CN109298382A - A kind of non-homogeneous line array direction of arrival angle estimation method based on the very big algorithm of expectation - Google Patents
A kind of non-homogeneous line array direction of arrival angle estimation method based on the very big algorithm of expectation Download PDFInfo
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- CN109298382A CN109298382A CN201811053102.4A CN201811053102A CN109298382A CN 109298382 A CN109298382 A CN 109298382A CN 201811053102 A CN201811053102 A CN 201811053102A CN 109298382 A CN109298382 A CN 109298382A
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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
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
- G01S3/14—Systems for determining direction or deviation from predetermined direction
- G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae
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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
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/78—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using electromagnetic waves other than radio waves
- G01S3/782—Systems for determining direction or deviation from predetermined direction
-
- 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
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
- G01S3/802—Systems for determining direction or deviation from predetermined direction
- G01S3/8027—By vectorial composition of signals received by plural, differently-oriented transducers
Abstract
The present invention provides a kind of based on the non-homogeneous line array direction of arrival angle estimation method for it is expected very big algorithm, to realize the efficient direction of arrival angular estimation under signal deletion condition, using EM algorithm under management loading SBL frame, the output signal of virtual uniform straight line array is recovered in the way of iterated interpolation by non-homogeneous line array output signal, and parameter Estimation is carried out, realize the estimation to direction of arrival angle.The present invention improves the resolution capability of direction of arrival angular estimation, reduces evaluated error, is with a wide range of applications in reality.
Description
Technical field
The present invention relates to signal processing technology field, be related to be it is a kind of it is non-with line array direction of arrival angle estimation method.
Background technique
Carrying out estimation to incoming signal direction of arrival angle DOA using sensor array is that sonar, radar, radio etc. are led
One important content in domain.Existing major part DOA estimation method is focused on using uniform straight line array, however, non-homogeneous line array
It is also widely paid close attention in many cases.Such as when the operative sensor of a uniform straight line array can not work, lose
The output signal of this operative sensor influences the performance of DOA estimation.We can not work normally this part array element equal
Even line array regards non-homogeneous line array as.
Common high resolution DOA estimation algorithm can be divided into based on subspace and based on two class method of rarefaction representation.First
The representative of class method is the multiple signal classification MUSIC algorithm that the order based on signal covariance matrix is decomposed, but this algorithm
It is not directly applicable the DOA estimation of coherent signal.In order to solve this problem, it introduces Search Space Smoothing and constructs positive semidefinite
Covariance matrix proposes the multiple signal classification SS-MUSIC algorithm based on space smoothing.However, the algorithm is only applicable to
The array element that continuous uniform is distributed in non-homogeneous line array, can not be fully utilized the effective aperture of array.In order to differentiate relevant letter
Number, sparse signal reconfiguring theory persistently attracts attention and studies in recent years.Second class method include L1-SVD, L1-SRACV,
SPICE algorithm etc., these algorithms have preferable resolution in space closing signal, fewer snapshots and low signal-to-noise ratio SNR
Power and robustness.But in above-mentioned algorithm, the corresponding signal of non-homogeneous line array (uniform straight line array lack part array element) is lacked
Situation is lost seldom to be considered.
Summary of the invention
For overcome the deficiencies in the prior art, the present invention provides a kind of based on the non-homogeneous line array for it is expected very big EM algorithm
Direction of arrival angle estimation method, to realize in signal deletion (corresponding uniform straight line array part delayed output signals missing) situation
Under efficient direction of arrival angular estimation utilize non-homogeneous line array using EM algorithm under management loading SBL frame
Output signal recovers the output signal of virtual uniform straight line array in a manner of iterated interpolation, and carries out parameter Estimation, realization pair
The estimation of direction of arrival angle.
The technical solution adopted by the present invention to solve the technical problems includes the following steps:
Step 1: forming non-homogeneous line array using M sensor, and suppose there is K far field and be concerned with narrow band signal with not
Same angle is incident on non-homogeneous line array, while white Gaussian noise is added in signal communication process, non-homogeneous using this
Line array receives sample space signal, obtains the output signal X of array, wherein X=[x (t1),…,x(tn),…,x(tN)] be
One M × N-dimensional matrix, x (tn) it is tnWhen the array output signal inscribed, n=1 ..., N, N is sampling number of snapshots, and X is known as
Each sensor array is referred to as an array element by fragmentary data；
Step 2: construction one M × M ' dimension transition matrix P obtains linear relation X=PY according to observation data X,
Wherein, Y is the output signal matrix for the uniform straight line array that M ' × N-dimensional Virtual array number is M ', and Y is referred to as complete
Data；
Step 3: gridding observation space angle constructs super complete base A (θ)；
Step 4: direction of arrival angle estimation problem is converted sparse signal reconfiguring problem by the thought of rarefaction representation, solves
Following sparse matrix equation:
Y=A (θ) S+E
Wherein, S is M ' × N-dimensional unknown matrix, and E is M ' × N-dimensional additive white Gaussian noise matrix；
Step 5: defining a hyper parameter vector γ=[γ1,…,γi,…,γM′]T, γiFor the i-th row element of matrix S
Variance is updated by iteration using the very big EM algorithm of expectation, the convergence solution of γ is calculated, wherein the condition of convergence is hyper parameter
The variable quantity of the adjacent iteration twice of vector is less than threshold value, and threshold value value is 10-3To 10-4。
Step 6: with observation space mesh point θ=[θ1,θ2,…,θG] it is abscissa, with the convergence solution of hyper parameter vector γ
Amplitude be ordinate, draw amplitude spectrogram, from amplitude spectrogram according to the sequence of amplitude from big to small obtain before K peak
It is worth, abscissa angle value corresponding to K peak value is required incoming signal direction of arrival angle.
The specific implementation steps are as follows for the step 2:
Step 2.1: firstly, the vector p=[p of construction one M ' × 1 dimension1,…,pi,…,pM′]T, piIs defined as:
Wherein, M ' > M；
Step 2.2: the row vector that element is all 0 in puncture table diag (p) obtains transition matrix P, wherein diag ()
It indicates that diagonal matrix operation will be constructed；
Step 2.3: fragmentary data X is X=PY by complete data Y linear expression.
The specific implementation steps are as follows for the step 3:
Step 3.1: observation space angular range [- 90 °, 90 °] being divided at equal intervals and obtains G angle mesh point, is observed
Space networks lattice point is expressed as θ=[θ1,θ2,…,θG], wherein G > > K；
Step 3.2: obtaining the super complete base of M ' × G dimension of the first uniform straight line array ULA of corresponding M ' after the rarefaction of airspace
Are as follows:
A (θ)=[a (θ1),a(θ2),…,a(θg),…,a(θG)]
Wherein,For observation angle θgCorresponding guiding arrow
Amount, { dm, m=1,2 ..., M ' } be each sensor of the ULA position coordinates set, λ is the wavelength of incident narrow band signal, and j is
Imaginary unit.
The beneficial effects of the present invention are:
(1) the case where being directed to non-homogeneous line array (the part element failure that can be regarded as uniform straight line array), according to repeatedly
The thinking of the uniform straight line array output data of more array numbers is provided for demosaicing, is obtained aperture extension, is improved wave and reach
The resolution capability of bearing estimate.
(2) theoretical based on management loading, use EM algorithm to solve DOA estimation problem in a manner of statistic op- timization
Middle sparse matrix equation, makes full use of the statistical property of observation data, and thinning parameter estimated result reduces evaluated error.
(3) present invention is without estimation incoming signal number in advance, while being applicable to the DOA estimation of relevant incoming signal
Problem is with a wide range of applications in reality.
Detailed description of the invention
Fig. 1 is the amplitude spectrum comparison diagram of the present invention with the direction of arrival angular estimation of L1-SVD algorithm；
Fig. 2 be the present invention with it is existing there are four types of direction of arrival angle estimation method under the conditions of different signal-to-noise ratio to three be concerned with into
Penetrate the root-mean-square error comparison diagram that the direction of arrival angle of signal is estimated；
Fig. 3 be the present invention with it is existing there are four types of direction of arrival angle estimation method under the conditions of different number of snapshots to three be concerned with into
Penetrate the root-mean-square error comparison diagram that the direction of arrival angle of signal is estimated.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
Steps are as follows for realization of the invention:
Step 1: obtaining the output signal matrix X of non-homogeneous linear array.
It suppose there is K far field and be concerned with narrow band signal with angleIncidence, it is non-using being made of M sensor
Uniform straight line array receives spacing wave and samples, and obtains the output signal matrix X=[x (t of M × N-dimensional array1),…,x
(tn),…,x(tN)], wherein x (tn) it is tnWhen the array output signal inscribed, n=1 ..., N, N is sampling number of snapshots.
Step 2: construction one M × M ' dimension transition matrix P obtains the defeated of M ' uniform straight line array ULA corresponding to the NLA
The linear representation of signal matrix Y and X out.
M member NLA can be regarded as in M ' the member ULA, ULA output signal Y of lack part array element comprising NLA output letter
Number X, X are known as ill-conditioned matrix, and Y is known as complete data.Later will according to complete data Y carry out parameter Estimation, need to obtain Y with
The relational expression of actual observation data X, is implemented as follows:
Firstly, the vector p=[p of construction one M ' × 1 dimension1,…,pi,…,pM′]T, wherein
Then, transition matrix P is obtained by the row vector that element in puncture table diag (p) is all 0, wherein diag
() indicates that diagonal matrix operation will be constructed, and subscript T indicates transposition.
Fragmentary data X can be X=PY by complete data Y linear expression.
Step 3: gridding observation space angle constructs super complete base A (θ).
Based on the characteristic that incoming signal spatial distribution is sparse, the parameter space of discretization observation model.In view of any letter
Number super complete base A (θ) can be constructed to linear expression complete data Y by a basic matrix linear expression.Specific implementation
It is as follows:
G angle mesh point is obtained firstly, [- 90 °, 90 °] of observation space angular range divide at equal intervals, is observed
Space networks lattice point is expressed as θ=[θ1,θ2,…,θG], wherein G > > K.
Then, the super complete base that M ' × G of the first uniform straight line array ULA of M ' is tieed up is corresponded to after obtaining airspace rarefaction
A (θ)=[a (θ1),a(θ2),…,a(θg),…,a(θG)],
Wherein,For observation angle θgCorresponding guiding arrow
Amount, { dm, m=1,2 ..., M ' } be each sensor of the ULA position coordinates set, λ is the wavelength of incident narrow band signal, and j is
Imaginary unit.
Step 4: direction of arrival angle estimation problem is converted sparse signal reconfiguring problem by the thought based on rarefaction representation,
Solve sparse matrix equation Y=A (θ) S+E.Wherein, S is M ' × N-dimensional unknown vector, and E indicates M ' × N-dimensional additive Gaussian
White noise.
Step 5: according to management loading theory, unknown matrix S being solved using the very big EM algorithm of expectation.
Specified S obeys Gaussian prior distribution, defines a hyper parameter vector γ=[γ1,γ2,…,γM′]TControl its association
Variance matrix, the mean value of S are 0, and covariance matrix is Γ=diag (γ).Define a hyper parameter variable β control additive Gaussian
The covariance matrix of white noise E, the mean value of E are 0, covariance matrix β-1IM′, wherein β-1For the inverse of β, IM′It is single for M ' rank
Bit matrix.γ and β are known as hyper parameter, obtain the mean value of unknown matrix S according to Bayesian formula, by it is expected very big EM algorithm
The more new formula of hyper parameter γ and β are obtained, obtains the optimal estimation value of hyper parameter γ in an iterative manner.It is implemented as follows:
(1) it initializes, hyper parameter γ(old)It is set as the vector that element is all 1, hyper parameter β(old)It is set as 1, unknown square
Battle array S(old)=(AH(θ)A(θ))-1AH(θ)X.Wherein, ()HIndicate conjugate transposition operation, ()-1Representing matrix is inverted.
(2) according to super complete base A (θ), transition matrix P and observation data X, perfect number in iterative process is calculated by following formula
According to Y(new)And unknown matrix S(new)With its covariance ΣS:
Y(new)=A (θ) g(oid)+PH(X-PA(θ)S(old),
ΣS=Γ-Γ AH(θ)Σ-1A (θ) Γ,
Wherein, Γ=diag (γ(old)), Σ=β(old)-1IM′+A(θ)ΓAH(θ), S·jIt is arranged for the jth of S, Y·jIt is the of Y
J column, IM′For M ' rank unit matrix, diag () indicates diagonal matrix, ()HIndicate conjugate transposition operation, ()-1Indicate square
Battle array is inverted.
(3) i-th of element γ of hyper parameter vector γ is updated respectively using the very big EM algorithm of expectationiWith hyper parameter variable β,
More new formula is as follows:
Wherein, Si·For the i-th row of S, S·jIt is arranged for the jth of S, (ΣS)iiFor ΣSI-th row i-th arranges corresponding element, | | |
|22 norm of vector is sought in expression, and Tr () representing matrix asks mark operation.
(4) judge whether updated γ restrains, if meetingThen stop iteration, obtains γ most
Excellent estimated value γ(*)=γ(new)；Otherwise, return step (2) continue iteration until meeting the above-mentioned condition of convergence.
Step 6: according to optimal estimation value γ(*)Direction instruction spectrogram is drawn, direction of arrival angle estimated value is obtained.
The optimal estimation value γ obtained in steps of 5(*)It is a sparse vector, most elements tend to 0, only include K
The angle value of a nonzero value, observation space mesh point corresponding to this K nonzero value is the direction of arrival angle of incoming signal.With
Observation space mesh point θ=[θ1,θ2,…,θG] it is abscissa (unit is degree), with optimal estimation value γ(*)Range value takes 10 times
Denary logarithm value be ordinate (unit is decibel dB), draw direction instruction spectrogram.According to from big from the spectrogram
Preceding K peak value is obtained to small sequence, abscissa angle value corresponding to these peak values is that required incoming signal wave reaches side
To angle.
Effect of the invention can be illustrated by following emulation:
1. simulated conditions:
Using 7 yuan of non-homogeneous line arrays, element position coordinate is [0,2,3,4,5,6,7] λ/2, is carrying out incoming signal
In direction of arrival angular estimation, use array number for 10 uniform straight line array, element position coordinate be [0,1,2,3,4,5,
6,7,8,9] λ/2, wherein λ is the wavelength of incident narrow band signal.Therefore, in structural transform matrix P, used vector is p
=[1,0,1,1,1,1,1,1,0,0]T.Observation space angle is [- 90 °, 90 °], and spatial gridding is divided into 1 ° between dividing.
The calculation formula of root-mean-square error RMSE is as follows:
Wherein, J expression experiment number, J=500,Direction of arrival angle for k-th of incoming signal in jth time experiment is estimated
Evaluation, θkFor the true direction of arrival angle of k-th of incoming signal.
2. emulation content and result:
Emulation 1: assuming that having 6 far fields narrowband coherent signal, respectively with -40 °, -20 °, 0 °, 20 °, 40 ° of direction of arrival angle
It is incident on the non-homogeneous line array with 60 °, the coherence factor of signal is 1, and sampling number of snapshots are 100, and Signal to Noise Ratio (SNR) is
0dB.DOA estimation is carried out using the present invention and existing L1-SVD algorithm respectively, obtained direction instruction spectrogram is as shown in Figure 1.
Abscissa is angle value in Fig. 1, and ordinate is normalization amplitude spectrum (each element value is divided by greatest member value).
It will be seen from figure 1 that 6 spectral peak ratio L1-SVD algorithms of the invention is more sharp, this is because the present invention utilizes
Direction of arrival angular estimation is carried out by the complete data with the uniform straight line array for more crossing array number that interpolation obtains, is equivalent to
Extend array aperture.
Emulation 2: assuming that there is 3 far fields narrowband coherent signal, this is incident on -10 °, 20 ° and 28 ° of direction of arrival angle respectively
On non-homogeneous line array, the coherence factor of signal is [1,0.6,0.8], and sampling number of snapshots are 100, Signal to Noise Ratio (SNR) from -5dB to
20dB variation carries out 500 times solely using the present invention and existing SS-MUSIC, L1-SVD, L1-SRACV and SPICE algorithm respectively
Vertical direction of arrival angular estimation experiment, calculates separately the root-mean-square error of each algorithm under the conditions of different signal-to-noise ratio, obtains root mean square
Error-signal-to-noise ratio curve is as shown in Figure 2.Abscissa is Signal to Noise Ratio (SNR) in Fig. 2, and ordinate is square error.
Figure it is seen that SS-MUSIC algorithm can not differentiate two targets in non-homogeneous line array；In low letter
It makes an uproar than in the case of, the present invention has best direction of arrival angular estimation performance.
Emulation 3: on the basis of emulating 2, fixed Signal to Noise Ratio (SNR) is 0dB, and sampling number of snapshots are changed from 20 to 400,
500 independent waves are carried out up to side using the present invention and existing SS-MUSIC, L1-SVD, L1-SRACV and SPICE algorithm respectively
It is tested to angular estimation, calculates separately the root-mean-square error of each algorithm under the conditions of different number of snapshots, obtain root-mean-square error-snap
Number curve is as shown in Figure 3.Abscissa is number of snapshots in Fig. 3, and ordinate is the root-mean-square error of DOA estimation.
From figure 3, it can be seen that the present invention has preferably estimation property under the conditions of fewer snapshots compared with other algorithms
Energy.
Claims (3)
1. a kind of based on the non-homogeneous line array direction of arrival angle estimation method for it is expected very big algorithm, it is characterised in that including following
Step:
Step 1: forming non-homogeneous line array using M sensor, and suppose there is K far field and be concerned with narrow band signal with different angles
Degree is incident on non-homogeneous line array, while white Gaussian noise is added in signal communication process, utilizes the non-homogeneous line array
Sample space signal is received, obtains the output signal X of array, wherein X=[x (t1),…,x(tn),…,x(tN)] it is a M
× N-dimensional matrix, x (tn) it is tnWhen the array output signal inscribed, n=1 ..., N, N is sampling number of snapshots, and X is referred to as incomplete
Each sensor array is referred to as an array element by data；
Step 2: construction one M × M ' dimension transition matrix P obtains linear relation X=PY, wherein Y according to observation data X
For the output signal matrix for the uniform straight line array that M ' × N-dimensional Virtual array number is M ', Y is known as complete data；
Step 3: gridding observation space angle constructs super complete base A (θ)；
Step 4: the thought of rarefaction representation converts sparse signal reconfiguring problem for direction of arrival angle estimation problem, solves as follows
Sparse matrix equation:
Y=A (θ) S+E
Wherein, S is M ' × N-dimensional unknown matrix, and E is M ' × N-dimensional additive white Gaussian noise matrix；
Step 5: defining a hyper parameter vector γ=[γ1,…,γi,…,γM′]T, γiFor the side of the i-th row element of matrix S
The convergence solution of γ is calculated using it is expected that very big EM algorithm updated by iteration in difference, wherein the condition of convergence for hyper parameter to
The variable quantity of the adjacent iteration twice of amount is less than threshold value, and threshold value value is 10-3To 10-4；
Step 6: with observation space mesh point θ=[θ1,θ2,…,θG] it is abscissa, with the width of the convergence solution of hyper parameter vector γ
Value is ordinate, draws amplitude spectrogram, K peak value before obtaining from amplitude spectrogram according to the sequence of amplitude from big to small, K peak
The corresponding abscissa angle value of value is required incoming signal direction of arrival angle.
2. according to claim 1 a kind of based on the non-homogeneous line array direction of arrival angular estimation side for it is expected very big algorithm
Method, it is characterised in that:
The specific implementation steps are as follows for the step 2:
Step 2.1: firstly, the vector p=[p of construction one M ' × 1 dimension1,…,pi,…,pM′]T, piIs defined as:
Wherein, M ' > M；
Step 2.2: the row vector that element is all 0 in puncture table diag (p) obtains transition matrix P, wherein diag () is indicated
Diagonal matrix operation will be constructed；
Step 2.3: fragmentary data X is X=PY by complete data Y linear expression.
3. according to claim 1 a kind of based on the non-homogeneous line array direction of arrival angular estimation side for it is expected very big algorithm
Method, it is characterised in that:
The specific implementation steps are as follows for the step 3:
Step 3.1: observation space angular range [- 90 °, 90 °] being divided at equal intervals and obtains G angle mesh point, observation space
Mesh point is expressed as θ=[θ1,θ2,…,θG], wherein G > > K；
Step 3.2: obtaining the super complete base of M ' × G dimension of the first uniform straight line array ULA of corresponding M ' after the rarefaction of airspace are as follows:
A (θ)=[a (θ1),a(θ2),…,a(θg),…,a(θG)]
Wherein,For observation angle θgCorresponding steering vector,
{dm, m=1,2 ..., M ' } be each sensor of the ULA position coordinates set, λ is the wavelength of incident narrow band signal, and j is imaginary number
Unit.
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Application publication date: 20190201 |