CN106093845A - A kind of quick DOA estimation method based on pseudo space spectrum search - Google Patents

Abstract

The invention discloses a kind of quick DOA estimation method based on pseudo space spectrum search, comprise the steps: 1: the radar signal that system receives is after matched filtering, and the output obtained at receiver is expressed as x (t_l), and construct a new data matrix X.2: calculate the covariance matrix R of X_X, and it is carried out Eigenvalues Decomposition, try to achieve its noise subspace U_XN.3: definition matrix J, construct a new data matrix Y=X+J*X；4: calculate the covariance matrix R of Y_Y, and it is carried out Eigenvalues Decomposition, try to achieve its noise subspace U_YN.5: construct the spatial spectrum function P of DOA based on matrix Y_music(θ), and to itsCarry out spectrum peak search, find out N number of DOA that N number of maximum point is correspondingThe absolute value of angle.6: construct the spatial spectrum function P ' of DOA based on matrix X_music(θ), and willSubstitute into function P ' respectively_music(θ), then obtain and compareWithValue, ifRelatively greatly thenIfRelatively greatly thenObtainIn the range of N number of DOAAngle value.The method that the present invention proposes, can make hunting zone halve, and reduces operand, saves operation time.

Description

A kind of quick DOA estimation method based on pseudo space spectrum search

Technical field

The invention belongs to radar signal processing field, relate to using the angle of the radar signal of spatial spectrum searching method to estimate Meter, a kind of method of quick Mutual coupling based on pseudo space spectrum search.

Background technology

In recent decades, direction of arrival (Direction of Arrival, DOA) estimates the one of always Estimation of Spatial Spectrum Individual important content, when utilizing the method for spectrum peak search to carry out angle on target estimation in spatial spectrum, its resolution is substantially better than biography Conventional beamformer (CBF) method of system.For utilizing the signal DOA estimation problem of spectrum peak search method, there has been proposed a large amount of Effective method.Such as at document: Schmidt R O.Multiple emitter location and signal Parameter estimation.IEEE Trans.on AP.1986.34 (3): in 276～280, it is proposed that multiple signal divides Class (MUSIC) algorithm；Such as at document: Stoica P, Nehorai A.MUSIC, maximum likelihood, and Cramer-Rao bound:futher results and comparisons.In Proc.ICASSP, 1989:2605～ In 2608, it is proposed that weighting MUSIC algorithm；These algorithms have the highest resolving power, estimated accuracy and stability, but these Method is when carrying out spectrum peak search, and its region of search isTherefore in calculating process, operand is more big, search time Longer.

Summary of the invention

For the most methodical deficiency, the present invention proposes a kind of novel quick DOA based on pseudo space spectrum search and estimates Meter method, the method improves on existing MUSIC algorithm, by the pseudo space spectrum of structure radar signal, spectral peak is searched Rope scope halves, and only needs searchJust can obtainIn the range of DOA value, reduce operand, shorten operation time.

Comprise the steps: for realizing the technical solution of the present invention

A kind of quick DOA estimation method based on pseudo space spectrum search, comprises the steps:

Step 1: the radar signal that reception system receives is after matched filtering, and the output obtained at receiver is permissible It is expressed as x (t_l), and construct a new data matrix X=[x (t₁),x(t₂),...,x(t_L)]；Wherein l=1,2 ..., L； L represents fast umber of beats；

Step 2: calculate the covariance matrix R of X_X=XX^H, and to R_XCarry out Eigenvalues Decomposition, try to achieve the noise subspace of X U_XN；

Step 3: definition matrix J, constructs a new data matrix Y:Y=X+J*X；

Step 4: calculate the covariance matrix R of Y_Y=YY^H, and to R_YCarry out Eigenvalues Decomposition, try to achieve its noise subspace U_YN；

Step 5: construct the spatial spectrum function P of DOA based on matrix Y_music(θ), and to itsCarry out spectral peak to search Rope, finds out the angle that N number of maximum point is corresponding, is the absolute value of N number of DOA angle estimation value, is designated as

Step 6: construct the spatial spectrum function P ' of DOA based on matrix X_music(θ), and willGeneration respectively Enter function P '_music(θ), the functional value of positive-angleIt is designated asThe functional value of negative angleNote ForWherein j=1,2 ..., N；Then compareWithValue, ifRelatively greatly thenIfRelatively greatly thenObtainIn the range of N number of DOA angle value

Further, x (t in step 1_l)=As (t_l)+n(t_l)；A=[a₁,a₂,...,a_n] represent M × N-dimensional array stream Type matrix, wherein M represents the element number of array of emission array, and N represents the element number of array of receiving array；

Steering vector a_n=a (θ_n)=[1, exp (j2 π dsin θ_n/λ),...,exp(j2π(M-1)dsinθ_n/λ)]^T, wherein θ_nRepresent the true DOA, n=1,2 of n-th group ..., N；D represents that array element distance, λ represent the wavelength of electromagnetic wave, ()^TRepresent and turn Put；

s(t_l) represent t_lThe emission signal vector of one N-dimensional of moment, n (t_l) represent t_lThe moment zero-mean of one M dimension is high This white noise.

Further, described in step 2 to R_XCarry out Eigenvalues Decomposition as follows:

$R_X=U_{XS}{\Σ}_{XS}{U}_{XS}^H+U_{XN}{\Σ}_{XN}{U}_{XN}^H$

Wherein, Σ_XSRepresent covariance matrix R_XTop n eigenvalue of maximum constitute diagonal matrix, U_XSIt is right with it to represent The characteristic vector answered, Σ_XNRepresenting the diagonal matrix that remaining M-N eigenvalue is constituted, corresponding characteristic vector is U_XN, U_XNNoise subspace for matrix X.

Further, the matrix J that defines described in step 3 particularly as follows:

Further, to R described in step 4_YCarry out Eigenvalues Decomposition as follows:

$R_Y=U_{YS}{\Σ}_{YS}{U}_{YS}^H+U_{YN}{\Σ}_{YN}{U}_{YN}^H$

Wherein, Σ_YSRepresent covariance matrix R_YN number of eigenvalue of maximum constitute diagonal matrix, U_YSRepresent corresponding Characteristic vector, Σ_YNRepresenting the diagonal matrix that remaining M-N eigenvalue is constituted, corresponding characteristic vector is U_YN, U_YN Noise subspace for matrix Y.

Further, the spatial spectrum function P of structure described in step 5_music(θ) expression formula is as follows:

Wherein: θ span is

B (θ)=[1+exp (j2 π (M-1) dsin θ/λ), exp (j2 π dsin θ/λ)+exp (j2 π (M-2) dsin θ/ λ),...,exp(j2π(M-1)dsinθ/λ)+1]^T。

Further, function P ' based on matrix X is constructed described in step 6_music(θ) expression formula is as follows:

$P_{music}^{\′}\left(\mathrm{\θ}\right)=\frac{1}{a^H\left(\mathrm{\θ}\right)U_{XN}{U}_{XN}^{H}a\left(\mathrm{\θ}\right)}.$

Beneficial effects of the present invention:

Compared with the conventional method, the present invention proposes a kind of novel quick DOA estimation side based on pseudo space spectrum search Method, makes hunting zone halve, and reduces operand, saves operation time.

Accompanying drawing explanation

Fig. 1 is implementing procedure figure of the present invention.

Fig. 2 is to be 10 in signal to noise ratio, in the case of fast umber of beats is 100 times, and the spatial spectrum function P of the present invention_music(θ) figure.

Detailed description of the invention

The invention will be further described with specific embodiment below in conjunction with the accompanying drawings.

As it is shown in figure 1, the quick DOA estimation method that the present invention proposes comprises the steps:

(1) radar signal that system receives is after matched filtering, and the output obtained at receiver is expressed as x (t_l)= As(t_l)+n(t_l), l=1,2 ..., in L formula:

L represents fast umber of beats；

A=[a₁,a₂,...,a_n] represent the array manifold matrix of M × N-dimensional, wherein M represents the array element of emission array Number, N represents the element number of array of receiving array, wherein

Steering vector a_n=a (θ_n)=[1, exp (j2 π dsin θ_n/λ),...,exp(j2π(M-1)dsinθ_n/λ)]^Tθ_n,n =1,2 ..., N represents that the true DOA, d of n-th group represents that array element distance, λ represent the wavelength of electromagnetic wave, () respectively^TRepresent and turn Put；

s(t_l) represent t_lThe emission signal vector of one N-dimensional of moment, n (t_l) represent t_lThe moment zero-mean of one M dimension is high This white noise.

And construct the data matrix X:X=[x (t of M × L dimension₁),x(t₂),...,x(t_L)]。

(2) the covariance matrix R of X is calculated_X=XX^H, wherein ()^HRepresent conjugate transpose.To R_XCarry out Eigenvalues Decomposition:

$R_X=U_{XS}{\Σ}_{XS}{U}_{XS}^H+U_{XN}{\Σ}_{XN}{U}_{XN}^H$

Wherein, Σ_XSRepresent covariance matrix R_XTop n eigenvalue of maximum constitute diagonal matrix, U_XSIt is right with it to represent The characteristic vector answered, Σ_XNRepresenting the diagonal matrix that remaining M-N eigenvalue is constituted, corresponding characteristic vector is U_XN, The referred to herein as noise subspace of matrix X.

(3) definition matrix J:

Construct a new data matrix Y:Y=X+J*X.

(4) the covariance matrix R of Y is calculated_Y=YY^H, wherein ()^HRepresent conjugate transpose.To R_YCarry out Eigenvalues Decomposition:

$R_Y=U_{YS}{\Σ}_{YS}{U}_{YS}^H+U_{YN}{\Σ}_{YN}{U}_{YN}^H$

Wherein, Σ_YSRepresent covariance matrix R_YN number of eigenvalue of maximum constitute diagonal matrix, U_YSRepresent corresponding Characteristic vector, Σ_YNRepresenting the diagonal matrix that remaining M-N eigenvalue is constituted, corresponding characteristic vector is U_YN, this In be referred to as matrix Y noise subspace.

(5) the spatial spectrum function P of DOA based on matrix Y is constructed_music(θ):

$P_{music}\left(\mathrm{\θ}\right)=\frac{1}{b^H\left(\mathrm{\θ}\right)U_{YN}{U}_{YN}^{H}b\left(\mathrm{\θ}\right)};$

Wherein: θ span is

$\begin{array}{c}b\left(\mathrm{\θ}\right)=[1+\exp (j2\mathrm{\π}(M-1)d\sin \mathrm{\θ}/\mathrm{\λ}),\exp (j2\mathrm{\π}d\sin \mathrm{\θ}/\mathrm{\λ}+\exp (j2\mathrm{\π}(M-2)d\sin \mathrm{\θ}/\mathrm{\λ}),...,\\ \exp (j2\mathrm{\π}(M-1)d\sin \mathrm{\θ}/\mathrm{\λ})+{1]}^T\end{array};$

And to itsCarry out spectrum peak search, find out the angle that N number of maximum point is corresponding, be estimating of N number of DOA angle The absolute value of evaluation, is designated as

(6) function P ' based on matrix X is constructed_music(θ):

$P_{music}^{\′}\left(\mathrm{\θ}\right)=\frac{1}{a^H\left(\mathrm{\θ}\right)U_{XN}{U}_{XN}^{H}a\left(\mathrm{\θ}\right)};$

Wherein θ span isAnd willSubstitute into P ' respectively_music(θ), the letter of positive-angle Numerical valueIt is designated asThe functional value of negative angleIt is designated asWherein j=1,2 ..., N； Then compareWithValue, ifRelatively greatly thenIfRelatively greatly thenObtainIn the range of N number of DOAAngle value.

Embodiment

Below in conjunction with emulation experiment, the effect of the present invention is described further.

In order to assess the performance of this method, it is considered to system, emission array is array element with receiving row, and spacing is electromagnetic wave The even linear array of half-wavelength, the element number of array M=11 of emission array, the element number of array N=10 of receiving array, it is assumed that far field has three Individual separate target, lays respectively at θ₁=-32 °, θ₂=7 °, θ₃=23 °.In all of test, background noise is assumed to be White Gaussian noise, fast umber of beats L=100.

Experiment condition

Use the present invention when signal to noise ratio (SNR) is 10dB, angle on target is carried out angle estimation, simulation result such as Fig. 2 with Shown in table 1.

Table 1

Experimental analysis

Figure it is seen that the present invention can estimate the absolute value of angle on target exactlyJ=1,2,3.

As it can be seen from table 1 in the present inventionWithValue there is bigger difference, can be by comparingWithValue accurately differentiates the actual value (sign) estimating angle on target.

The a series of detailed description of those listed above is only for the feasibility embodiment of the present invention specifically Bright, they also are not used to limit the scope of the invention, all equivalent implementations made without departing from skill of the present invention spirit Or change should be included within the scope of the present invention.

Claims (7)

1. a quick DOA estimation method based on pseudo space spectrum search, it is characterised in that comprise the steps:

Step 1: the radar signal that reception system receives is after matched filtering, and the output obtained at receiver can represent For x (t_l), and construct a new data matrix X=[x (t₁),x(t₂),...,x(t_L)]；Wherein l=1,2 ..., L；L table Show fast umber of beats；

Step 2: calculate the covariance matrix R of X_X=XX^H, and to R_XCarry out Eigenvalues Decomposition, try to achieve the noise subspace U of X_XN；

Step 3: definition matrix J, constructs a new data matrix Y:Y=X+J*X；

Step 4: calculate the covariance matrix R of Y_Y=YY^H, and to R_YCarry out Eigenvalues Decomposition, try to achieve its noise subspace U_YN；

Step 5: construct the spatial spectrum function P of DOA based on matrix Y_music(θ), and to itsCarry out spectrum peak search, find out The angle that N number of maximum point is corresponding, is the absolute value of N number of DOA angle estimation value, is designated asStep 6: structure The spatial spectrum function P ' of DOA based on matrix X_music(θ), and willSubstitute into function P ' respectively_music(θ), The functional value of positive-angleIt is designated asThe functional value of negative angleIt is designated asWherein j= 1,2,...,N；Then compareWithValue, ifRelatively greatly thenIfRelatively greatly thenObtainIn the range of N number of DOA angle value

A kind of quick DOA estimation method based on pseudo space spectrum search the most according to claim 1, it is characterised in that step X (t in rapid 1_l) expression formula be: x (t_l)=As (t_l)+n(t_l)；A=[a₁,a₂,...,a_n] represent M × N-dimensional array manifold Matrix, wherein M represents the element number of array of emission array, and N represents the element number of array of receiving array；

Steering vector a_n=a (θ_n)=[1, exp (j2 π d sin θ_n/λ),...,exp(j2π(M-1)d sinθ_n/λ)]^T, wherein θ_n Represent the true DOA, n=1,2 of n-th group ..., N；D represents that array element distance, λ represent the wavelength of electromagnetic wave, ()^TRepresent and turn Put；

s(t_l) represent t_lThe emission signal vector of one N-dimensional of moment, n (t_l) represent t_lThe zero-mean gaussian white noise of one M dimension of moment Sound.

A kind of quick DOA estimation method based on pseudo space spectrum search the most according to claim 1, it is characterised in that step Described in rapid 2 to R_XCarry out Eigenvalues Decomposition as follows:

$R_X=U_{XS}{\mathrm{\Σ}}_{XS}{U}_{XS}^H+U_{XN}{\mathrm{\Σ}}_{XN}{U}_{XN}^H$

Wherein, Σ_XSRepresent covariance matrix R_XTop n eigenvalue of maximum constitute diagonal matrix, U_XSRepresent corresponding Characteristic vector, Σ_XNRepresenting the diagonal matrix that remaining M-N eigenvalue is constituted, corresponding characteristic vector is U_XN, U_XNFor The noise subspace of matrix X.

A kind of quick DOA estimation method based on pseudo space spectrum search the most according to claim 1, it is characterised in that step The matrix J that defines described in rapid 3 particularly as follows:

A kind of quick DOA estimation method based on pseudo space spectrum search the most according to claim 1, it is characterised in that step To R described in rapid 4_YCarry out Eigenvalues Decomposition as follows:

$R_Y=U_{YS}{\mathrm{\Σ}}_{YS}{U}_{YS}^H+U_{YN}{\mathrm{\Σ}}_{YN}{U}_{YN}^H$

Wherein, Σ_YSRepresent covariance matrix R_YN number of eigenvalue of maximum constitute diagonal matrix, U_YSRepresent corresponding spy Levy vector, Σ_YNRepresenting the diagonal matrix that remaining M-N eigenvalue is constituted, corresponding characteristic vector is U_YN, U_YNFor square The noise subspace of battle array Y.

A kind of quick DOA estimation method based on pseudo space spectrum search the most according to claim 1, it is characterised in that step The spatial spectrum function P of structure described in rapid 5_music(θ) expression formula is as follows:

$P_{music}\left(\mathrm{\θ}\right)=\frac{1}{b^H\left(\mathrm{\θ}\right)U_{YN}{U}_{YN}^{H}b\left(\mathrm{\θ}\right)};$

Wherein:

B (θ)=[1+exp (j2 π (M-1) d sin θ/λ), exp (j2 π d sin θ/λ)+exp (j2 π (M-2) d sin θ/ λ),...,exp(j2π(M-1)d sinθ/λ)+1]^T。

A kind of quick DOA estimation method based on pseudo space spectrum search the most according to claim 2, it is characterised in that step Function P ' based on matrix X is constructed described in rapid 6_music(θ) expression formula is as follows:

$P_{music}^{\′}\left(\mathrm{\θ}\right)=\frac{1}{a^H\left(\mathrm{\θ}\right)U_{XN}{U}_{XN}^{H}a\left(\mathrm{\θ}\right)}.$