CN104898085B - A kind of dimensionality reduction MUSIC algorithms of polarization sensitive array parameter Estimation - Google Patents
A kind of dimensionality reduction MUSIC algorithms of polarization sensitive array parameter Estimation Download PDFInfo
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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
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- 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
- G01S3/146—Systems for determining direction or deviation from predetermined direction by comparing linear polarisation components
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Abstract
The invention discloses a kind of dimensionality reduction MUSIC algorithms of polarization sensitive array parameter Estimation, belong to array signal process technique field.The signal correlation matrix that array received data obtain is carried out Eigenvalues Decomposition and obtains noise subspace by the present invention；Direction of arrival angle and polarization information in the steering vector of signal are separated, obtain intermediate variable；By the search function of intermediate variable construction direction of arrival angle, spectrum peak search obtains the estimation of direction of arrival angle；The estimate of direction of arrival angle is substituted into dimensionality reduction MUSIC Power estimations, coordinate obtains polarization estimation as corresponding to spectral peak.Four-dimensional spectrum peak search is reduced to two-dimentional spectrum peak search by the algorithm of the present invention so that the calculating magnitude of algorithm is from o { n4It is reduced to o { n2, the computational complexity of algorithm is greatly reduced, improves the operation efficiency of system.
Description
Technical field
The invention belongs to array signal process technique field, more particularly to polarization sensitive array Signal parameter estimation algorithm
Improve, be concretely to reduce algorithm operation quantity, improve the dimensionality reduction MUSIC algorithms of operation efficiency.
Background technology
The space that polarization sensitive array can not only obtain signal by the difference of the locus of array element reaches angle information,
And can enough obtains signal possessed polarization information in itself by the difference of array element quadrature phase, and the output of its array element is containing pole
Change the Vector Message of information rather than common scalar information, this characteristic has established the property of further raising polarization sensitive array
The basis of energy, while also cause us to be possible to further improve the disposal ability of array signal.Compared to common scalar array,
Performance advantage existing for polarization sensitive array, it can be showed in terms of following four：(1) stronger antijamming capability；(2)
Sane detectability；(3) higher resolution capability；(4) ability of polarization multiple access.
Signal parameter estimation problem is a basic problem of array signal processing, and since the 1960s, DOA estimates
Meter technology obtains development at full speed, has emerged in large numbers substantial amounts of excellent algorithm.It is that Burg estimated in the maximum entropy spectrum proposed in 1967 first
Meter method and SchmidtRO indicate that array antenna exists in the minimum variance Power estimation method proposed in 1969, both algorithms
Improvement is obtained in terms of resolution capability.Multiple signal classification (Multiple Signal Classification, MUSIC) algorithm
It is proposed so that the development of high-resolution direction finding technology has to be broken through tremendously.MUSIC algorithms be substantially using noise subspace and
Obtained from the orthogonality principle of signal subspace.MUSIC algorithms have just obtained extensive research and application since being suggested,
It is a kind of high-resolution features Structure Method for producing progressive unbiased esti-mator.
Multiple signal classification algorithm is used for the signal source angle of arrival of polarization sensitive array and the thought of polarization estimation
Mainly by carrying out the mathematic decomposition such as feature decomposition or singular value decomposition to receiving data, data will be received and be divided into two phases
Mutually orthogonal subspace, i.e. signal subspace and noise subspace, then using the relation of array manifold vector subspace come
Tectonic syntaxis is composed, so as to obtain signal source angle of arrival and polarization estimation according to spectral peak.Traditional MUSIC combined spectrums method of estimation
It is as follows：
1) array output covariance matrix is first obtained；
2) Eigenvalues Decomposition is carried out to covariance matrix, obtains noise subspace span { Un}；
3) by noise subspace and array manifold matrixThe subspace opened and noise subspace span
{UnOrthogonal principle, construction MUSIC joint Power estimations：
To estimate that the angle of arrival of signal source and polarization parameter need to carry out four-dimensional spectrum peak search it can be seen from formula (1), need
Huge operand and storage capacity are paid, is not easy to realize.
The content of the invention
The invention provides a kind of dimensionality reduction MUSIC algorithms of polarization sensitive array parameter Estimation, estimate in no reduction algorithm
While counting error performance, four-dimensional spectrum peak search is reduced to two-dimentional spectrum peak search so that the calculating magnitude of algorithm is from o { n4Drop
For o { n2(n be hunting zone in points), the computational complexity of algorithm is greatly reduced, improves the operation efficiency of system.
The present invention solve the above problems the technical scheme that uses for：
The dimensionality reduction MUSIC algorithms of a kind of polarization sensitive array parameter Estimation, it is characterised in that comprise the following steps：
Step 1. establishes the mathematical modeling of array received signal
Space has K incoherent signals to incide in array, according to the angle of arrival of incoming signalAnd polarization ginseng
Number (γ, η) and noise obtain the expression formula of array received signal model
Wherein, θ ∈ [- pi/2, pi/2) be the incoming signal angle of pitch,For incoming signal azimuth, γ ∈ [0,
Pi/2) for polarization explement, η ∈ [- π, π) for polarization phases it is poor.Manifold matrix A=[a of whole array1,a2,...,aK], s (n)
=[s1(n),s2(n),...,sK(n)]TFor signal phasor, v (n) is noise.Array scanning vectorIt is that polarization is led
To vectorWith steric direction vectorKronecker product, i.e.,
Its steering vector that polarizes is expressed as：
Wherein,Represent the transformation relation matrix between spherical coordinate system and rectangular coordinate system unit vector, Ek(γ,
η) represent the Jones vectors of perfact polarization ripple.
It is noted that the difference in step 1 according to demandSix components can not have to all make
With.
The n times snapshot data for the array received signal that step 2. is obtained using step 1, obtain estimating signal correlation matrix
Step 3. obtains noise subspace span { U by carrying out Eigenvalues Decomposition to correlation matrix Rn}
In formula, P is to takeComponent number, M is element number of array.Λ=diag { λ1,λ2,...,λPM, and
And PM-K minimum characteristic value is equal, is equal to array received noise intensity.Characteristic vector structure corresponding to K big characteristic values
Into signal subspace<S>=span { Us, characteristic vector corresponding to PM-K small characteristic values forms noise subspace<N>=span
{Un}.Array manifold matrix is identical with signal subspace into subspace and orthogonal with noise subspace, is expressed as：
Span { A }=span { Us} (7)
span{A}⊥span{Un} (8)
Step 4. calculates the angle of pitch and azimuth process of signal source
Dimensionality reduction MUSIC algorithms are peeled off direction of arrival angle and polarization parameter in MUSIC Power estimations, according to traditional
MUSIC Power estimationsDefined function
Order
By subspace principal, the subspace of array manifold matrix is orthogonal with noise subspace, i.e.,：
span{A}⊥span{Un} (8)
Formula (8) is substituted into formula (9) to obtain
When γ ∈ (0, pi/2), E is understood by formula (4)H(γ, η) is sequency spectrum, whenFor non-full rank, i.e.,Formula (12) is set up, then the angle of pitch and azimuthal estimation
Step 5. calculates the polarization parameter process of signal source
By the required angle of pitch and azimuthIntermediate variable is substituted into, is obtained
Then polarization estimation：
Signal source angle of arrival and polarization parameter are separated search by the present invention it can be seen from formula (13) and formula (15),
One four-dimensional spectrum peak search is changed into two two-dimentional spectrum peak searches, by the method for the present invention, estimates incoming signal angle and pole
The amount of calculation for changing parameter substantially reduces, and has good correctness and accuracy.
Brief description of the drawings
Fig. 1 is the even linear array to forming by biorthogonal electric dipole.
Embodiment
Even linear array is formed to being arranged along the y-axis by M biorthogonal electric dipole as shown in Figure 1, biorthogonal electric dipole pair
Placed respectively along x-axis and y-axis, array element spacing is d, and dimensionality reduction MUSIC algorithms is implemented as follows in this example：
Step 1. establishes array received signal mathematical modeling：
Known spatial has K signal to incide in polarization sensitive array, and incident narrow band signal is orthogonal, θ ∈ [- pi/2,
Pi/2) it is the incoming signal angle of pitch,For incoming signal azimuth, γ ∈ [0, pi/2) for polarization explement, η ∈ [- π,
π) poor for polarization phases, the receipt signal model x (n) of array can be expressed as：
A=[a in formula1,a2,...aK] be whole array manifold matrix, wherein ak(k=1,2...K) it is polarizations
Domain-spatial domain joint steering vector；Signal phasor s (n)=[s1(n),s2(n),...,sK(n)]T；V (n) is that average is zero, variance
For σ2White complex gaussian noise；akIt is polarization steering vector (akp) and steric direction vector (aks) Kronecker product, i.e.,：
Wherein,
In formula,λ represents wavelength.
For the electric dipole pair along x-axis and y-axis placement, its steering vector a that polarizeskpTwo components only are used, are expressed as：
Formula (19) is substituted into formula (17) to obtain
Step 2. seeks the autocorrelation matrix of signal
The autocorrelation matrix of array received signal is：
Rx=E [x (n) xH(n)]=ARsAH+σ2I (21)
Wherein, A be whole array manifold matrix, RsFor the auto-correlation function of incoming signal, I is unit battle array.
In Practical Project, the N number of observation sample value x (0) of generally use, x (1) ..., x (N-1) obtain estimating for correlation matrix
MeterWithInstead of RxCalculated, wherein：
Step 3. solves noise subspace：
The estimation for the correlation matrix that step 3 is tried to achieveEigenvalues Decomposition is carried out, tries to achieve noise subspace：
Wherein ΛsAnd ΛnValue matrix is characterized, corresponds respectively to K big characteristic value and 2M-K small characteristic values.UsFor K
Characteristic vector corresponding to big characteristic value, its into space be signal subspace, UnFor corresponding to 2M-K small characteristic values
Characteristic vector, its into space be noise subspace.
Step 4. calculates the angle of pitch and the azimuth of signal source
Defining detection limit first is：
Formula in step 1 (20) is substituted into formula (24) to obtain
Due toSet up, then formula (25) can be expressed as：
By formula (26) it can be seen that the direction of arrival angle information of incoming signal and polarization parameter information are separated and come, now
Define intermediate variable：
By subspace principal, the subspace of array manifold matrix is orthogonal with the characteristic vector of noise subspace
span{A}⊥span{Un} (28)
Formula (28) is substituted into formula (26) to obtain
The E when γ ∈ (0, pi/2)H(γ, η) is sequency spectrum, to be causedThenNon- full rank,
I.e.K minimum of the spectrum of estimation zero, the position of these minimums are obtained according to optimized search methodThe as estimation of signal source angle of arrival.For convenience's sake, generally its K maximum is searched for the inverse of zero spectrum.It is fixed
Adopted dimensionality reduction MUSIC spectrums：
Wherein coordinate corresponding to K spectral peak is the angle-of- arrival estimation of signal source
Step 5. calculates the polarization parameter of signal source：
The signal source angle of arrival that step 4 is obtained is substituted into formula (27), obtains the estimation of intermediate variable
Estimation for polarization parameter, it can search for obtain by following Power estimation：
For the signal source angle of arrival and polarization estimation of polarization sensitive array, traditional joint MUSIC algorithms need
Spectrum peak search is carried out simultaneously to four parameters, its amount of calculation is o (n4), wherein n is to be counted in hunting zone, and the calculation of the present invention
The angle of arrival of signal source and polarization parameter are carried out separation search by method, and its amount of calculation is o (2n2), it can be seen that greatly reduce
Operand, improve the operation efficiency of system.
Claims (1)
1. the dimensionality reduction MUSIC algorithms of a kind of polarization sensitive array parameter Estimation, it is characterised in that comprise the following steps：
Step 1. establishes the mathematical modeling of array received signal
Space has K incoherent signals to incide in array, according to the angle of arrival of incoming signalAnd polarization parameter
(γ, η) and noise obtain the expression formula of array received signal model：
Wherein, θ ∈ [- pi/2, pi/2) be the incoming signal angle of pitch,For incoming signal azimuth, γ ∈ [0, pi/2) be
Polarize explement, and η ∈ [- π, π) it is that polarization phases are poor；Manifold matrix A=[a of whole array1,a2,...,aK], s (n)=[s1
(n),s2(n),...,sK(n)]TFor signal phasor, v (n) is noise；Array scanning vectorIt is that polarization is oriented to arrow
AmountWith steric direction vectorKronecker product, i.e.,：
Its steering vector that polarizesIt is expressed as：
Wherein,Represent the transformation relation matrix between spherical coordinate system and rectangular coordinate system unit vector, Ek(γ, η) table
Show the Jones vectors of perfact polarization ripple；
The n times snapshot data for the array received signal that step 2. is obtained using step 1, obtain estimating signal correlation matrix：
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Step 3. obtains noise subspace span { U by carrying out Eigenvalues Decomposition to correlation matrix Rn}
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In formula, P is to takeComponent number, M is element number of array, Λ=diag { λ1,λ2,...,λPM, and most
PM-K small characteristic value is equal, is equal to array received noise intensity；Characteristic vector corresponding to K big characteristic values forms letter
Work song space<S>=span { Us, characteristic vector corresponding to PM-K small characteristic values forms noise subspace<N>=span { Un}；
Array manifold matrix is identical with signal subspace into subspace and orthogonal with noise subspace, is expressed as：
Span { A }=span { Us} (7)
span{A}⊥span{Un} (8)
Step 4. calculates the angle of pitch and azimuth process of signal source
Direction of arrival angle and polarization parameter in MUSIC Power estimations are peeled off, according to traditional MUSIC Power estimationsDefined function：
Order
By subspace principal, the subspace of array manifold matrix is orthogonal with noise subspace, i.e.,：
span{A}⊥span{Un} (8)
Formula (8) is substituted into formula (9) to obtain
When γ ∈ (0, pi/2), E is known by formula (4)H(γ, η) is sequency spectrum；WhenFor non-full rank, i.e.,Formula (12) is set up；
The then angle of pitch and azimuthal estimation：
Step 5. calculates the polarization parameter process of signal source
By the required angle of pitch and azimuthIntermediate variable is substituted into, is obtained
Then polarization estimation：
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