character.Second order cone naturalization algorithm not only sparse reconstructed error is low, can both accurately estimate when low and signal correction in signal to noise ratio (S/N ratio).Specifically be described below:

First, the sparse domain matrix model of array signal is established:

For a basis matrix A, its each linear independence, if vectorial y can by this basis matrix perfect representation, that is:

y＝Ax (2)

Wherein, || x|| ₀≤ K and K < N, then this signal is called as K-sparse signal.K-sparse signal set on basis matrix A is also defined as:

∑ _K＝{y＝Ax：||x|| ₀≤K) (3)

The definition of sparse signal shows the no more than K of number of the nonzero element in the coefficient vector x of a K-sparse signal on basis matrix A, and namely the implication of " sparse " is the element major part of signal itself or the coefficient vector of signal on certain base is zero.

Be directed to simple noiseless sparse signal just to be represented by formula (2) as above, wherein the sparse matrix of y corresponding to the array signal that is expressed, such as, foregoing sampling matrix, x is unknown expression coefficient, matrix A ∈ R ^{n × M}(representing matrix A is that N × M ties up real number matrix), M < N, A full rank.Unknown number number clearly in this model, more than equation number, has infinite solution, such problem is called the Solve problems of the underdetermined system of equations.

In order to obtain the unique solution of the underdetermined system of equations, can use restraint to x, making it meet certain characteristic.Have a lot to the method that x retrains, such as, what utilize x opennessly carries out retraining.Suppose that unknown quantity x has certain sparse characteristic, namely contain more neutral element in x, utilize this characteristic formula (3) to be constrained to and there is unique solution.Utilizing sparse characteristic to carry out constraint to x can make the first prime number approaching the non-zero required for original signal y less, thus simplifies the representation of array signal, saves the cost of signal transacting.Mathematically, the optimization form of signal sparse characteristic is as follows:

min{J(x)|Ax＝y} (4)

Wherein y=Ax is called as constraint condition, and J (x) is objective function, and its meaning is that constraint x is the solution with certain characteristic.According to different application, select different objective functions.

Secondly, Minimum-Norm Method is adopted to carry out sparse reconstruct:

Get objective function be J (x)=|| x|| ₁, then optimization is expressed as:

min{||x|| ₁|Ax＝y} (5)

Since J (x)=|| x|| ₁be convex, the globally optimal solution of formula (5) existence anduniquess can be learnt.When the x in formula (5) is real number time, l ₁norm problem can change into linear programming problem to solve simply.But when x is a plural number, the method for Second-order cone programming can be utilized to solve.

Finally, the present invention devises based on l ₁the method of the Second-order cone programming of norm solves this problem:

Exporting one of sparse reconstruct direction of arrival (Direction ofArrival, DOA) method of estimation of Sparse representation based on narrow-band array is l ₁-SVD, this method extracts useful information in data to reduce the complexity of sparse restructing algorithm by Eigenvalues Decomposition.

When steadily fast beat of data can obtain multiframe, sparse domain matrix model easily extensible is as above:

Y＝AX (6)

Wherein Y=[y (t ₁), y (t ₂) ..., y (t _l)] data matrix when be array signal being multiframe, X=[x ¹, x ²..., x ^l] be corresponding sparse solution matrix.

When there being multiframe data available, the sparse process of multi-frame joint is more more sane than single frames, and joint sparse refers to that the target direction of each signal source remains unchanged between the fast beat of data of difference, change be only amplitude.When frame number is more, traditional joint sparse represent required calculated amount along with snap Frame be that ultralinear increases, the Mutual coupling requirement of inapplicable real time implementation.

In order to address this problem, first svd (SVD is carried out to the sampling matrix comprising multiframe frame data, Singular Value Decomposition) and observation data is transformed on signal subspace, only signal subspace is processed, because target source number is much smaller than fast umber of beats, so substantially increase counting yield.

The new observation model obtained is:

Y _SVD＝AX _SVD(7)

Sparse domain matrix model after dimensionality reduction maintains the openness and sparsity structure of former sparse domain matrix model, does not therefore affect its estimation to sense.

For the sparse domain matrix model corresponding to the sampling matrix comprising multiframe frame data, the decomposition result of svd is:

Y＝AX+N＝ULV (8)

Utilize l ₁the data that-SVD extracts are expressed as:

Y _SVD＝YV ^HD _K′(9)

＝AXV ^HD _K′+NV ^HD _K′

＝AX _SVD+N _SVD

Wherein, D _{k '}=[I _{k '}, 0 _{k ' × (M-K ')}] ^t.

To the data Y of above formula _sVDcarry out the structure of sparse reconstruct base tracing problem based, obtain:

$\underset{{\tilde{X}}_{\mathrm{SV}}}{\min }{\left|\right|{\tilde{X}}_{\mathrm{SVD}}\left|\right|}_{\mathrm{2,1}}s.t.{\left|\right|{\hat{Y}}_{\mathrm{SVD}}-\tilde{A}{\tilde{X}}_{\mathrm{SVD}}\left|\right|}_F\&le;\mathrm{\&epsiv;}---\left(10\right)$

Wherein similar with the definition of x, be the X of row coefficient expansion _sVD.

By calculating the representation that can obtain Second-order cone programming, as shown in formula (1).

According to the target source direction-finding method of the array signal of the invention described above, the present invention also provides a kind of target source direction-finding system of array signal, and just the embodiment of the target source direction-finding system of array signal of the present invention is described in detail below.The structural representation of the embodiment of the target source direction-finding system of array signal of the present invention has been shown in Fig. 2.For convenience of explanation, part related to the present invention is merely illustrated in fig. 2.

As shown in Figure 2, the target source direction-finding system of the array signal in the present embodiment, comprises acquisition module 201, decomposing module 202, direction finding module 203, wherein:

Acquisition module 201, for carrying out to array signal to be measured the sampling matrix that signal sampling obtains described array signal, and obtains the basis matrix and regularization parameter preset;

Decomposing module 202, obtaining observation data for carrying out svd to described sampling matrix, forwarding described observation data to signal subspace, obtaining objective matrix;

Direction finding module 203, for solving according to described objective matrix, described basis matrix, described regularization parameter and default second order cone the target source direction that formula determines described array signal, described second order cone solves formula and is:

$\begin{array}{c}\min (s+{\mathrm{\&lambda;}1}^{T}t)\\ s.t.z=Y_{\mathrm{SVD}}-A{\hat{X}}_{\mathrm{SVD}},\\ {\left|\right|z\left|\right|}_2\&le;s,\\ {\left|\right|\mathrm{Re}\left({\hat{X}}_{\mathrm{SVDi}}\right),\mathrm{Im}\left({\hat{X}}_{\mathrm{SVDi}}\right)\left|\right|}_2\&le;t_i,i\&Element;\{\mathrm{1,2},...,N\}\end{array}$

Wherein, Y _sVDrepresent described objective matrix, represent the expression matrix of coefficients of described array signal, t represents evaluated error, and A represents described basis matrix, and λ represents described regularization parameter.

Wherein in an embodiment, direction finding module 203 can solve formula according to described objective matrix, described basis matrix, described regularization parameter and described second order cone and obtain the pseudo-spectrogram in space corresponding to described array signal, determines the target source direction of described array signal according to the pseudo-spectrogram in described space.

Wherein in an embodiment, minimize (s+Param*t) as the objective function solved, is called the convex optimization tool of CVX and solves described second order cone and solve formula, obtain the target source direction of described array signal by direction finding module 203.

The target source direction-finding system of array signal of the present invention and the target source direction-finding method one_to_one corresponding of array signal of the present invention, the technical characteristic of setting forth in the embodiment of the target source direction-finding method of above-mentioned array signal and beneficial effect thereof are all applicable to, in the embodiment of target source direction-finding system of array signal, hereby state.

For the ease of understanding the present invention program, below in conjunction with Fig. 3 to a Fig. 6 and concrete example, to this technological invention scheme bring to be effectively described further.

Concrete example

This concrete example utilizes the uniform linear array of 10 array element compositions to emulate the present invention program, wherein.This array element distance is the half-wavelength of incident far field narrow band signal.Fig. 3 utilizes MATLAB to emulate based on l ₁the pseudo-spectrogram in the normalization space that the Second-order cone programming algorithm of-SVD obtains, wherein target source direction is-10 ° and 10 °.From Fig. 3, mark position is known, and this algorithm can estimate the angle of target source accurately, namely determine target source direction, and resolving power is very high, clearly can differentiate two signals.

The validity of the method adopted is verified herein by more various different DOA estimation method.The method of estimation of contrast is had living space MUSIC algorithm classical in Power estimation and other two kinds of Minimum-Norm Methods.The estimation these two aspects of the main computing time from often kind of algorithm, root-mean-square error emulates below.

(1) computing time is one of factor of a measurement algorithm computation complexity.Consideration signal to noise ratio (S/N ratio) is 10dB, and fast umber of beats is 200, and sampling grid is uniform sampling from-90 ° to 90 °, and sampling interval is 0.1 °.Utilize MATLAB to emulate 100 writing times, try to achieve mean value in table 1.Experiment is based on MATLAB R2009b, and 3.19GHz, 1.96GB RAM PC, by table 1, we can be clear that the computing time of MUSIC algorithm and OMP algorithm is obviously much smaller than other two kinds of algorithms.

The average calculation times of table 1 four kinds of algorithms

(2) DOA estimated accuracy is weighed by root-mean-square error (RMSE:root mean square error), is defined as:

$\mathrm{RMSE}=\sqrt{\frac{1}{100}\underset{i=1}{\overset{100}{\mathrm{\&Sigma;}}}{({\widehat{\mathrm{\&theta;}}}_i-\mathrm{\&theta;})}^2}---\left(11\right)$

Wherein be test the angle estimated i-th time, the target direction of this experiment is 10 °.

Root-mean-square error is with the change of fast umber of beats: consideration signal to noise ratio (S/N ratio) is 10dB.Result is as Fig. 4, and root-mean-square error reduces along with the increase of fast umber of beats (i.e. the frame number of aforesaid array signal), and wherein iteration weighted least-square method evaluated error when low fast umber of beats is larger.

Root-mean-square error is with the change of target direction: in this experiment, set signal to noise ratio (S/N ratio) is 10dB, and fast umber of beats is 200, and target direction is change from-10 ° to 70 °.As shown in Figure 5, when target direction is greater than 40 °, the evaluated error of various angle all can have obvious increase, and namely target direction more vertically more can accurately be estimated.

Root-mean-square error is with the change of array number: target setting direction is-10 ° and 10 °, and fast umber of beats is 200, and signal to noise ratio (S/N ratio) is 10dB, and array number is from 2 to 20 changes.As shown in Figure 6, estimate that root-mean-square error increases along with array number and reduces, show that the information received is more, to estimation angle advantageously.Wherein, iteration weighted least-square method is maximum to the requirement of array number, and other three kinds of algorithms also can be estimated substantially when array number is less.

The above embodiment only have expressed several embodiment of the present invention, and it describes comparatively concrete and detailed, but therefore can not be interpreted as the restriction to the scope of the claims of the present invention.It should be pointed out that for the person of ordinary skill of the art, without departing from the inventive concept of the premise, can also make some distortion and improvement, these all belong to protection scope of the present invention.Therefore, the protection domain of patent of the present invention should be as the criterion with claims.

Claims (6)

1. a target source direction-finding method for array signal, is characterized in that, comprise the steps:

The sampling matrix that signal sampling obtains described array signal is carried out to array signal to be measured, and obtains the basis matrix and regularization parameter preset;

Svd is carried out to described sampling matrix and obtains observation data, forward described observation data to signal subspace, obtain objective matrix;

The form solved according to described objective matrix, described basis matrix, described regularization parameter and default second order cone determines the target source direction of described array signal, and described second order cone solves formula and is:

min(s+λ1 ^Tt)

$s.t.z=Y_{\mathrm{SVD}}-A{\hat{X}}_{\mathrm{SVD}},$

||z|| ₂≤s，

${\left|\right|\mathrm{Re}\left({\hat{X}}_{\mathrm{SVDi}}\right),\mathrm{Im}\left({\hat{X}}_{\mathrm{SVDi}}\right)\left|\right|}_2\&le;t_i,i\&Element;\{\mathrm{1,2},...,N\}$

Wherein, Y _sVDrepresent described objective matrix, represent the expression matrix of coefficients of described array signal, t represents evaluated error, and A represents described basis matrix, and λ represents described regularization parameter.

2. the target source direction-finding method of array signal according to claim 1, it is characterized in that, describedly solve formula according to described objective matrix, described basis matrix, described regularization parameter and default second order cone and determine that the step in the target source direction of described array signal comprises the steps:

Solve formula according to described objective matrix, described basis matrix, described regularization parameter and described second order cone and obtain the pseudo-spectrogram in space corresponding to described array signal;

The target source direction of described array signal is determined according to the pseudo-spectrogram in described space.

3. the target source direction-finding method of array signal according to claim 1, it is characterized in that, describedly solve formula according to described objective matrix, described basis matrix, described regularization parameter and default second order cone and determine that the step in the target source direction of described array signal comprises the steps:

Using minimize (s+Param*t) as the objective function solved, call the convex optimization tool of CVX and solve described second order cone and solve formula, obtain the target source direction of described array signal.

4. a target source direction-finding system for array signal, is characterized in that, comprising:

Acquisition module, for carrying out to array signal to be measured the sampling matrix that signal sampling obtains described array signal, and obtains the basis matrix and regularization parameter preset;

Decomposing module, obtaining observation data for carrying out svd to described sampling matrix, forwarding described observation data to signal subspace, obtaining objective matrix;

Direction finding module, for solving according to described objective matrix, described basis matrix, described regularization parameter and default second order cone the target source direction that formula determines described array signal, described second order cone solves formula and is:

min(s+λ1 ^Tt)

$s.t.z=Y_{\mathrm{SVD}}-A{\hat{X}}_{\mathrm{SVD}},$

||z|| ₂≤s，

${\left|\right|\mathrm{Re}\left({\hat{X}}_{\mathrm{SVDi}}\right),\mathrm{Im}\left({\hat{X}}_{\mathrm{SVDi}}\right)\left|\right|}_2\&le;t_i,i\&Element;\{\mathrm{1,2},...,N\}$

Wherein, Y _sVDrepresent described objective matrix, represent the expression matrix of coefficients of described array signal, t represents evaluated error, and A represents described basis matrix, and λ represents described regularization parameter.

5. the target source direction-finding system of array signal according to claim 4, is characterized in that:

Described direction finding module solves formula according to described objective matrix, described basis matrix, described regularization parameter and described second order cone and obtains the pseudo-spectrogram in space corresponding to described array signal, determines the target source direction of described array signal according to the pseudo-spectrogram in described space.

6. the target source direction-finding system of array signal according to claim 4, is characterized in that:

Minimize (s+Param*t) as the objective function solved, is called the convex optimization tool of CVX and solves described second order cone and solve formula, obtain the target source direction of described array signal by described direction finding module.