CN107255796A - Arrowband near-field signals source localization method under a kind of non-uniform noise - Google Patents
Arrowband near-field signals source localization method under a kind of non-uniform noise Download PDFInfo
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- CN107255796A CN107255796A CN201710613731.7A CN201710613731A CN107255796A CN 107255796 A CN107255796 A CN 107255796A CN 201710613731 A CN201710613731 A CN 201710613731A CN 107255796 A CN107255796 A CN 107255796A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/04—Position of source determined by a plurality of spaced direction-finders
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Abstract
The present invention relates to arrowband near-field signals source localization method under a kind of non-uniform noise, first, eliminated using the main back-diagonal element for the estimate for receiving data array covariance matrix apart from unknown quantity, and construct Teoplitz structure matrix, non-uniform noise is converted into Uniform noise；Then, information source directional information is estimated using Wave arrival direction estimating method on the toeplitz matrix of construction；Finally, the Teoplitz structure matrix only contained apart from unknown quantity is constructed using the estimate of the second back-diagonal element and direction of arrival that receive array of data covariance matrix, the estimate of arrowband near-field signals source distance is obtained using Teoplitz structure matrix.Noise problem heterogeneous when the present invention efficiently solves near-field source localization, and calculate simple, there is good estimation performance in direction of arrival and apart from upper.
Description
Technical field
The invention belongs to array signal process technique field, and in particular to near-field signals source in arrowband under a kind of non-uniform noise
Localization method.
Background technology
Near-field source localization technology is in the speaker's alignment system, family expenses secondary navigation system, thunder using microphone array
Reach, the field such as sonar, radio communication and geological prospecting has important application.Have many fixed for solving near-field signals source
The method of position problem is suggested, such as weighted linear Forecasting Methodology (WLP) and near field positioning (N-GESPRIT) side based on ESPRIT
Method etc..However, these methods are assumed based on uniform white noise mostly, that is, assume that array noise is unknown uniform white noise
Or it is easily converted to any noise of the known statistical property of uniform white noise.Obviously, in actual applications, Uniform noise
Hypothesis not always set up.To adapt to more generally apply, noise model is generally established as non-homogeneous white noise.At this
Under noise model, the performance of aforementioned algorism can be greatly affected, and estimated accuracy is substantially reduced.
The content of the invention
It is an object of the invention to overcome problems of the prior art, there is provided arrowband near field under a kind of non-uniform noise
Signal source localization method, can be applied to non-uniform noise model, and estimated accuracy is high.
In order to achieve the above object, the present invention is adopted the following technical scheme that：
Comprise the following steps：
(1) estimate for receiving data array covariance matrix is tried to achieve using the array output signal of symmetrically and evenly linear array
(2) estimate for receiving data array covariance matrix is utilizedMain back-diagonal element eliminate apart from unknown
Amount, and construct Teoplitz structure matrixNon-uniform noise is converted into Uniform noise；
(3) in the toeplitz matrix of constructionUpper use Wave arrival direction estimating method obtains arrowband near-field signals source direction
Estimate
(4) estimate for receiving data covariance matrix is utilizedThe second back-diagonal element and arrowband near-field signals source
The estimate in direction constructs the Teoplitz structure matrix only contained apart from unknown quantity
(5) Teoplitz structure matrix is usedObtain the estimate of arrowband near-field signals source distance
Wherein, arrowband near-field signals are to incide K incoherent signal in symmetrically and evenly linear arrayIt is symmetrical equal
Even linear array includes 2M+1 omnidirectional's sensor array element, and M span is M >=K, and array element spacing is d, the side of arrowband near-field signals
Position information beθkRepresent k-th of incoherent signal sk(n) direction of arrival angle, direction of arrival angle is k-th of non-phase
Dry signal sk(n) relative to the angle counterclockwise of symmetrically and evenly linear array normal direction, rkIt is k-th of incoherent signal sk(n) relative to right
Claim the distance at the center of even linear array.
Further, the estimate for receiving data array covariance matrix is obtained in step (1)Specifically include following step
Suddenly：
101st, the center for making symmetrically and evenly linear array is reference array element, and array output signal is
Y (n)=A (θ, r) s (n)+w (n) (1)
Wherein, Α is array response matrix,A is steering vector,
It is defined as(·)TRepresent transposition, τmkRepresent that k-th of arrowband near field is believed
Number on m-th of sensor caused by time delay phase delay, j represents unit imaginary number, j2=-1；
When k-th of arrowband near-field signals is in Fresnel region, by τmkUse Taylor series expansion：
Wherein, λ is arrowband near-field signals wavelength, and d is array element
Spacing, O () represents that single order is infinitely small；
Array noise w (n) is the incoherent zero-mean gaussian random process of space-time, and uncorrelated to receiving signal, then：
Wherein Q represents noise covariance matrix, is defined as：
Wherein,Represent the noise power in m-th of array element；
102nd, reception data array covariance matrix R is tried to achieve according to array output signal：
R=E { y (n) yH(n)} (4)
103rd, due to limited sampling in practical application, using the estimate for receiving data array covariance matrixCome approximate
R is substituted, its calculation is：
Wherein, N represents hits.
Further, Teoplitz structure matrix in step (2)Specific configuration step include：
201st, spread out according to the definition for receiving data array covariance matrix R, R (p, q) individual element is：
Wherein, pkRepresent the power in k-th of arrowband near-field signals source, a (θk,rk) represent that k-th of arrowband near-field signals source is corresponding
Steering vector, Q represents noise covariance matrix,Comprise only directional information,
Contain directional information and range information；
202nd, φ is madekCoefficient (p-M-1)2-(q-M-1)2Equal to zero, eliminate apart from unknown quantity rk, obtain p, q relation
For：Q=2M+2-p, selection receives the estimate of data array covariance matrixThe middle main back-diagonal member for meeting this relation
Element：
Wherein, δs,tRepresent Kronecker function；
203rd, Teoplitz structure matrix is constructed
Further, in step (3), derived by algebraically, by Teoplitz structure matrixTurn to：Wherein A1(θ) is defined as Represent information source covariance matrix, IM+1Table
Show the unit matrix of (M+1) × (M+1) dimensions；It is rightSingular value decomposition is carried out, is estimated using classical Wave arrival direction estimating method
The estimate in information source direction
Further, classical Wave arrival direction estimating method uses MUSIC algorithms.
Further, in step (4), Teoplitz structure matrix is constructedSpecific steps include：
301st, spread out according to the definition for receiving data array covariance matrix R, R (p, q) individual element is：
Wherein, pkRepresent the power in k-th of arrowband near-field signals source, a (θk,rk) represent that k-th of arrowband near-field signals source is corresponding
Steering vector, Q represents noise covariance matrix,Comprise only directional information,
Contain directional information and range information；
302nd, q=2M-p is made, selection receives the estimate of data array covariance matrixIt is middle to meet the of this relation
Two back-diagonal elements：
Wherein, δs,tRepresent Kronecker function,
303rd, Teoplitz structure matrix is constructed
Further, the estimate of arrowband near-field signals source distance is obtainedSpecific steps include：
Derived by algebraically, by what is obtainedTurn to：Wherein A2(θ, it is r) fixed
Justice is
IMRepresent the unit matrix of M × M dimensions；Due to having obtained the estimate in arrowband near-field signals source direction in step (3), thenIn
Comprise only apart from unknown quantity, it is rightSingular value decomposition is carried out, arrowband near-field signals source is obtained using the method for Mutual coupling
The estimate of distance
Compared with prior art, the present invention has following beneficial technique effect：
The present invention is positioned to near-field signals source under non-uniform noise, utilizes the master for receiving data array covariance matrix
Back-diagonal element constructs Teoplitz structure matrix, eliminates direction unknown quantity and by non-uniform noise conversion in order to equal
Even noise, first estimation obtains the direction of arrival angle of signal, recycles the estimate of direction of arrival and receives data array covariance
The second back-diagonal element construction of matrix only contains the Teoplitz structure matrix apart from unknown quantity, estimates the distance of information source
Information.Noise problem heterogeneous when the present invention efficiently solves near-field source localization, and calculate simple.Compared to existing
Near-field source localization algorithm, present invention estimated accuracy in the case of low signal-to-noise ratio is substantially better than WPL and N-GESPRIT and calculated
Method, has good estimation performance, the present invention is easy and effective and suitable for more generally noise in direction of arrival and apart from upper
Scene, application is wider.
Brief description of the drawings
Fig. 1 is array junctions composition of the present invention.
Fig. 2 (a) is the estimation performance of near-field signals direction of arrival angular dimensions with signal to noise ratio (SNR) change curve, Fig. 2
(b) it is the estimation performance of near-field signals distance parameter with the change curve of signal to noise ratio.
Fig. 3 (a) is the estimation performance of near-field signals direction of arrival angular dimensions with hits (N) change curve, Fig. 3 (b)
For near-field signals distance parameter estimation performance with hits change curve.
Embodiment
The present invention is described in further details below in conjunction with the accompanying drawings.
In the present invention, first, distance is eliminated not using the main back-diagonal element for receiving array of data covariance matrix
The amount of knowing, and Teoplitz structure matrix is constructed, non-uniform noise is converted into Uniform noise；Then, in Top's profit of construction
Hereby information source directional information is estimated on matrix using classical Wave arrival direction estimating method；Finally, using receiving array of data
Second back-diagonal element of covariance matrix and the estimate of direction of arrival construct the Top's profit only contained apart from unknown quantity
Hereby structure matrix, and being estimated using the method similar with direction of arrival signal distance information.Arrowband near-field signals be into
It is mapped to K incoherent signal in symmetrically and evenly linear arraySymmetrically and evenly linear array includes 2M+1 omnidirectional's sensor array
Member, M span is M >=K, and array element spacing is d, and the azimuth information of arrowband near-field signals isθkRepresent kth
Individual incoherent signal sk(n) direction of arrival angle, direction of arrival angle is k-th of incoherent signal sk(n) relative to symmetrically and evenly line
The tactical deployment of troops to angle counterclockwise, rkIt is k-th of incoherent signal sk(n) relative to symmetrically and evenly linear array center distance.
Hereinafter, for aleatory variable a,Represent variable a estimate.
Arrowband near-field signals source localization method, implements step summary as follows under a kind of non-uniform noise：
1) estimate for receiving data array covariance matrix R is calculated
2) useMain back-diagonal element construction comprise only the Teoplitz structure matrix of information source directional information
3) useEstimate information source direction
4) useThe second back-diagonal element construction Teoplitz structure matrix
5) useEstimate information source distance
It is specifically described below.
K incoherent signalIncide in symmetrically and evenly linear array, this symmetrically and evenly linear array it is complete comprising 2M+1
To sensor array element, M span is M >=K, and array element spacing is d, and the azimuth information of arrowband near-field signals is
θkRepresent k-th of incoherent signal sk(n) relative to the angle counterclockwise (direction of arrival angle) of symmetrically and evenly linear array normal direction, rkIt is
K-th of incoherent signal sk(n) relative to symmetrically and evenly linear array center distance.Referring to Fig. 1.
The center for making symmetrically and evenly linear array is reference array element, and array output signal is
Y (n)=A (θ, r) s (n)+w (n) (1)
Wherein, Α is array response matrix,A is steering vector,
It is defined as(·)TRepresent transposition, τmkRepresent k-th of signal at m-th
On sensor caused by time delay phase delay, j represents unit imaginary number, j2=-1.When k-th of signal is in Fresnel
Area (i.e. rk∈(0.62(D3/λ)1/2,2D2/ λ), wherein D represents array aperture) when, can be by τmkWith Taylor (Taylor) series
Expansion：
Wherein, λ is arrowband near-field signals wavelength, and d is array element
Spacing, O () represents that single order is infinitely small.
W (n) is array noise, and array noise is the incoherent zero-mean gaussian random process of space-time, and believed with receiving
It is number uncorrelated, i.e.,：
Wherein Q represents noise covariance matrix, is defined as：
Wherein,Represent the noise power in m-th of array element.
Step 1) calculate reception data array covariance matrix valueSpecific method be：
Reception data array covariance matrix R is tried to achieve according to real array output signal：
R=E { y (n) yH(n)} (4)
Wherein, y (n) represents array output signal.Due to limited sampling in practical application, it is impossible to directly asked according to (4) formula
Data array covariance matrix R must be received, using estimateCarry out approximate substitution R, its calculation is：
Wherein, N represents hits, and y (n) represents array output signal.
Step 2) useMain back-diagonal element construction comprise only the Teoplitz structure matrix of information source directional informationSpecific method is：
A, according to receive data array covariance matrix R definition spread out, R (p, q) individual element (pth row q
Arrange corresponding element) be：
Wherein, pkRepresent the power of k-th of information source, a (θk,rk) the corresponding steering vector of k-th of information source is represented, Q represents to make an uproar
Sound covariance matrix,Comprise only directional information,Containing directional information and
Range information, λ is incoming signal wavelength, and d is array element spacing；
B, make φkCoefficient (p-M-1)2-(q-M-1)2Equal to zero, so as to eliminate apart from unknown quantity rk.P is obtained, q's
Relation is：Q=2M+2-p, selection receives data array covariance matrix valueThe middle element for meeting this relation (is led
Back-diagonal element)：
Wherein, δs,tRepresent Kronecker function；
C, construction Teoplitz structure matrix
Step 3) useEstimate information source directionSpecific method is：
Derive, will can obtain in (8) by algebraicallyTurn to：Wherein A1
(θ) is defined as Represent information source covariance matrix, IM+1Represent the unit matrix of (M+1) × (M+1) dimensions.It can see
Go out, now non-uniform noise has been converted into Uniform noise, andIn comprise only direction unknown quantity, it is therefore, rightCarry out unusual
Value is decomposed, and the estimate in information source direction is just can obtain using classical Wave arrival direction estimating method (such as MUSIC algorithms)
Step 4) useThe second back-diagonal element construction Teoplitz structure matrixSpecific method be：
A, according to receive data array covariance matrix R definition spread out, R (p, q) individual element (pth row q
Arrange corresponding element) be：
Wherein, pkRepresent the power of k-th of information source, a (θk,rk) the corresponding steering vector of k-th of information source is represented, Q represents to make an uproar
Sound covariance matrix,Comprise only directional information,Containing directional information and
Range information；
B, make q=2M-p, selection receives data array covariance matrix valueThe middle element for meeting this relation is (i.e.
Second back-diagonal element)：
Wherein, δs,tRepresent Kronecker function,
C, construction Teoplitz structure matrix
Step 5) useEstimate information source distanceSpecific method be：
Derive, will can obtain in formula (11) by algebraicallyTurn to：Wherein
A2(θ r) is defined as
IMRepresent the unit matrix of M × M dimensions.Due to step 3) in obtained information source direction estimation value, thereforeIn comprise only distance not
The amount of knowing is therefore, rightSingular value decomposition is carried out, just may be used using the method (such as MUSIC algorithms) similar to Mutual coupling
Obtain the estimate of information source distance
The effect of the above method is illustrated below by following different situations：
There is a unknown incoming signal of two direction of arrival angle (i.e. arrowband near-field signals) in space, its azimuth information be respectively (-
13 °, 1.7 λ), (28 °, 2.5 λ), symmetrically and evenly linear array contains 2M+1=9 array element, and array element is at intervals of d=λ/4.It is right in emulation
The present invention is compared and weighted linear predicts (WPL) and near field positioning (N-GESPRIT) algorithm based on ESPRIT, provided simultaneously
CRB circle, referring to Fig. 2 (a) and Fig. 2 (b) and Fig. 3 (a) and Fig. 3 (b).In addition, signal to noise ratio (SNR) calculation formula is：
In formula, pkThe power of k-th of information source is represented,Represent the noise power in m-th of array element.Each simulation result
All obtained via P=1000 independent repetition experiment.Array noise model is the incoherent zero-mean of space-time heterogeneous
Gaussian noise, noise covariance matrix is：
Q=diag { 2,20,5,1,0.5,3.7,3,7,18 }
It can see by Fig. 2 (a) and Fig. 2 (b), present invention estimated accuracy in the case of low signal-to-noise ratio is substantially better than WPL
And N-GESPRIT algorithms.The present invention calculates simple and is applied to more generally noise scenarios simultaneously, and application is wider.
When signal to noise ratio is very high, there is saturated characteristic in the inventive method, and estimated accuracy lifting tends to be steady, but such case actually should
It will not be run into substantially in, therefore not influence the application and popularization of the present invention.
It can see by Fig. 3 (a) and Fig. 3 (b), inventive algorithm has good estimation in direction of arrival angle and apart from upper
Performance.
Claims (7)
1. arrowband near-field signals source localization method under a kind of non-uniform noise, it is characterised in that：Comprise the following steps：
(1) estimate for receiving data array covariance matrix is tried to achieve using the array output signal of symmetrically and evenly linear array
(2) estimate for receiving data array covariance matrix is utilizedMain back-diagonal element eliminate apart from unknown quantity, and structure
Produce Teoplitz structure matrixNon-uniform noise is converted into Uniform noise；
(3) in the toeplitz matrix of constructionUpper use Wave arrival direction estimating method obtains estimating for arrowband near-field signals source direction
Evaluation
(4) estimate for receiving data covariance matrix is utilizedThe second back-diagonal element and arrowband near-field signals source direction
Estimate construct only contain apart from unknown quantity Teoplitz structure matrix
(5) Teoplitz structure matrix is usedObtain the estimate of arrowband near-field signals source distance
Wherein, arrowband near-field signals are to incide K incoherent signal in symmetrically and evenly linear arraySymmetrically and evenly line
Battle array includes 2M+1 omnidirectional's sensor array element, and M span is M >=K, and array element spacing is d, and the orientation of arrowband near-field signals is believed
Cease and beθkRepresent k-th of incoherent signal sk(n) direction of arrival angle, direction of arrival angle is incoherent k-th
Signal sk(n) relative to the angle counterclockwise of symmetrically and evenly linear array normal direction, rkIt is k-th of incoherent signal sk(n) relative to symmetrical
The distance at the center of even linear array.
2. arrowband near-field signals source localization method under a kind of non-uniform noise according to claim 1, it is characterised in that：Step
Suddenly the estimate for receiving data array covariance matrix is obtained in (1)Specifically include following steps：
101st, the center for making symmetrically and evenly linear array is reference array element, and array output signal is
Y (n)=A (θ, r) s (n)+w (n) (1)
Wherein, Α is array response matrix,A is steering vector, definition
For(·)TRepresent transposition, τmkRepresent that k-th of arrowband near-field signals exists
On m-th of sensor caused by time delay phase delay, j represents unit imaginary number, j2=-1；
When k-th of arrowband near-field signals is in Fresnel region, by τmkUse Taylor series expansion：
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Array noise w (n) is the incoherent zero-mean gaussian random process of space-time, and uncorrelated to receiving signal, then：
Wherein Q represents noise covariance matrix, is defined as：Its
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102nd, reception data array covariance matrix R is tried to achieve according to array output signal：
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103rd, due to limited sampling in practical application, using the estimate for receiving data array covariance matrixCarry out approximate substitution
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Wherein, N represents hits.
3. arrowband near-field signals source localization method under a kind of non-uniform noise according to claim 2, it is characterised in that：Step
Suddenly Teoplitz structure matrix in (2)Specific configuration step include：
201st, spread out according to the definition for receiving data array covariance matrix R, R (p, q) individual element is：
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Wherein, pkRepresent the power in k-th of arrowband near-field signals source, a (θk,rk) represent that k-th of arrowband near-field signals source is corresponding
Steering vector, Q represents noise covariance matrix,Comprise only directional information,
Contain directional information and range information；
202nd, φ is madekCoefficient (p-M-1)2-(q-M-1)2Equal to zero, eliminate apart from unknown quantity rk, p is obtained, q relation is：Q=
2M+2-p, selection receives the estimate of data array covariance matrixThe middle main back-diagonal element for meeting this relation：
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<mn>2</mn>
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</mrow>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<msub>
<mi>p</mi>
<mi>k</mi>
</msub>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>j</mi>
<mn>2</mn>
<mrow>
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<mi>M</mi>
<mo>+</mo>
<mn>2</mn>
<mo>-</mo>
<mi>p</mi>
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</mrow>
<msub>
<mi>&psi;</mi>
<mi>k</mi>
</msub>
</mrow>
</msup>
<mo>+</mo>
<msub>
<mi>&delta;</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>M</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>M</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, δs,tRepresent Kronecker function；
203rd, Teoplitz structure matrix is constructed
4. arrowband near-field signals source localization method under a kind of non-uniform noise according to claim 3, it is characterised in that：Step
Suddenly in (3), derived by algebraically, by Teoplitz structure matrixTurn to：Wherein
A1(θ) is defined as Represent information source covariance matrix, IM+1Represent the unit matrix of (M+1) × (M+1) dimensions；It is rightEnter
Row singular value decomposition, the estimate in information source direction is estimated using classical Wave arrival direction estimating method
5. arrowband near-field signals source localization method under a kind of non-uniform noise according to claim 4, it is characterised in that：Through
Allusion quotation Wave arrival direction estimating method uses MUSIC algorithms.
6. arrowband near-field signals source localization method under a kind of non-uniform noise according to claim 2, it is characterised in that：Step
Suddenly in (4), Teoplitz structure matrix is constructedSpecific steps include：
301st, spread out according to the definition for receiving data array covariance matrix R, R (p, q) individual element is：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
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<mrow>
<mo>&lsqb;</mo>
<mi>R</mi>
<mo>&rsqb;</mo>
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<mrow>
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<mi>H</mi>
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<mrow>
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<mi>k</mi>
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<mi>q</mi>
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</mrow>
<msub>
<mi>&phi;</mi>
<mi>k</mi>
</msub>
</mrow>
</msup>
<mo>+</mo>
<msub>
<mrow>
<mo>&lsqb;</mo>
<mi>Q</mi>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>q</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, pkRepresent the power in k-th of arrowband near-field signals source, a (θk,rk) represent that k-th of arrowband near-field signals source is corresponding
Steering vector, Q represents noise covariance matrix,Comprise only directional information,
Contain directional information and range information；
302nd, q=2M-p is made, selection receives the estimate of data array covariance matrixMiddle the second opposition for meeting this relation
Diagonal element：
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<msub>
<mi>g</mi>
<mi>p</mi>
</msub>
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<mi>&Delta;</mi>
</mover>
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<mi>e</mi>
<mrow>
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<mi>j</mi>
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</mrow>
<msub>
<mi>&eta;</mi>
<mi>k</mi>
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</mrow>
</msup>
<mo>+</mo>
<msub>
<mi>&delta;</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>M</mi>
</mrow>
</msub>
<msubsup>
<mi>&sigma;</mi>
<mi>M</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, δs,tRepresent Kronecker function,
303rd, Teoplitz structure matrix is constructed
7. arrowband near-field signals source localization method under a kind of non-uniform noise according to claim 6, it is characterised in that：Obtain
Obtain the estimate of arrowband near-field signals source distanceSpecific steps include：
Derived by algebraically, by what is obtainedTurn to：Wherein A2(θ r) is defined asIMTable
Show the unit matrix of M × M dimensions；Due to having obtained the estimate in arrowband near-field signals source direction in step (3), thenIn containing only
Have apart from unknown quantity, it is rightSingular value decomposition is carried out, arrowband near-field signals source distance is obtained using the method for Mutual coupling
Estimate
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