CN102608565A - Direction-of-arrival estimation method on basis of uniform circular array - Google Patents

Abstract

The invention relates to a direction-of-arrival estimation method on the basis of a uniform circular array, in particular to a direction-of-arrival estimation method for independent signals and coherent signals on the basis of the uniform circular array. The direction-of-arrival estimation method on the basis of the uniform circular array includes: preprocessing estimation parameters of direction-of-arrival; removing noise of pattern space; increasing aperture of the array and performing direction-of-arrival estimation to independent signals; and eliminating independent signals and performing direction-of-arrival estimation to coherent signals. The direction-of-arrival estimation method has higher estimation precision, the aperture of the array can be utilized more sufficiently, the loss of the aperture of the array due to array transformation of a virtual array is recovered, estimation performance can be improved further, calculation is simple and calculation quantity is low.

Description

A kind of Wave arrival direction estimating method based on the uniform circular array row

Technical field

The present invention relates to a kind of direction of arrival (Direction of Arrival is called for short DOA) method of estimation, be specifically related to based on the independent signal of uniform circular array row (Uniform CircularArray is called for short UCA) and the Wave arrival direction estimating method of coherent signal.

Background technology

In the middle of the actual signal environment; Independent signal and coherent signal are simultaneous often; The DOA algorithm for estimating mainly is to design separately to independent signal or coherent signal mostly; Do not consider the simultaneous situation of independent signal and coherent signal, the characteristics that more do not make full use of independent signal and coherent signal are carried out the DOA estimation.At document: Ye Z F, Zhang Y F, Liu C.Direction-of-arrival estimation for uncorrelated and coherent signals with fewer sensors [J] .IEEE Trans.on Microwaves; Antennas&Propagation; 2009,3 (3): among the 473-482, considered the DOA estimation problem of independent signal and coherent signal; But it is applicable to the uniform line array DOA estimation condition of (Uniform LinearArray is called for short ULA).

The UCA array distribution in one plane, it is provider's parallactic angle and angle of pitch information simultaneously, and its azimuth information that provides is 360 ° and does not have and blur.But because UCA array steering vector does not have the Vandermonde structure, much the direction finding algorithm based on the ULA array can not be used for the UCA array, especially under the situation that coherent signal exists.In order to let direction finding algorithm based on the ULA array be applicable to UCA array and even array arbitrarily, numerous scholars have proposed a lot of methods, with the virtual ULA array that is transformed to of non-ULA array.Wherein relatively more classical several method has: to the model space conversion of UCA array, to the interior slotting converter technique and the popular isolation technics of any array.Utilize the virtual converter technique of aforesaid array can any array is virtual for the ULA array, and then utilize and obtain corresponding direction of arrival based on the DOA algorithm for estimating of ULA array.But often there is array aperture loss in various degree through virtual conversion array later, makes estimated performance decrease; And may non-linearly be amplified after the virtual conversion of noise process, this will make that estimated performance further worsens, especially in the less situation of signal to noise ratio (S/N ratio).

Summary of the invention

It is simple to the objective of the invention is to propose a kind of estimation procedure, the Wave arrival direction estimating method based on the uniform circular array row that calculated amount is little.

The objective of the invention is to realize like this:

Wave arrival direction estimating method based on the uniform circular array row of the present invention comprises the steps:

(1) direction of arrival estimated parameter pre-service:

A. according to array output data matrix X:X=AS+Z, ask the reception data covariance matrix R:R=E [XX of uniform circular array row ^H]=AR _SA ^H+ σ ²I;

Wherein, A representes the M * N dimension array flow pattern matrix of uniform circular array row, and M representes element number of array, N expression signal number, and independent signal and coherent signal number are respectively N among the N _iAnd N _c,

D is relevant information source group number, n _kBe the signal number of the relevant information source of k group, S representes N * L dimensional signal data matrix, and L representes fast umber of beats, and Z representes M * L dimension white Gaussian noise data matrix, X ^HThe conjugate transpose of expression X, R _SBe signal data covariance matrix, σ ²Be the power of white Gaussian noise, I is the unit matrix with the R same dimension;

B. utilize model space transformation matrix T:

Reception data R to the uniform circular array row carries out conversion, obtains the reception data covariance matrix R of uniform line array in the model space ₁:

Wherein, J ₀Be 2K+1 dimension diagonal matrix, J ₀Element on the diagonal positions is J ₀(k, k)=j ^(k-1-K)B _(k-1-K)(-β), B _(k-1-K)() is the first kind Bessel function on k-1-K rank, k=1 ..., 2K+1; F is the discrete Fourier transformation matrix, F=[w _-Kw _-K+1W _K], w _q=[1e ^-jpE ^{-jp (M-1)}] ^H,

Q=-K ..., K; A ₁Be (2K+1) * N dimension flow pattern matrix of virtual uniform linear array, A ₁=[a ₁a ₂A _N],

I=1 ..., N;

(2) remove the model space noise:

Ask the not data covariance matrix R of noisy composition ₂:

Noise power σ ²Through R is carried out characteristic value decomposition, and to its M-(N _i+ D) individual little eigenwert is asked on average and is obtained;

(3) improve array aperture, independent signal carried out direction of arrival estimate:

Dividing spectrum peak search method to carry out direction of arrival with multiple signal estimates, searches out N _i+ D the corresponding spectrum peak of big eigenwert, its corresponding estimation angle has comprised N _iDirection of arrival angle that individual independent signal is corresponding and the corresponding direction of arrival angle of D group coherent signal are selected the maximum N of amplitude _iThe direction of arrival angle of individual spectrum peak amplitude correspondence is as the direction of arrival estimated result of independent signal;

(4) eliminate independent signal, coherent signal carried out direction of arrival estimate:

The data covariance matrix R of coherent signal ₃:

Wherein, J is and R ₂With the opposition angular unit matrix of dimension, A _1cThe flow pattern matrix that expression is made up of the steering vector of coherent signal, R _ScThe signal covariance matrix of expression coherent signal,

Expression R _ScTransposition, separate relevantly before and after utilizing to the vector restructing algorithm, obtain not having the coherent signal data matrix of order loss, and utilize the direction of arrival that total least square-invariable rotary subspace algorithm is found the solution coherent signal.

Beneficial effect of the present invention is:

Compare with existing direction finding algorithm based on the uniform circular array row, the present invention does not receive noise effect in the DOA estimation procedure, have higher estimated accuracy, and especially signal to noise ratio (S/N ratio) improves a lot than a hour estimated performance; Through independent signal and coherent signal being estimated separately array aperture has obtained utilizing more fully, remedies because the array aperture that the virtual array conversion brings loses, estimated performance is promoted further; Owing to adopt the model space conversion, what adopt during DOA estimates all is the algorithm that is suitable for even linear array, calculates easyly, and operand is little.

Description of drawings

Fig. 1 is the Wave arrival direction estimating method process flow diagram that the present invention is based on the uniform circular array row;

Fig. 2 is under the same conditions, and when incoming signal was independent signal, the inventive method was estimated relatively synoptic diagram of root-mean-square error with the model space MUSIC algorithm of not denoising;

Fig. 3 is under the same conditions, and when incoming signal was the mixing of independent signal and coherent signal, the inventive method compared synoptic diagram with the estimation root-mean-square error of the TLS-ESPRIT algorithm of separating coherent approach based on Toeplitz.

Embodiment

Core concept of the present invention is to utilize data structure characteristics in the model space conversion process, eliminates even white Gaussian noise to the DOA estimation effect, improves estimated performance; And adopt independent signal and coherent signal to separate estimation approach, the noise effect after the conversion of elimination UCA array process model space, the effective array aperture after the conversion of increase UCA array process model space.

The UCA array has very big superiority because of it can provide nothing fuzzy azimuth information and two dimension angular information.But, especially there is the situation of coherent signal because the singularity of its element position makes that a lot of traditional direction finding algorithms based on the ULA array are inapplicable to the UCA array.Along with the introducing of model space transform method, can be with the virtual ULA array that converts into of UCA array, but have the array aperture loss after the conversion, and noise power can be exaggerated under model space, and then influence the precision of DOA estimation.

When independent signal and coherent signal exist simultaneously, if utilize two kinds of signal self characteristics, it is separately carried out DOA estimate, will improve array aperture effectively.According to data structure, the method for elimination noise reasonable in design is with greatly improving the precision that DOA estimates in the middle of estimation procedure.

Below in conjunction with accompanying drawing Wave arrival direction estimating method of the present invention is described in detail.

Fig. 1 is the Wave arrival direction estimating method process flow diagram that the present invention is based on the UCA array.As shown in Figure 1, this method comprises the steps:

(1) direction of arrival estimated parameter pre-service:

One, the fast beat of data that is received by each array element obtains array output data matrix X, X=AS+Z, and wherein, A representes the M * N dimension array flow pattern matrix of UCA array, M representes element number of array, N expression signal number, wherein independent signal and coherent signal number are respectively N _iWith

D is relevant information source group number, n _kBe the signal number of the relevant information source of k group); Z representes N * L dimensional signal data matrix, and L representes fast umber of beats; N representes M * L dimension white Gaussian noise data matrix.Obtain the reception data covariance matrix R of UCA array by X:

R＝E[XX ^H]＝AR _SA ^H+σ ²I

Wherein, X ^HThe conjugate transpose of expression X, R _SBe signal data covariance matrix, σ ²Be the power of white Gaussian noise, I is the unit matrix with the R same dimension.

Two, structural model spatial alternation matrix T is following:

$T=\frac{1}{M}{J_0}^{-1}{F}^H$

Wherein, J ₀Be 2K+1 dimension diagonal matrix, then J ₀Element on the diagonal positions is J ₀(k, k)=j ^(k-1-K)B _(k-1-K)(-β), B _(k-1-K)() is the first kind Bessel function on k-1-K rank, k=1 ..., 2K+1; F is the discrete Fourier transformation matrix, F=[w _-Kw _-K+1W _K], w _q=[1e ^-jpE ^{-jp (M-1)}] ^H,

Q=-K ..., K.

R is carried out the model space conversion, obtain the data covariance matrix R in the model space ₁:

${\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA0000146190930000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_1={\mathrm{TRT}}^H=A_1{R}_S{A}_1^H+{\mathrm{\&sigma;}}^2{\mathrm{TT}}^H$ (formula 5)

Wherein, A ₁Be (2K+1) * N dimension flow pattern matrix of virtual uniform linear array, A ₁=[a ₁a ₂A _N],

I=1 ..., N.

(2) remove the model space noise:

Can be known that by step 3 formula 5 space white noise originally remains white noise at model space, but noise power can become big and inhomogeneous, this has had a strong impact on estimated performance.By R ₁Obtain the not data covariance matrix R of noisy composition ₂:

${\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000146190930000012.png,HDA0000146190930000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_2=R_1-{\mathrm{\&sigma;}}^2{\mathrm{TT}}^H=A_1{R}_S{A}_1^H$ (formula 6)

Can know by formula 6, as long as known noise power σ ²Can try to achieve the not data covariance matrix R of noisy with T ₂Noise power σ ²Can be through R be carried out characteristic value decomposition, and to its M-(N _i+ D) individual little eigenwert is asked on average and is obtained; And T obtains in the middle of step 2.

(3) improve array aperture, independent signal carried out direction of arrival estimate:

To R ₂Carry out svd, obtain M-(N _i+ D) the corresponding noise subspace U of individual little eigenwert _NAdopting the MUSIC spectrum peak search method to carry out DOA estimates:

$P_{\mathrm{MUSIC}}\left(\mathrm{\&theta;}\right)=\frac{1}{a^H\left(\mathrm{\&theta;}\right)U_N{U}_N^{H}a\left(\mathrm{\&theta;}\right)}.$

Can search out N _i+ D the corresponding spectrum peak of big eigenwert, its corresponding estimation angle has comprised N _iDOA angle that individual independent signal is corresponding and the corresponding DOA angle of D group coherent signal.Because the corresponding steering vector of one group of coherent signal is not a canonical form, thereby its orthogonality with noise subspace is good not as independent signal, and the spectrum peak amplitude of correspondence is littler.Can select the direction of arrival estimated result of the corresponding DOA angle of Ni maximum spectrum peak amplitude of amplitude as independent signal.

(4) eliminate independent signal, coherent signal carried out direction of arrival estimate:

Independent signal has been carried out the DOA estimation in the step 5,, be necessary to remove the information of whole independent signals for fear of repeating estimation to improve the array utilization factor.According to formula 6, and utilize the Toeplitz characteristic of independent signal and noise data covariance matrix, obtain the data covariance matrix R of coherent signal ₃:

${\mathrm{<figure-callout\; id="3"\; label="R"\; filenames="HDA0000146190930000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_3=R_2-{\mathrm{JR}}_2^{T}J=A_{1c}(R_{\mathrm{Sc}}-R_{\mathrm{Sc}}^T)A_{1c}^H$ (formula 7)

Wherein, J is and R ₂With the opposition angular unit matrix of dimension, A _1cThe flow pattern matrix that expression is made up of the steering vector of coherent signal, R _ScThe signal covariance matrix of expression coherent signal,

Expression R _ScTransposition.Obviously, R ₃In do not contain the information of any independent signal and noise.

It is relevant to utilize front and back to separate to the vector restructing algorithm, to R ₃Carry out svd, obtain 2D the corresponding signal subspace U of big eigenwert _S

To R ₄Carry out svd, get D the corresponding signal subspace U of big eigenwert _S1=[u ₁, u ₂..., u _D], the coherent signal data matrix of structure row full rank:

$R_5=[R_1^{\mathrm{fb}},{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000146190930000012.png,HDA0000146190930000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_2^{\mathrm{fb}},\&CenterDot;\&CenterDot;\&CenterDot;,R_D^{\mathrm{fb}}]$

Wherein,

k=1;, D.

For by u _kThe M that constitutes ₀* L _FkThe dimension data matrix, M ₀=M+1-max{L _Fk,

Serve as reasons

The M that constitutes ₀* L _FkThe dimension data matrix, L _Fb=n _k-L _Fk

Utilize the direction of arrival that total least square-coherent signal is found the solution in invariable rotary subspace algorithm (TLS-ESPRIT): R ₅₁And R ₅₂The corresponding R of difference ₅Preceding M ₀-1 row and back M ₀The matrix that-1 row is formed, R ₆=[R ₅₁, R ₅₂].To R ₆Carry out svd, Q is N in its right singular matrix _cIndividual little eigenwert characteristic of correspondence vector matrix, dimension is 2N * N, and Q=[Q ₁Q ₂], Q ₁And Q ₂Be the matrix of N * N, according to the TLS-ESPRIT principle

$\mathrm{\&Psi;}=-Q_1{Q}_2^{-1}$

Ψ is carried out feature decomposition, try to achieve the direction of arrival of coherent signal according to its eigenwert

In the formula, i=1 ..., N _c, γ _i(Ψ) i the eigenwert of representing matrix Ψ.

The DOA method of estimation that the present invention proposes does not receive the model space The noise, the estimated performance of the direction finding algorithm that greatly improves.Through independent signal and coherent signal are separately estimated, make array aperture be utilized effectively, remedy the model space conversion and brought the deficiency of array aperture loss.More than 2 enforcement effectively solved two defectives of UCA array in the middle of DOA estimates, greatly expanded the application of UCA array.

Claims (1)

1. the Wave arrival direction estimating method based on the uniform circular array row is characterized in that, comprises the steps:

(1) direction of arrival estimated parameter pre-service:

A. according to array output data matrix X:X=AS+Z, ask the reception data covariance matrix R:R=E [XX of uniform circular array row ^H]=AR _SA ^H+ σ ²I;

Wherein, A representes the M * N dimension array flow pattern matrix of uniform circular array row, and M representes element number of array, N expression signal number, and independent signal and coherent signal number are respectively N among the N _iAnd N _c,

D is relevant information source group number, n _kBe the signal number of the relevant information source of k group, S representes N * L dimensional signal data matrix, and L representes fast umber of beats, and Z representes M * L dimension white Gaussian noise data matrix, X ^HThe conjugate transpose of expression X, R _SBe signal data covariance matrix, σ ²Be the power of white Gaussian noise, I is the unit matrix with the R same dimension;

B. utilize model space transformation matrix T:

Reception data R to the uniform circular array row carries out conversion, obtains the reception data covariance matrix R of uniform line array in the model space ₁:

Wherein, J ₀Be 2K+1 dimension diagonal matrix, J ₀Element on the diagonal positions is J ₀(k, k)=j ^(k-1-K)B _(k-1-K)(-β), B _(k-1-K)() is the first kind Bessel function on k-1-K rank, k=1 ..., 2K+1; F is the discrete Fourier transformation matrix, F=[w _-Kw _-K+1W _K], w _q=[1 e ^-jpE ^{-jp (M-1)}] ^H, Q=-K ..., K; A ₁Be (2K+1) * N dimension flow pattern matrix of virtual uniform linear array, A ₁=[a ₁a ₂A _N], I=1 ..., N;

(2) remove the model space noise:

Ask the not data covariance matrix R of noisy composition ₂:

Noise power σ ²Through R is carried out characteristic value decomposition, and to its M-(N _i+ D) individual little eigenwert is asked on average and is obtained;

(3) improve array aperture, independent signal carried out direction of arrival estimate:

Dividing spectrum peak search method to carry out direction of arrival with multiple signal estimates, searches out N _i+ D the corresponding spectrum peak of big eigenwert, its corresponding estimation angle has comprised N _iDirection of arrival angle that individual independent signal is corresponding and the corresponding direction of arrival angle of D group coherent signal are selected the maximum N of amplitude _iThe direction of arrival angle of individual spectrum peak amplitude correspondence is as the direction of arrival estimated result of independent signal;

(4) eliminate independent signal, coherent signal carried out direction of arrival estimate:

The data covariance matrix R of coherent signal ₃:

Wherein, J is and R ₂With the opposition angular unit matrix of dimension, A _1cThe flow pattern matrix that expression is made up of the steering vector of coherent signal, R _ScThe signal covariance matrix of expression coherent signal,

Expression R _ScTransposition, separate relevantly before and after utilizing to the vector restructing algorithm, obtain not having the coherent signal data matrix of order loss, and utilize the direction of arrival that total least square-invariable rotary subspace algorithm is found the solution coherent signal.

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