CN106569172B - Arrival direction estimation method - Google Patents
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- CN106569172B CN106569172B CN201610895302.9A CN201610895302A CN106569172B CN 106569172 B CN106569172 B CN 106569172B CN 201610895302 A CN201610895302 A CN 201610895302A CN 106569172 B CN106569172 B CN 106569172B
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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
Abstract
The present invention provides arrival direction estimation method, under the hypothesis that there is coupling between P adjacent array element, pass through the selection of reconstruction and auxiliary array element to array direction vector matrix, the higher two kinds of DOA algorithm for estimating of two kinds of accuracy are proposed, and propose the processing method in signal coherence.Two methods proposed by the present invention can accurately estimate uniform rectangular antenna plane there are the two-dimentional DOA under coupling condition under signal coherence and incoherent situation.
Description
Technical field
The present invention relates to fields of communication technology, more particularly, to DOA estimation method.
Background technique
Currently, DOA (direction of arrival) estimation has very always in field of signal processing, such as radar, Sonar system
Important role.
In the past few decades, Many researchers have been that the DOA algorithm for estimating of even linear array has made many contributions,
Such as multiple signals are classified (MUSIC) algorithm, ESPRIT algorithm etc., wherein MUSIC algorithm be the algorithm that is most widely used it
One.But these algorithms are all to be not present under the hypothesis of coupling to propose between antennas, this will make final DOA estimate
Generate serious error.When the distance between antenna is lesser, coupling between antenna on DOA estimation bring influence compared with
To be serious, this influences whether the performance of DOA algorithm for estimating.It is influenced to make up antenna coupling bring, researchers propose
Some new algorithms reinforce the performance of algorithm.For example, the influence of antenna coupling is made up by the coupled impedance received, this
Kind of method is easily achieved, but since the coupled relation between antenna is usually at any time and environmental change, in reality
Accomplish that real-time measurement coupled impedance is very difficult in.There is scholar to propose new algorithm again later, most using antenna
The a period of time in outside as auxiliary a period of time, only uses intermediate submatrix member to receive signal, accordingly even when the case where antenna couples
Under, original MUSIC algorithm still can be used directly.With the help of assisting array element, we can be estimated DOA
Meter, it is then correct under coupling condition so as to redefine by calculating the coefficient of coup between antenna to the DOA of pre-estimation
Array direction vector matrix.Above algorithm is most of both for uniform linear array (ULA) proposition, in practical application
In, uniform linear array can only be realized to the one-dimensional estimated of DOA, and due to uniform rectangular planar array (URA) can to DOA into
The two-dimensional estimation of row, and the accuracy estimated is higher than uniform linear array, therefore to URA in the case where antenna couples
The research of DOA estimation is more with practical value.
Summary of the invention
The present invention provides two kinds of methods for overcoming the above problem or at least being partially solved the above problem.
This patent exists between P adjacent array element under the hypothesis of coupling, passes through the weight to array direction vector matrix
The selection for building and assisting array element proposes the higher two kinds of DOA algorithm for estimating of two kinds of accuracy, and proposes in signal phase
Processing method in dry situation.
According to an aspect of the present invention, a kind of arrival direction estimation method is provided, comprising:
S1, based on the assumption that there are couplings between each antenna element and P adjacent a period of time in uniform rectangular planar antenna array
On the basis of conjunction relationship, tectonic coupling matrix and receipt signal model；
S2 is based on the receipt signal model, acquires its correlation matrix, and carries out Eigenvalues Decomposition and obtain noise sky
Between；
S31 is based on coupling matrix and noise subspace, using sense vector matrix restructing algorithm is based on, estimates two
Tie up DOA.
According to a further aspect of the present invention, another arrival direction estimation method is provided, comprising:
S1, based on the assumption that there are couplings between each antenna element and P adjacent a period of time in uniform rectangular planar antenna array
On the basis of conjunction relationship, tectonic coupling matrix and receipt signal model；
S2 is based on the receipt signal model, acquires its correlation matrix, and carries out Eigenvalues Decomposition and obtain noise sky
Between；
S32 is based on coupling matrix and noise subspace using companion matrix Meta algorithm, utilizes companion matrix Meta algorithm, estimation two
Tie up DOA.
The application proposes arrival direction estimation method, under the hypothesis that there is coupling between P adjacent array element, by right
The reconstruction of array direction vector matrix and the selection for assisting array element propose the higher two kinds of DOA estimation of two kinds of accuracy and calculate
Method, and propose the processing method in signal coherence.Two methods proposed by the present invention can in signal coherence and
In incoherent situation, uniform rectangular antenna plane is accurately estimated there are the two-dimentional DOA under coupling condition.
Detailed description of the invention
Fig. 1 is the structural schematic diagram according to the uniform rectangular aerial array of the embodiment of the present invention；
Fig. 2 is according to the coefficient of coup schematic diagram between uniform rectangular aerial array each a period of time of the embodiment of the present invention；
Fig. 3 is to be shown according to the structure of the auxiliary array element and center subarray based on companion matrix Meta algorithm of the embodiment of the present invention
It is intended to；
Fig. 4 is to divide schematic diagram according to the array of the Search Space Smoothing of the embodiment of the present invention.
Specific embodiment
With reference to the accompanying drawings and examples, specific embodiments of the present invention will be described in further detail.Implement below
Example is not intended to limit the scope of the invention for illustrating the present invention.
Firstly, to the present invention is based on existing algorithm be illustrated.
1, MUSIC algorithm
For uniform linear array, there is no couplings between antennas, and receive in the incoherent situation of signal, construct
Receipt signal model X=AS+n；Then its covariance matrix R is asked to receipt signal modelx=E [XXH]；To RxCarry out feature point
Solve available noise subspace En；Construct space spectral function:
Wherein a (θ) is the direction vector of signal.When signal is injected, due to the direction vector and noise subspace of signal
Orthogonal, the denominator of the formula is approximately 0, so it is only necessary that θ changes, calculates spectral function, right by searching for the peak value of spectral function
The angle, θ answered is the direction of arrival (DOA) of signal.
2, the arrival direction estimation method in the case where intercoupling
For the uniform rectangular antenna plane of a M × N, it is assumed that in the incoherent situation of signal, each antenna element
Only there are coupled relation, the reception signals of tectonic coupling Matrix C and uniform rectangular antenna plane with 8 antenna element around it
Model X=CAS+n；Antenna element on the four edges of uniform rectangular aerial array boundary is considered as auxiliary array element, therefore is actually connect
Effective a period of time of the collection of letters number is intermediate (M-2) × (N-2) a a period of time, for effective a period of time, writes out coupling matrix again and connects
It receives signal model and covariance matrix R is calculated according to traditional MUSIC algorithmxWith noise subspace En, in the case of tectonic coupling
Space spectral function
For space spectral function, since the coefficient of coup in coupling matrix is unknown, cannot be calculated by traditional MUSIC
Method obtains two-dimentional DOA, it is therefore desirable to carry out the transformation on formula to Ca (θ), can makeWhereinFor a scalar, the orthogonality of sense vector and noise subspace is not influenced, can be ignored, therefore former spectral function
It can write:It at this time can be by converting two dimension angularSearch the peak value of spectral function
To obtain two-dimentional DOA.
The specific coupling matrix of the available uniform rectangular face battle array of two dimension DOA backstepping calculated.Due to signal vector
Have with the orthogonality of noise subspaceBy calculating above, EnWithIt is known that therefore passing through one
Fixed fortran can find out coupling matrix C.
3, in an aerial array, there are a kind of new methods that the DOA of unknown coupling estimates
For linear antenna array, it is irrelevant in signal and exist coupling in the case where tectonic coupling Matrix C and
Receipt signal model X=CAS+n；Covariance matrix and noise subspace are calculated using traditional MUSIC algorithm；By to coupling
In the case of direction vector be reconstructed, i.e., carry out certain fortran to Ca, can make finally using MUSIC algorithm
Unknown coupling matrix bring can be ignored by asking when DOA influence, and finds out the DOA of signal.Specifically see second part background skill
Art.
In a specific embodiment of the invention, a kind of arrival direction estimation method is shown.On the whole, comprising: S1, base
In assuming that there are on the basis of coupled relation between each antenna element and P adjacent a period of time in uniform rectangular planar antenna array,
Tectonic coupling matrix and receipt signal model；S2 is based on the receipt signal model, acquires its correlation matrix, and carry out feature
Value decomposition obtains noise subspace；S31 is based on coupling matrix and noise subspace, using based on sense vector matrix weight
Structure algorithm estimates two dimension DOA.
In another specific embodiment of the invention, step is based on coupling matrix and noise subspace, using based on signal side
To vector matrix restructing algorithm, estimates two dimension DOA: the direction vector matrix of signal is reconstructed；It is calculated using traditional MUSIC
Method, the sense vector matrix based on reconstruct estimate DOA.
It is reconstructed firstly the need of the direction vector matrix to signal:
；Wherein for CiaxIt can write again:
Ciax=Tx(α,β)ci=[Tx1(α,β)+Tx2(α,β)]ci
Ci=[cI, 0 cI, 1 … CI, P-1]T,
It can similarly obtain:
Ty=Ty1(α, β)+Ty2(α, β),
So that
, when there is coupling between antenna, there is following formula establishment in DOA estimation according to traditional MUSIC method:
After the direction vector matrix reconstruction of signal, which be can be written as:
It enablesThen have:
cHQ (α, β) c=0,
According to above formula it is estimated that the 2-d direction finding of signal is as follows:
In another specific embodiment of the invention, a kind of arrival direction estimation method.On the whole, comprising: S1, based on vacation
If being constructed between each antenna element and P adjacent a period of time there are on the basis of coupled relation in uniform rectangular planar antenna array
Coupling matrix and receipt signal model；S2 is based on the receipt signal model, acquires its correlation matrix, and carries out characteristic value point
Solution obtains noise subspace；S32 is based on coupling matrix and noise subspace, using companion matrix Meta algorithm, estimates two dimension DOA.
In another specific embodiment of the invention, in a kind of arrival direction estimation method, step is based on coupling matrix and makes an uproar
Two dimension DOA is estimated using companion matrix Meta algorithm in phonon space, further includes: in the battle array of squaerial face, enable outermost P-1 row
It is companion matrix member with the array element on P-1 column, only using intermediate a array element of (M-P) × (N-P) as effective array element of reception signal,
As shown in figure 3, the signal model so received is answered are as follows:
Wherein:
G=[P0 P1 P0],
P0It is the full null matrix of (M-2P+2) (N-2P+2) × (P-1) N rank, and P1It is a block diagonal matrix, it can be with
Writing:
Wherein [0 J=(N-2P+2)×(P-1)I(N-2P+2)0(N-2P+2)×(P-1)]。
Coupling matrix is reconstructed below, is enabledSo coupling matrix then reconstructs are as follows:
WhereinAccording to the coupling matrix of reconstruct, receipt signal model be can be written as:
So correlation matrix of signal are as follows:
The direction vector matrix of signal can indicate are as follows:
Wherein:
According to traditional MUSIC algorithm (it is to be understood that the present invention is not limited to be counted using traditional MUSIC algorithm
Calculate), there should be following formula establishment:
Certain transformation can be carried out to above formula:
Due toWithThere is similar structure, it is possible to lower relation of plane is obtained,
So that
Since c (α, β) is a scalar, as c (α, β) ≠ 0,With UNBetween orthogonality will not be affected,
That is:
Therefore tradition MUSIC algorithm can be rewritten are as follows:
The calculating that DOA estimates, which is not present, in antenna coupling at this time influences, can be by searching for PMUSICSpectral peak find signal
Corresponding DOA.
As c (α, β)=0, (α, β) is referred to as blind angle at this time, and when signal is injected from the angle, which cannot estimate
The DOA of signal out, but such case occur probability it is smaller, only need to pay attention to when design aerial array adjustment aerial array away from
From changing the coefficient of coup can avoid such case.
According to the DOA angle estimated, the coefficient of coup of squaerial face battle array can be calculated.Assuming that the two dimension estimated
DOA angle isHad according to traditional MUSIC algorithmIt is available by converting by the formula
Define a new matrix Q:
Therefore former formula can be write:
Qc=0,
That is:
Wherein ()#It indicates pseudo inverse matrix, all coefficients of coup of squaerial face battle array can be found out according to above formula, according to
The available coupling matrix of the coefficient of coup acquired can be obtained by calculation accurate in the case where known coupling matrix
Signal DOA.
In practical applications, signal is often relevant, this will affect the calculating to signal noise subspace, space smoothing
Squaerial face battle array is divided into the submatrix of several overlappings by technology, and it is empty to find out accurate noise by these submatrixs
Between, DOA is estimated to influence to exclude signal coherence.
For the matrix of M × N rank, several M can be divided into1×N1The submatrix of rank, and to every sub- square
Battle array number is (i, j), i=1,2 ..., M-M1+ 1, j=1,2 ..., N-N1+ 1, as shown in figure 4, then (m, n) a submatrix
Receive signal are as follows:
Whereinnmn(t) be respectively the submatrix reception signal direction vector matrix and noise matrix,
Dx,DyIt can respectively indicate are as follows:
Dx=diag [u (α1, β1), u (α2, β2) ..., u (αK, βK)]
Dy=diag [v (α1, β1), v (α2, β2) ..., v (αK, βK)],
It is hereby achieved that the coherence matrix of (m, n) a submatrix are as follows:
As depicted in figs. 1 and 2, in another specific embodiment of the invention, it is assumed that uniform rectangular planar antenna array
There are coupled relations between interior each antenna element and P adjacent a period of time.The step includes: the squaerial face of a M × N
Battle array, the row and column of face battle array be located at in the X-axis and the parallel straight line of Y-axis in rectangular coordinate system, every two phase on row and column
Adjacent the distance between antenna element is d, as shown in Figure 1.If thering is K signal to inject from unknown direction, with a (αi, βi) indicate
The direction vector of i-th of signal, wherein αiFor azimuth, βiFor the elevation angle, then planar array can be constructed there are antenna couplings
In the case of receipt signal model be x (t)=CAs (t)+n (t), x (t) be rectangle battle array reception signal, C is coupling matrix, A
For the direction vector matrix of signal, A=[a (α can be expressed as1, β1), a (α2, β2) ..., a (αK, βK)], s (t) is source signal
Vector, n (t) are noise vector.
In another specific embodiment of the invention, a kind of arrival direction estimation method, step tectonic coupling matrix, vacation
If only there are coupled relations between a period of time within P row adjacent thereto for certain a line antenna element in the battle array of face, C is usediIndicating should
The coefficient of coup matrix of the i-th capable and adjacent thereto row, i=0,1 ..., P-1, as shown in Fig. 2, so coupling matrix C can be with structure
It makes as follows:
As can be seen that coupling matrix C is a symmetrical toeplitz matrix, each of matrix Elements CiWith knot
Structure is similar and a symmetrical toeplitz matrix, uses cj(cj≤ 1) some antenna element and jth adjacent thereto are indicated
The coefficient of coup between a a period of time, then CiIt can indicate are as follows:
In another specific embodiment of the invention, a kind of arrival direction estimation method, if there is K signal from unknown parties
To squaerial face battle array, signal wavelength λ is injected, then receiving signal can indicate are as follows:
X (t)=CAs (t)+n (t).
Wherein C is coupling matrix, and A is direction vector matrix, can be indicated are as follows:
A=[a (α1, β1), a (α2, β2) ..., a (αK, βK)],
a(αi, βi) indicate i-th of signal direction vector, αiFor the azimuth of the signal, βiFor the elevation angle of the signal, and
And have:
Indicate Kronecker product, ax(αi, βi) and ay(αi, βi) respectively indicate point that direction vector prolongs X-axis and Y-axis
Amount, can indicate are as follows:
ax(αi, βi)=[1 u u2 … uM-1]T
ay(αi, βi)=[1 v v2 … vN-1]T,
Wherein:
S (t) and n (t) respectively indicate K source signal vector matrix and noise matrix, may be expressed as:
S (t)=[s1(t), s2(t) ..., sK(t)]
N (t)=[n1(t), n2(t) ..., nK(t)],
According to the receipt signal model of antenna plane, the correlation matrix that can calculate it is as follows:
Rx=E [x (t) xH(t)]=CARsAHCH+σ2I,
Wherein ()HIndicate the conjugation transformation of ownership, Rs=E [s (t) s (t)H].Obtain correlation matrix RxIt afterwards, can be to RxCarry out feature
Value is decomposed:
Wherein ∑S∈RNIt is signal power diagonal matrix, ∑N∈RM-NIt is noise power diagonal matrix, US∈CM×NFor signal
Subspace, UN∈CMx(M-N)For noise subspace.
In another specific embodiment of the invention, before step S1 further include: judge whether injection face battle array signal is concerned with,
If so, uniform rectangular antenna plane to be divided into the submatrix of several overlappings using Search Space Smoothing.
In another specific embodiment of the invention, before step S1 further include: judge whether injection face battle array signal is concerned with,
If so, uniform rectangular antenna plane to be divided into the submatrix of several overlappings using Search Space Smoothing.
As shown in figure 4, in another specific embodiment of the invention, before step S1 further include: judge injection face battle array letter
Number whether it is concerned with, if so, uniform rectangular antenna plane to be divided into the submatrix of several overlappings using Search Space Smoothing:
In two-dimensional space smoothing technique, actual coherence matrix is RmnAverage value:
Wherein:
Coherence matrix is full rank at this time, by the available correct noise subspace of Eigenvalues Decomposition, to avoid
Signal coherence bring in DOA estimation influences.
Finally, the present processes are only preferable embodiment, it is not intended to limit the scope of the present invention.It is all
Within the spirit and principles in the present invention, any modification, equivalent replacement, improvement and so on should be included in protection of the invention
Within the scope of.
Claims (8)
1. a kind of arrival direction estimation method, which comprises the following steps:
S1 couples pass based on the assumption that existing between each antenna element and P adjacent a period of time in uniform rectangular planar antenna array
On the basis of system, tectonic coupling matrix and receipt signal model；
S2 is based on the receipt signal model, acquires its correlation matrix, and carry out Eigenvalues Decomposition and obtain noise subspace；
S31 is based on coupling matrix and noise subspace, and using sense vector matrix restructing algorithm is based on, estimation is two-dimentional
DOA。
2. the method as described in claim 1, which is characterized in that the step S31 further include:
Based on coupling matrix, the direction vector matrix of signal is reconstructed；
Based on noise subspace, DOA is estimated.
3. a kind of arrival direction estimation method, which comprises the following steps:
S1 couples pass based on the assumption that existing between each antenna element and P adjacent a period of time in uniform rectangular planar antenna array
On the basis of system, tectonic coupling matrix and receipt signal model；
S2 is based on the receipt signal model, acquires its correlation matrix, and carry out Eigenvalues Decomposition and obtain noise subspace；
S32 is based on coupling matrix and noise subspace, using companion matrix Meta algorithm, estimates two dimension DOA；
The step S32 further include:
In uniform rectangular planar antenna array, enabling array element on outermost P-1 row and P-1 column is companion matrix member, only will in
Between a array element of (M-P) × (N-P) as receive signal effective array element；
Coupling matrix is reconstructed；
Using modified MUSIC, the sense vector matrix based on reconstruct estimates DOA.
4. method as claimed in claim 1 or 3, which is characterized in that in the step S1, it is assumed that uniform rectangular planar array antenna
It arranges interior each antenna element and there are coupled relations between P adjacent a period of time, comprising: the uniform rectangular flat plane antenna of a M × N
Array, the row and column of uniform rectangular planar antenna array are located at and the X-axis and the parallel straight line of Y-axis in rectangular coordinate system
On, the distance between every two adjacent antenna element is d on row and column, if there is K signal to inject from unknown direction, uses a
(αi,βi) indicate the direction vector of i-th of signal, wherein αiFor azimuth, βiFor the elevation angle, put down then uniform rectangular can be constructed
Surface antenna array is being uniform rectangular there are the receipt signal model x (t) under antenna coupling condition=CAs (t)+n (t), x (t)
The reception signal of planar antenna array, C are coupling matrix, and A is the direction vector matrix of signal, can be expressed as A=[a (α1,
β1), a (α2, β2) ..., a (αK, βK)], s (t) is source signal vector, and n (t) is noise vector.
5. method as claimed in claim 1 or 3, which is characterized in that in the step S1, tectonic coupling matrix further include: use Ci
The coefficient of coup matrix of certain a line array element and the i-th row adjacent thereto in expression uniform rectangular planar antenna array, i=0,
1 ..., P-1, coupling matrix C construction is as follows,
6. method as claimed in claim 1 or 3, which is characterized in that in the step S2, further includes:
According to the receipt signal model of uniform rectangular planar antenna array, the correlation matrix that can calculate it is as follows
Rx=E [x (t) xH(t)]=CARsAHCH+σ2I,
Wherein ()HIndicate the conjugation transformation of ownership, Rs=E [s (t) s (t)H], obtain correlation matrix RxAfterwards, to RxCarry out Eigenvalues Decomposition:
Wherein ∑S∈RNIt is signal power diagonal matrix, ∑N∈RM-NIt is noise power diagonal matrix, US∈CM×NFor signal subspace sky
Between,For noise subspace.
7. method as claimed in claim 1 or 3, which is characterized in that before the step S1 further include: uniform rectangular is injected in judgement
Whether planar array antenna column signal is concerned with, if so, being divided into uniform rectangular planar antenna array using Search Space Smoothing
The submatrix of several overlappings.
8. the method for claim 7, which is characterized in that the step S1 further include: will be uniform using Eigenvalues Decomposition
Rectangle plane aerial array is divided into the submatrix of several overlappings.
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| CN107907854B (en) * | 2017-10-31 | 2021-04-27 | 大连大学 | DOA estimation method under impulse noise environment |
| CN108519576B (en) * | 2018-03-21 | 2021-07-20 | 华南理工大学 | Underwater direction of arrival estimation method and device based on included angle adjustable non-uniform linear array |
| CN108414967A (en) * | 2018-04-11 | 2018-08-17 | 华南理工大学 | Based on L gusts of underwater two-dimension Wave arrival direction estimating method and device of angle adjustable double |
| CN109870668A (en) * | 2018-12-24 | 2019-06-11 | 哈尔滨工程大学 | A kind of planar array Adaptive beamformer coupling automatic correcting method based on auxiliary array element |
| CN110018438B (en) * | 2019-04-23 | 2020-09-25 | 北京邮电大学 | Direction-of-arrival estimation method and device |
| CN110542880A (en) * | 2019-08-13 | 2019-12-06 | 唐晓杰 | DOA estimation strategy under partial overlapping condition of frequency points |
| CN111413667A (en) * | 2020-03-25 | 2020-07-14 | 北京邮电大学 | Method and device for determining direction of arrival of signal and electronic equipment |
| CN112379327A (en) * | 2020-12-01 | 2021-02-19 | 北京工业大学 | Two-dimensional DOA estimation and cross coupling correction method based on rank loss estimation |
| CN113673317B (en) * | 2021-07-12 | 2023-04-07 | 电子科技大学 | Atomic norm minimization dimension reduction-based two-dimensional lattice DOA estimation method |
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