CN104749552A - Estimation method of co-prime array DOA (Direction Of Arrival) angle based on sparse reconstruction - Google Patents

Abstract

The invention discloses an estimation method of a co-prime array DOA (Direction Of Arrival) angle based on sparse reconstruction, and mainly solves the problems that a prior art is higher in operand, less in identification information source amount and large in passive location evaluated error, and needs more priori knowledge. The method comprises the realizing steps of forming a co-prime array by an antenna receiver; obtaining observation data to spatial signal sampling; receiving data vectors by a virtual array element obtained by observation data; dividing spatial grids to form over-complete bases; receiving a spare relationship between the data vectors and the over-complete bases by the virtual array element to build a spare restraint equation; resolving the spare restraint equation by adopting a convex optimization method to obtain sparest resolution; drawing a magnitude spectrogram by a relative relationship between the sparest resolution and the spatial angle to obtain a DOA angle value. According to the method provided by the invention, the passive direction-finding precision and operating speed can be improved under a condition of low priori knowledge, the number of the recognized information source can be improved, and the estimation precision of a signal direction angle can be improved in a low signal to noise ratio, therefore the estimation method can be used for target reconnaissance and passive location.

Description

Based on the relatively prime array direction of arrival angular estimation method of sparse reconstruct

Technical field

The invention belongs to signal processing technology field, particularly the array signal process technique of acoustic signal, electromagnetic signal, specifically a kind of relatively prime array direction of arrival angular estimation method based on sparse reconstruct, can be used for target reconnaissance and passive location.

Background technology

The direction of arrival angle DOA estimation of signal is an important branch in Array Signal Processing field, it refers to and utilizes aerial array that spatial-acoustic signal, electromagnetic signal are carried out to induction and received, use modern signal processing method to estimate the direction of signal source fast and accurately again, in fields such as radar, sonar, radio communications, there is significant application value.Along with the continuous progress of science and technology, to the degree of accuracy of signal Mutual coupling and and resolution also have more and more higher requirement.

The DOA estimation method in past, normally used is typical linear uniform array.For the typical linear battle array of a L array element, traditional detectable number of source of MUSIC class computing method is L-1.In order to obtain as far as possible large angular freedom under few array element condition, detect more information source, some new array structures are suggested, and more representational is nested array and relatively prime array.For the DOA estimation technique of these arrays, usual way is level and smooth MUSIC subspace method (S-MUSIC), but S-MUSIC method needs more priori: need to know signal number in advance, know noise profile variance accurately, or expensive computing carrys out estimating noise distribution variance.In recent years, the viewpoint of some novelties: the DOA estimation method amassing covariance sparse reconstruct in subspace based on Khatri-Rao, is also applied in DOA estimation.But existing method needs to calculate autocorrelation matrix, cross-correlation matrix when calculating virtual array reception data in relatively prime array, extract sequence afterwards, and selected dictionary non-optimal, thus maximum number of sources can not be estimated, in the process of sparse reconstruct, do not provide a good error distributed parameter yet, cause larger DOA evaluated error.And in actual applications, number of source and noise profile are all generally unknown, there is the defects such as the large and evaluated error of operand is large in above-mentioned classic method, can bring greater impact the speed of target detection, passive location and precision: can not detection target real-time, even None-identified when target number is a lot, causes target acquistion failure.

Summary of the invention

The object of the invention is to identify the problems such as the number of signal sources is not enough under needing known number of source and equal conditions in above-mentioned prior art, a kind of relatively prime array direction of arrival angular estimation method based on sparse reconstruct is proposed, when reducing operand, improve target reconnaissance accuracy, improve passive location at low signal-to-noise ratio, low fast umber of beats, DOA estimated accuracy under low priori condition, avoid the target reconnaissance error because angle estimation error causes, under certain array number condition, add discernible number of source simultaneously, particularly outstanding more than performance during array element number at target of investication.

For achieving the above object, performing step of the present invention comprises as follows:

1) form relatively prime array with 2M+N-1 aerial receiver, each aerial receiver is called an array element, and hypothesis has K target acoustical or electromagnetic signal to incide this relatively prime array, K >=1.

1a) form uniform linear array 1 with N number of aerial receiver, be called for short linear array 1, uniform linear array 2 is formed with 2M-1 aerial receiver, be called for short linear array 2, the array element distance of linear array 1 is Md, and the array element distance of linear array 2 is Nd, wherein N>M >=2 and M, N are relatively prime, 0<d≤λ/2, λ is the narrow band signal wavelength inciding relatively prime array, and first array element of definition linear array 1 is the array element 0 of relatively prime array;

1b) combination linear array 1 and linear array 2 are relatively prime array: be apart the position of Nd after first of linear array 2 array element being positioned over array element 0, all array elements of linear array 2 insert in linear array 1 successively, linear array 1 and linear array 2 are on the same line, from relatively prime array elements 0, each array element is named to be followed successively by array element 0 from the head to the tail, array element 1 ..., array element 2M+N-2.

2) by relatively prime array antenna receiver, the acoustics of extraterrestrial target or electromagnetic signal are sampled, obtain array output signal Y (t), definition Y _mt () is the output signal of m array element, m=0,1 ..., 2M+N-2.

3) calculate virtual array according to relatively prime array output signal Y (t) and receive data vector y.

4) stress and strain model is carried out to detection direction of arrival angle observation space, spatial domain, construct super complete base Φ (θ), and define a spatial domain sparse vector s.

5) detection spatial domain direction of arrival angular estimation be converted into solve following sparse constraint equation:

min ||s|| ₁

subject to ||y-Φ(θ)s|| ₂≤η,

s≥0

Wherein s is the unknown vector that Q × 1 is tieed up, and η is the error distributed parameter needing to pre-estimate, || || ₁the single order norm of matrix, || || ₂it is the second order norm of matrix.

6) adopt convex Optimization Method sparse constraint equation, obtain the most sparse solution of unknown vector s

7) with direction of arrival angular region θ=[θ ₁, θ ₂..., θ _q..., θ _q] value be x-axis coordinate, with the range value of vector is y-axis coordinate, draws amplitude spectrogram, and K spectrum peak before larger according to order searching amplitude from high to low from this amplitude spectrogram, the x-axis coordinates corresponding to peak point at these spectrum peaks are the direction of arrival angle value of target.

The present invention compared with prior art has the following advantages:

1) during relatively prime arrayed applications is estimated to DOA by the present invention, actual array element Received signal strength is converted into virtual array Received signal strength, by selecting irredundant virtual Received signal strength, reduce signal data amount, reduce operand, under adding array element number certain condition, the discernible number of source of array.

2) the present invention adopts rarefaction representation technology that the estimation at direction of arrival angle is converted into the reconstruct of sparse signal, it is the combination of new theory technology and traditional problem, the spatial domain sparse characteristic of incident signal source is utilized to carry out modeling, breach the Rayleigh limit of array resolution, improve target reconnaissance and the DOA estimated accuracy of passive location under low signal-to-noise ratio, low fast umber of beats, low priori condition, avoid the target reconnaissance error because angle estimation error causes.

3) the present invention utilizes the angle that in the openness sparse solution obtained in the spatial domain of signal source, large coefficient is corresponding, and be the direction of arrival angle of signal source, the coefficient that aimless deflection is corresponding approximates 0, therefore without the need to knowing the number of target in advance; The cross-correlation information of array is adopted when calculating virtual array Received signal strength, the auto-correlation information of noise do not have or seldom measure be brought into the virtual array Received signal strength that model chooses, therefore without the need to known or estimating noise distribution variance, there is in actual environment using value widely.

Accompanying drawing explanation

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is the relatively prime array structure schematic diagram of the present invention;

The all possible location sets hum pattern of Virtual array when Fig. 3 is M=2, N=3 in the present invention;

Fig. 4 is the estimation effect comparison diagram of the present invention and existing a kind of tradition relatively prime array direction of arrival angular estimation method;

Fig. 5 is that the present invention is to the design sketch estimating number of source extended capability.

Embodiment

Referring to accompanying drawing, technical scheme of the present invention and effect are described in further detail.

Embodiment 1

In military surveillance, such as in field of radar, surveyor does not know the information such as number and direction of arrival angle of target in advance, and these information are particularly important, for obtaining these information, common way is the number first estimating target, then the spatial spectrum of echo signal is obtained by methods such as subspaces, Traditional Space Power estimation be all be generally based upon target number known when, and the target numbers of traditional scheme identification will be less than array number, if the target numbers of catching will more than array element number, traditional way is the array element number increasing array acceptor, this adds cost to a certain extent or scene cannot realize, in classic method, the defect such as the large and evaluated error of operand will to target detection, speed and the precision of passive location bring greater impact: can not detection target real-time, None-identified when target number is a lot, target acquistion unsuccessfully etc.

For this reason, the present invention, through innovation research, provides a kind of relatively prime array direction of arrival angular estimation method based on sparse reconstruct, and with reference to Fig. 1, performing step of the present invention is as follows:

1) form relatively prime array with 2M+N-1 aerial receiver, each aerial receiver is called an array element, and hypothesis has K narrow band signal to incide this relatively prime array, K >=1.

1a) see Fig. 2, place an aerial receiver every Md, place N number of aerial receiver altogether, form uniform linear array 1, be called for short linear array 1, an aerial receiver is placed again every Nd, place 2M-1 aerial receiver altogether, form uniform linear array 2, be called for short linear array 2, the array element distance of linear array 1 is Md, the array element distance of linear array 2 is Nd, its its N>M >=2 and M, N is mutual, suppose have individual K far field narrow band signal to incide in this linear array, and signal adds the white complex gaussian noise that average is 0 in communication process, 0<d≤λ/2, λ is the narrow band signal wavelength inciding relatively prime array, first array element of definition linear array 1 is the array element 0 of relatively prime array.

1b) combination linear array 1 and linear array 2 are relatively prime array: be apart the position of Nd after first of linear array 2 array element being positioned over array element 0, due to N>M >=2, first array element of linear array 2 is necessarily after the 2nd array element of linear array 1, linear array 2 is interspersed among linear array 1, sees Fig. 2.In theory when array length is very large time, linear array 1 and linear array 2 in the distance may be overlapping, due to M, the selected of N is relatively prime, and the length that linear array 1 and linear array 2 are chosen is limited, so in the present invention, linear array 1 and linear array 2 can not be overlapping, all array elements of linear array 2 insert in linear array 1 successively, linear array 1 and linear array 2 on the same line, from relatively prime array elements 0, each array element is named to be followed successively by array element 0 from the head to the tail, array element 1 ..., array element 2M+N-2.

2) by relatively prime array antenna receiver, extraterrestrial target signal is sampled, obtain array output signal Y (t), definition Y _mt () is the output signal of m array element, m=0,1 ..., 2M+N-2.

3) calculate virtual array according to relatively prime array output signal Y (t) and receive data vector y.

4) stress and strain model is carried out to detection direction of arrival angle observation space, spatial domain, construct super complete base Φ (θ) and define a spatial domain sparse vector s.

5) detection spatial domain direction of arrival angular estimation be converted into solve following sparse constraint equation:

min ||s|| ₁

subject to ||y-Φ(θ)s|| ₂≤η,

s≥0

Theoretical according to sparse signal reconfiguring, arbitrary signal can by a basis matrix linear expression, the object of super complete base Φ (θ) matrix herein constructed is exactly by the reception data y of virtual array, showed by the form of matrix, be convenient to build sparse matrix equation, further solving of direction of arrival angular estimation be converted into solving spatial domain sparse vector s.

Wherein s is the unknown vector that Q × 1 is tieed up, and η is the error distributed parameter needing to pre-estimate, || || ₁the single order norm of representing matrix, || || ₂the second order norm of representing matrix.

6) adopt convex Optimization Method sparse constraint equation, obtain the most sparse solution of unknown vector s due to convex optimization method much and relative maturity, the methods such as Newton iteration method can be adopted to solve, or adopt ripe kit to process, the sparse solution of s can be obtained, can select according to specific environment, not add to repeat at this.

7) the most sparse solution that obtains of step 6 vector is a K sparse vector, and namely wherein only have K value for nonzero value, its residual value is zero, in fact null value is approximate null value, see Fig. 4, and K=2 in Fig. 4, the direction in space angle that these 2 nonzero values are corresponding is exactly the direction of arrival angle of incoming signal, therefore, with direction of arrival angular region θ=[θ ₁, θ ₂..., θ _q..., θ _q] value be x-axis coordinate, with the range value of vector is y-axis coordinate, draws amplitude spectrogram, and K spectrum peak before larger according to order searching amplitude from high to low from this amplitude spectrogram, the x-axis coordinates corresponding to peak point at these spectrum peaks are required direction of arrival angle value.

During relatively prime arrayed applications is estimated to DOA by the present invention, actual array element Received signal strength is converted into virtual array Received signal strength, by selecting irredundant virtual Received signal strength, reduce signal transacting data volume, reduce operand, under the condition that array element number is certain, add the discernible number of source of array.

Embodiment 2

Based on the relatively prime array direction of arrival angular estimation method of sparse reconstruct with embodiment 1, wherein step 3) calculate virtual array according to actual array output signal Y (t) and receive data vector y, comprise the following steps:

3a) obtain actual array position vector v by relatively prime array position information, the corresponding relatively prime array of value of v is from the head to the tail every the array element information at d place, interval from array element 0, if there is array element, then array element information is 1, if without array element, then array element information is 0.

3b) calculate Virtual array location sets ω (n) by actual array position vector v, ω (n)=(v*v ^-) (n), in formula, * represents convolution, v ^-represent reversing of v, n=-(2M-1) N,-(2M-1) N+1 ..., (2M-1) N-1, (2M-1) N, n is possible of the multiple for d of each array element relative distance in relatively prime array, see Fig. 3, as the M=2 of relatively prime array, during N=3, Virtual array location sets ω (n) obtained.

3c) choose break-even Virtual array positional information n=-1 is chosen ,-2 by ω (n) ...-(2M-1) N, and the element of ω (n) ≠ 0, formed not choosing other elements herein, is contain noise information, n=1 because of virtual Received signal strength during n=0,2, ..., virtual Received signal strength during (2M-1) N and n=-1 ,-2, ..., the virtual Received signal strength conjugation each other of-(2M-1) N, can not increase the estimated accuracy at direction of arrival angle, if ω (n) is M=2 shown in Fig. 3, N=3, selected break-even Virtual array positional information this break-even Virtual array positional information is the n value eliminating ω (0) value and ω (n) conjugation each other.

3d) calculate the Virtual array positional information chosen corresponding virtual reception vector y, the wherein reception data y of r Virtual array _r=Y _p(t) × Y _q ^h(t)/T, () ^hrepresenting matrix conjugate transpose operation, wherein p, q get and satisfy condition any one group of integer pair of 0≤p≤2M-1,0≤q≤N-1, || represent and take absolute value.

The present invention adopts rarefaction representation technology that the estimation at direction of arrival angle is converted into the reconstruct of sparse signal, the technical matters of classic method existence is solved by new theory technology, the spatial domain sparse characteristic of incident signal source is utilized to carry out modeling, need when simplifying the relatively prime array received data of conventional process to calculate autocorrelation matrix, cross-correlation matrix, extract the process of sequence afterwards, and improve virtual array select dictionary, virtual array is made to receive data more excellent, thus estimate maximum number of sources, breach the Rayleigh limit of array resolution, raising target reconnaissance and passive location are at low signal-to-noise ratio, low fast umber of beats, DOA estimated accuracy under low priori condition, avoid the target reconnaissance error because angle estimation error causes.

Embodiment 3

Based on the relatively prime array direction of arrival angular estimation method of sparse reconstruct with embodiment 1-2, wherein step 5) calculating to error distributed parameter η parameter, comprise the following steps:

5a) calculate the reception data y at w (0) place, Virtual array position ₀, y ₀=Y ₀(t) × Y ₀ ^h(t)/T, () ^hthe conjugate transpose operation of representing matrix.

5b) according to formula error of calculation distributed parameter η, wherein G is the length receiving data vector y, and T is the fast umber of beats of sampling, represent vector y second order norm square.

The present invention is without the need to knowing the number of target in advance; The cross-correlation information of array is adopted when calculating virtual array Received signal strength, the auto-correlation information of noise is not brought into or is seldom with in the virtual array Received signal strength selected by human model, The present invention gives the model error distributed parameter of virtual array Received signal strength in relatively prime array, without the need to known or estimating noise distribution variance, simplify computation process, there is using value widely in actual environment.

Embodiment 4

Based on the relatively prime array direction of arrival angular estimation method of sparse reconstruct with embodiment 1-3, wherein in step 4, stress and strain model is carried out to direction of arrival angle observation space, spatial domain, constructs super complete base Φ (θ) and the process defining a spatial domain sparse vector s comprises:

4a) according to the spatial domain sparse characteristic that incident signal source has, space lattice is carried out to observation spatial domain and divides process, be about to observation spatial domain [-90 °, 90 °] and be divided into Q angle at equal intervals, θ=[θ ₁, θ ₂..., θ _q..., θ _q], θ represents direction of arrival angular region, θ _qbe q angular interval, q=1,2, ..., Q, Q>>M, the value at stress and strain model interval is according to expecting that the angle estimation precision reached sets, and the interval of stress and strain model is less, and the angle estimation value precision finally obtained is higher.

The guiding matrix Φ (θ) of G × Q dimension corresponding after 4b) constructing a signal rarefaction.

Φ(θ)＝[α(θ ₁),...,α(θ _q),...,α(θ _Q)]

Wherein, α (θ _q) represent deflection θ _qcorresponding steering vector:

$\mathrm{\&alpha;}\left({\mathrm{\&theta;}}_q\right)={[e^{\widehat{\mathrm{\&omega;}}\left(1\right)\frac{j2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin {\mathrm{\&theta;}}_q},...,e^{\widehat{\mathrm{\&omega;}\left(n\right)\frac{j2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}}\sin {\mathrm{\&theta;}}_q}]}^T$

Wherein, n=1,2..., (2M-1) N, () ^trepresenting matrix transpose operation, j is imaginary unit.

This guiding matrix has incorporated all possible angle set in detection spatial domain, obtains most sparse solution by solving obtain the coefficient of each possibility angle, the corresponding object wave of large coefficient reaches deflection, and little coefficient represents that the party is to driftlessness.

Effect of the present invention illustrates by following emulation:

Embodiment 5

Based on the relatively prime array direction of arrival angular estimation method of sparse reconstruct with embodiment 1-4,

1. simulated conditions:

9 aerial receivers are adopted to form relatively prime array, wherein the array element distance of relatively prime array midline battle array 1 is 3d, the array element distance of linear array 2 is 4d, d is the half of incoming signal wavelength, sampling number is 500, observation spatial domain angular range is [-90 °, 90 °], and space lattice divides and is spaced apart 0.1 °.

2. emulate content and result:

Emulation 1:

Suppose have 2 incoherent narrow band signals to incide relatively prime linear array with angle-40 ° and 10 ° respectively, signal to noise ratio (S/N ratio) is by-5db, the present invention and existing S-MUSIC method is utilized to carry out the experiment of direction of arrival angular estimation respectively, experimental result as shown in Figure 4, wherein: in Fig. 4, horizontal ordinate represents spatial domain angle, ordinate represents that normalized power is composed, and solid line represents that the spatial spectrum curve that the inventive method obtains, dotted line represent the spatial spectrum curve that traditional S-MUSIC method obtains.

As can be seen from Figure 4, the present invention utilizes the angle that in the openness sparse solution obtained in the spatial domain of signal source, large coefficient is corresponding, for the direction of arrival angle of signal source, the coefficient that aimless deflection is corresponding approximates 0, when observer does not know target numbers, the present invention can obtain more sparse result, and sharp-pointed spectrum peak is conducive to obtaining more excellent DOA and estimates, obtains better angular resolution.

Embodiment 6

Based on the relatively prime array direction of arrival angular estimation method of sparse reconstruct with embodiment 1-4,

Emulation 2:

Suppose have 18 incoherent narrow band signals to incide relatively prime linear array, signal to noise ratio (S/N ratio) is 4db.Utilize the present invention to carry out the experiment of direction of arrival angular estimation, experimental result as shown in Figure 5, wherein:

In Fig. 5, horizontal ordinate represents spatial domain angle, and ordinate represents that normalized power is composed.

As can be seen from Figure 5, when M=3, N=4, the present invention can estimate maximum 18 signal sources, and more than the discernible MN=12 of a traditional S-MUSIC signal source, the present invention shows outstanding performance on multi-targets recognition.

To sum up, a kind of relatively prime array direction of arrival angular estimation method based on sparse reconstruct disclosed by the invention, mainly solve prior art operand large, need priori many, identification number of source is few, the problem that passive location evaluated error is large, implementation step is: 1) utilize aerial receiver to form relatively prime linear array; 2) sampling is carried out to spacing wave and obtain observation data; 3) obtain Virtual array by observation data and receive data vector; 4) by spatial domain stress and strain model, super complete base is constructed; 5) receive the rarefaction representation relation of data vector and super complete base according to Virtual array, set up sparse constraint equation; 6) adopt convex Optimization Method sparse constraint equation, obtain most sparse solution; 7) according to sparse solution and space angle relation one to one, draw amplitude spectrogram, obtain direction of arrival angle value.The present invention improves the arithmetic speed of passive direction finding when not needing excessive priori, improve the estimated performance to sense angle under the discernible number of source of relatively prime array in certain array number situation and low signal-to-noise ratio.

The present invention does not need a lot of prioris, in the non-co-operation signals such as signal blind Detecting detect advantageously, while reducing DOA estimation operand, ensure that rapid reaction and the accurate and effective of target reconnaissance and passive location, avoid simultaneously number of sources more time None-identified problem, can be used for target reconnaissance and passive location.

Claims (4)

1., based on a relatively prime array direction of arrival angular estimation method for sparse reconstruct, it is characterized in that, comprise the following steps:

1) form relatively prime array with 2M+N-1 aerial receiver, each aerial receiver is called an array element, and hypothesis has K signal to incide this relatively prime array, K >=1;

1a) form uniform linear array 1 with N number of aerial receiver, be called for short linear array 1, uniform linear array 2 is formed with 2M-1 aerial receiver, be called for short linear array 2, the array element distance of linear array 1 is Md, and the array element distance of linear array 2 is Nd, wherein N>M >=2 and M, N are relatively prime, 0<d≤λ/2, λ is the narrow band signal wavelength inciding relatively prime array, and first array element of definition linear array 1 is the array element 0 of relatively prime array;

1b) combination linear array 1 and linear array 2 are relatively prime array: first of linear array 2 array element be positioned over array element 0 at a distance of the position for Nd, all array elements of linear array 2 insert in linear array 1 successively, from relatively prime array elements 0, each array element is named to be followed successively by array element 0 from the head to the tail, array element 1,, array element 2M+N-2;

2) by relatively prime array antenna receiver, extraterrestrial target signal is sampled, obtain array output signal Y (t), definition Y _mt () is the output signal of m array element, m=0,1 ..., 2M+N-2;

3) calculate virtual array according to relatively prime array output signal Y (t) and receive data vector y;

4) stress and strain model is carried out to detection direction of arrival angle observation space, spatial domain, construct super complete base Φ (θ), and define a spatial domain sparse vector s;

5) detection spatial domain direction of arrival angular estimation be converted into solve following sparse constraint equation:

min||s|| ₁

subject to ||y-Φ(θ)s|| ₂≤η,

s≥0

Wherein s is the unknown vector that Q × 1 is tieed up, and η is the error distributed parameter needing to pre-estimate, || || ₁the single order norm of representing matrix, || || ₂the second order norm of representing matrix;

6) adopt convex Optimization Method sparse constraint equation, obtain the most sparse solution of unknown vector s

7) with direction of arrival angular region θ=[θ ₁, θ ₂..., θ _q..., θ _q] value be x-axis coordinate, with the range value of vector is y-axis coordinate, draws amplitude spectrogram, and K spectrum peak before larger according to order searching amplitude from high to low from this amplitude spectrogram, the x-axis coordinates corresponding to peak point at these spectrum peaks are the direction of arrival angle value of target.

2. a kind of relatively prime array direction of arrival angular estimation method based on sparse reconstruct according to claim 1, is characterized in that, wherein step 3) described in virtual array receive data vector y, by following formal construction:

3a) obtain actual array position vector v by relatively prime array position information, the corresponding relatively prime array of value of v is from the head to the tail every the array element information at d place, interval from array element 0, if there is array element, then array element information is 1, if without array element, then array element information is 0;

3b) calculate Virtual array location sets ω (n) by actual array position vector v, ω (n)=(v*v ^-) (n), in formula, * is convolution, v ^-reversing of v, n=-(2M-1) N ,-(2M-1) N+1 ..., (2M-1) N-1, (2M-1) N, n are the institute's likely multiples for d of each array element relative distance in relatively prime array;

3c) choose break-even Virtual array positional information n=-1 is chosen ,-2 by ω (n) ... ,-(2M-1) N, and the element of ω (n) ≠ 0, formed r=1,2 ... G, G are length;

3d) calculate the Virtual array positional information chosen corresponding virtual reception vector y, the wherein reception data y of r Virtual array _r=Y _p(t) × Y _q ^h(t)/T, () ^hrepresenting matrix conjugate transpose operation, wherein p, q get and satisfy condition any one group of integer pair of 0≤p≤2M-1,0≤q≤N-1, || represent and take absolute value.

3. a kind of relatively prime array direction of arrival angular estimation method based on sparse reconstruct according to claim 1, is characterized in that, wherein step 5) described in error parameter η, by following formal construction:

5a) calculate the reception data y at w (0) place, Virtual array position ₀, y ₀=Y ₀(t) × Y ₀ ^h(t)/T, () ^hthe conjugate transpose operation of representing matrix;

5b) according to formula error of calculation distributed parameter η, wherein G is break-even Virtual array positional information length, T for sampling fast umber of beats, represent vector y second order norm square.

4. a kind of relatively prime array direction of arrival angular estimation method based on sparse reconstruct according to claim 1, is characterized in that, wherein step 4) described in the super complete base Φ (θ) of structure, by following formal construction:

4a) according to the spatial domain sparse characteristic of signal source, adopt space lattice division methods, spatial domain [-90 °, 90 °] will be observed to be divided into Q angle at equal intervals, be defined as direction of arrival angular region θ=[θ ₁, θ ₂..., θ _q..., θ _q], θ _qfor the arrival bearing angle of echo signal, q=1,2 ..., Q, Q>>M;

4b) construct the super complete base Φ (θ) after a spatial domain rarefaction:

Φ(θ)＝[α(θ ₁),...,α(θ _q),...,α(θ _Q)]

Wherein, α (θ _q) represent deflection θ _qcorresponding steering vector:

$\mathrm{\&alpha;}\left({\mathrm{\&theta;}}_q\right)={[e^{\widehat{\mathrm{\&omega;}}\left(1\right)\frac{j2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin {\mathrm{\&theta;}}_q},...,e^{\widehat{\mathrm{\&omega;}}\left(n\right)\frac{j2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin {\mathrm{\&theta;}}_q}]}^T$

Wherein, n=1,2..., (2M-1) N, () ^trepresenting matrix transpose operation, j is imaginary unit.