CN103323810B - L-array azimuthal angle and pitch angle paired signal processing method - Google Patents

Abstract

The invention relates to an L-array azimuthal angle and pitch angle paired signal processing method, and belongs to the field of radio signal processing. The L-array azimuthal angle and pitch angle paired signal processing method is used for solving the paired problem generated when an L-array two-dimensional arrival angle estimation problem is decomposed into two one-dimensional arrival angle estimation problems. The L-array azimuthal angle and pitch angle paired signal processing method aims at achieving automatic pairing between two sets of one-dimensional arrival angles on the basis that the two sets of one-dimensional arrival angles are measured. The estimation algorithm and the pairing algorithm of the two sets of one-dimensional arrival angles are independently carried out. The one-dimensional arrival angles are paired based on the maximum-likelihood criterion so that the L-array azimuthal angle and pitch angle paired signal processing method can have high robustness. The L-array azimuthal angle and pitch angle paired signal processing method has the advantages that the pairing and the estimation of the one-dimensional arrival angles are independently carried out, the processing procedure of the paired method is not influenced by the estimation procedure of the one-dimensional arrival angles, the L-array azimuthal angle and pitch angle paired signal processing method has high robustness under the conditions of the low signal-to-noise ratio and the small snapshot number, and under the conditions of a coherent source and an uneven L array, the L-array azimuthal angle and pitch angle paired signal processing method is still applicable.

Description

The signal processing method of a kind of L battle array position angle and angle of pitch pairing

Technical field

The present invention relates to the signal processing method of a kind of L battle array position angle and angle of pitch pairing, belong to radio signal process field.

Background technology

L battle array is the simple two-dimentional battle array be made up of two linear arrays intersected vertically, and can obtain position angle and the angle of pitch of target simultaneously, in two-dimentional DOA estimate, have many advantages, be subject to the extensive concern of scholar in recent years.Be the one dimension DOA estimate of two linear arrays usually by the two-dimentional DOA estimate PROBLEM DECOMPOSITION of L battle array in engineering, then angle reached to estimated two groups of one-dimensional waves and obtain, without fuzzy azimuth of target and the angle of pitch, effectively to reduce operand etc. like this by pairing.

L battle array matching method roughly can be divided three classes at present: one, to the array be made up of acoustics vector sensor, can directly utilize the space vector characteristic of sensor to realize automatic matching, but the method is limited and restricted application by sensor type.Two, by two one dimension DOA estimate with pairing Process fusion together with, these class methods will construct a special general covariance matrix usually, containing the corresponding relation between two linear array array manifolds in this covariance matrix, this corresponding relation is utilized to realize pairing, but generally these class methods cause more greatly feature decomposition computing quantitative change large due to covariance matrix dimension, and are often only applicable to even L battle array and incoherent source situation.Three, two groups of one dimension DOA estimate are first carried out, then independently match, as estimated incoming wave by Toeplitz method and two linear array one-dimensional waves reach cosine of an angle difference, with this difference for medium realizes pairing, the method is effectively same in coherent source situation, but two linear arrays must be even linear arrays, and due to the poor Algorithm robustness that causes of Toeplitz method precision not high; Whether first reach angle by estimated two groups of one-dimensional waves to draw one " information source covariance matrix ", be then Hermite matrix for criterion judges whether that pairing is correct with this matrix, but in equal strength independent source situation, Algorithm robustness is slightly poor.

To sum up, the two-dimentional ripple of current L battle array reaches angle matching method and there is the shortcomings such as robustness is low, the scope of application is limited.Based on this, the present invention is based on maximum-likelihood criterion and propose a kind of new matching method, the method belongs to above-mentioned 3rd class, target pairing in without any prior imformation situation can be realized, first carry out two groups of one dimension DOA estimate, the reception data of one-dimensional wave Da Jiao and two linear array then utilizing these two groups to estimate obtain the maximal possibility estimation of two information source covariance matrixes, finally realize pairing according to the displacement relation of these two covariance matrixes by the method optimized.Compare existing matching method, the matching method that the present invention carries is more flexible, and still has higher robustness at low signal-to-noise ratio and fewer snapshots situation, and to information source, whether whether relevant and array does not evenly have particular/special requirement.

The matching method had in prior art is restricted application by sensor type restriction, or is only applicable to even L battle array and incoherent source situation, and robustness is not high; Advantage of the present invention is: the first, and pairing of the present invention and one dimension DOA estimate independently carry out, and can make full use of the decorrelation LMS of the one dimensional linear array of existing comparative maturity, Sources number estimation and DOA estimate algorithm; The second, the present invention still has higher robustness under low signal-to-noise ratio and fewer snapshots condition; 3rd, under coherent source and non-homogeneous L battle array condition, this matching method is still suitable for.A large amount of Simulation results shows, this invention has very high actual application value.

Summary of the invention

The object of the invention is to reach automatic matching basis, angle realized between them measuring two groups of one-dimensional waves.The estimation that two groups of one-dimensional waves reach angle independently is carried out with pairing algorithm, makes the scope of application of the present invention wider, matches make the present invention have higher robustness based on maximum-likelihood criterion.Suppose that to reach angle be priori or estimated for the number of targets of two linear arrays and one-dimensional wave, and the angle of target and two linear arrays is distinguishable.

Basic step of the present invention is:

According to existing one dimensional linear array direction of arrival estimation method, step one: pre-service, show that two groups of one-dimensional waves of target and two linear arrays reach angle; If two linear array X, Y intersect at initial point, array number is respectively M+1, N+1, and total array number is M+N+1; The far field narrow band signal being provided with K concentricity frequency is received by this L battle array, and λ is carrier frequency wavelength, θ _kwith represent position angle and the angle of pitch of a kth incoming wave signal respectively suppose that information source can be divided in two linear arrays, now the two-dimentional DOA estimate problem of L battle array is broken down into two one dimension DOA estimate;

Note a _x, a _yfor the steering vector of linear array X, Y, x _mfor m array element in X-axis to initial point distance (m=1,2 ... M), y _nfor the n-th array element in Y-axis to initial point distance (n=1,2 ..., N), then the steering vector of information source k can be expressed as:

$\left\{\begin{array}{c}{a}_x\left({\mathrm{\α}}_k\right)={[1,e^{-j\frac{2\mathrm{\π}{x}_1}{\mathrm{\λ}}\cos {\mathrm{\α}}_k},e^{-j\frac{2\mathrm{\π}{x}_2}{\mathrm{\λ}}\cos {\mathrm{\α}}_k},\·\·\·,e^{-j\frac{2\mathrm{\π}{x}_M}{\mathrm{\λ}}\cos {\mathrm{\α}}_k}]}^{T}k=\mathrm{1,2},\·\·\·,K\\ a_y\left({\mathrm{\β}}_k\right)={[1,e^{-j\frac{2\mathrm{\π}{y}_1}{\mathrm{\λ}}\cos {\mathrm{\β}}_k},e^{-j\frac{2\mathrm{\π}{y}_2}{\mathrm{\λ}}\cos {\mathrm{\β}}_k},\·\·\·,e^{-j\frac{2\mathrm{\π}{y}_N}{\mathrm{\λ}}\cos {\mathrm{\β}}_k}]}^{T}k=\mathrm{1,2},\·\·\·,K\end{array}\right.---\left(1\right)$

Wherein, note A _x, A _ybe respectively the array manifold of linear array X and linear array Y, A _x(α)=[a _x(α ₁), a _x(α ₂) ..., a _x(α _k)], A _y(β)=[a _y(β ₁), a _y(β ₂) ..., a _y(β _k)]; s _kfor the complex envelope of a kth information source, then echoed signal can be expressed as s (t)=[s ₁(t), s ₂(t) ..., s _k(t)] ^t;

Note n _x, n _yfor white Gaussian noise, then the reception data of x-ray battle array and Y linear array are respectively:

$\left\{\begin{array}{c}X\left(t\right)=A_x\left(\mathrm{\α}\right)s+n_x=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{a}_x\left({\mathrm{\α}}_k\right)s_k\left(t\right)+n_x\left(t\right)\\ Y\left(t\right)=A_y\left(\mathrm{\β}\right)s+n_y=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{a}_y\left({\mathrm{\β}}_k\right)s_k\left(t\right)+n_y\left(t\right)\end{array}\right.---\left(2\right)$

One dimension direction of arrival estimation method is adopted to estimate the angle of target and two linear array X, Y respectively with

Step 2: reach angle by the reception data of one of them linear array with the one-dimensional wave estimated by this linear array and obtain an information source covariance matrix; Under white Gaussian noise background, first information source covariance matrix maximal possibility estimation be expressed as:

${\hat{R}}_s=E\left\{{\hat{s}\hat{s}}^H\right\}=E\{{\hat{A}}_y^{+}\·{\mathrm{YY}}^H\·{\left({\hat{A}}_y^H\right)}^{+}\}={\hat{A}}_y^{+}{R}_{\mathrm{yy}}{\left({\hat{A}}_y^H\right)}^{+}---\left(4\right)$

Wherein for estimated by the linear array Y the array manifold of structure, in the order of each angle any, for moore-Penrose inverse, R _yyfor linear array Y receives the covariance matrix of data:

$R_{\mathrm{yy}}=E\left\{{\mathrm{YY}}^H\right\}=A_y\·E\left\{{\mathrm{ss}}^H\right\}\·A_y^H+{\mathrm{\σ}}^{2}I=A_y{R}_s{A}_y^H+{\mathrm{\σ}}^{2}I---\left(5\right)$

Step 3: reach angle with the reception data of two linear arrays and estimated two groups of one-dimensional waves simultaneously and obtain second information source covariance matrix; To linear array X, note with the array manifold of corresponding linear array X is if for rear N capable, second information source covariance matrix is:

$\begin{array}{c}{R}_s^{\′}={\hat{A}}_x^{+}\·E\left\{{\mathrm{XY}}^H\right\}\·{\left({\hat{A}}_y^{\′H}\right)}^{+}\\ ={\hat{A}}_x^{+}{R}_{\mathrm{xy}}{\left({\hat{A}}_y^{\′H}\right)}^{+}\end{array}---\left(6\right)$

Wherein a ' _y, Y ' is respectively A _y, Y rear N capable;

By optimization method, step 4: utilize a permutation matrix two information source covariance matrix equivalences to be coupled together, show that two groups of one-dimensional waves reach angle one to one; Define a K × K and tie up permutation matrix T, if T _ijfor the i-th row j column element of matrix T, then

$\left\{\begin{array}{cc}\∀T_{\mathrm{ij}}\∈\left\{\mathrm{0,1}\right\}& \\ \underset{i=1}{\overset{K}{\mathrm{\Σ}}}{T}_{\mathrm{ij}}=1& j=\mathrm{1,2},\·\·\·,K\\ \underset{j=1}{\overset{K}{\mathrm{\Σ}}}{T}_{\mathrm{ij}}=1& i=\mathrm{1,2},\·\·\·,K\end{array}\right.---\left(7\right)$

If keep order constant, corresponding incoming wave and the angle of linear array X are [α ₁, α ₂..., α _k] T, then the array manifold that two linear arrays are corresponding is ${\hat{A}}_y,{\hat{A}}_{x}T.$ If ${\hat{A}}_{x}T\≈A_x,$ Then ${\hat{A}}_x^{+}\≈T{A}_x^{+},$ Formula (6) can turn to

$R_s^{\′}={\hat{A}}_x^{+}{R}_{\mathrm{xy}}{\left({\hat{A}}_y^{\′H}\right)}^{+}\≈{\mathrm{TA}}_x^{+}\left(A_x{R}_s{A}_y^{\′H}\right){\left({\hat{A}}_y^{\′H}\right)}^{+}\≈{\mathrm{TR}}_s\≈{T\hat{R}}_s---\left(8\right)$

When information source independence, can directly by draw T, then T is revised the form shown in an accepted way of doing sth (7), can draw corresponding relation; Note

$J_{\mathrm{PMLS}}=\underset{T}{\min }{\left|\right|R_s^{\′}-{T\hat{R}}_s\left|\right|}_F^2=\underset{T}{\min }{\left|\right|\left({\hat{A}}_x^{+}{R}_{\mathrm{xy}}{\left({\hat{A}}_y^{\′H}\right)}^{+}\right)-T\·\left({\hat{A}}_y^{+}{R}_{\mathrm{yy}}{\left({\hat{A}}_y^H\right)}^{+}\right)\left|\right|}_F^2---\left(9\right)$

An above formula demand once moore-Penrose inverse, because of can exist at most K! Kind possible pairing situation, therefore need to carry out K! Secondary computing; When information source number K is larger, the operand of formula (9) increases, further dimensionality reduction optimization, if i-th row of note T is designated as T _i, R ' _sthe i-th row be designated as R ' _si, then

$J_{\mathrm{MPMLS}}=\underset{T_i}{\min }{\left|\right|R_{\mathrm{si}}^{\′}-T_i{\hat{R}}_s\left|\right|}_F^2---\left(10\right)$

T _isolution be e ₁=[1 0 ... 0], e ₂=[0 1 ... 0] ..., e _k=[0 0 ... 1] one in, and the solution that T often goes is different, therefore only needs to calculate (K-1) (K+2)/2 time formula (10) and can draw T;

Step 5: the space geometry relation reaching angle according to two groups of one-dimensional waves draws position angle and the angle of pitch of target; The azimuth angle theta of target _kand the angle of pitch

Draw θ _kafterwards according to cos α _k, cos β _kpositive and negatively determine θ _kin the position of four quadrants, adjustment θ _ksize.

Accompanying drawing explanation

Fig. 1 is L battle array spacing wave model;

Fig. 2 aSNR=5dB, target pitch-orientation planisphere during pairing not yet in effect;

Fig. 2 bSNR=5dB, adopts the present invention to match rear target pitch-orientation planisphere;

Fig. 3 be the present invention be paired in independent source situation power make an uproar with the letter than situation of change;

Fig. 4 be the present invention be paired in coherent source situation power make an uproar with the letter than situation of change;

Fig. 5 is that the present invention is paired into the situation of change of power with fast umber of beats when SNR=-5dB;

Fig. 6 is gained target pitch angle-position angle planisphere after the present invention matches under multi-target condition.

Embodiment

Below in conjunction with accompanying drawing and example, the present invention will be described in more detail.

The signal model of L battle array

L battle array is made up of two mutually perpendicular linear arrays, as shown in Figure 1.If two linear array X, Y intersect at initial point, array number is respectively M+1, N+1, and total array number is M+N+1.The far field narrow band signal being provided with K concentricity frequency is received by this L battle array, and λ is carrier frequency wavelength, θ _kwith represent position angle and the angle of pitch of a kth incoming wave signal respectively suppose that information source can be divided in two linear arrays, now the two-dimentional DOA estimate problem of L battle array can be decomposed into two one dimension DOA estimate.

Note a _x, a _yfor the steering vector of linear array X, Y, x _mfor m array element in X-axis to initial point distance (m=1,2 ... M), y _nfor the n-th array element in Y-axis to initial point distance (n=1,2 ..., N), then the steering vector of information source k can be expressed as

$\left\{\begin{array}{c}{a}_x\left({\mathrm{\α}}_k\right)={[1,e^{-j\frac{2\mathrm{\π}{x}_1}{\mathrm{\λ}}\cos {\mathrm{\α}}_k},e^{-j\frac{2\mathrm{\π}{x}_2}{\mathrm{\λ}}\cos {\mathrm{\α}}_k},\·\·\·,e^{-j\frac{2\mathrm{\π}{x}_M}{\mathrm{\λ}}\cos {\mathrm{\α}}_k}]}^{T}k=\mathrm{1,2},\·\·\·,K\\ a_y\left({\mathrm{\β}}_k\right)={[1,e^{-j\frac{2\mathrm{\π}{y}_1}{\mathrm{\λ}}\cos {\mathrm{\β}}_k},e^{-j\frac{2\mathrm{\π}{y}_2}{\mathrm{\λ}}\cos {\mathrm{\β}}_k},\·\·\·,e^{-j\frac{2\mathrm{\π}{y}_N}{\mathrm{\λ}}\cos {\mathrm{\β}}_k}]}^{T}k=\mathrm{1,2},\·\·\·,K\end{array}\right.---\left(1\right)$

Wherein, note A _x, A _ybe respectively the array manifold of linear array X and linear array Y, A _x(α)=[a _x(α ₁), a _x(α ₂) ..., a _x(α _k)], A _y(β)=[a _y(β ₁), a _y(β ₂) ..., a _y(β _k)].S _kfor the complex envelope of a kth information source, then echoed signal can be expressed as s (t)=[s ₁(t), s ₂(t) ..., s _k(t)] ^t.

Note n _x, n _yfor white Gaussian noise, then the reception data of X array and Y array are respectively

$\left\{\begin{array}{c}X\left(t\right)=A_x\left(\mathrm{\α}\right)s+n_x=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{a}_x\left({\mathrm{\α}}_k\right)s_k\left(t\right)+n_x\left(t\right)\\ Y\left(t\right)=A_y\left(\mathrm{\β}\right)s+n_y=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{a}_y\left({\mathrm{\β}}_k\right)s_k\left(t\right)+n_y\left(t\right)\end{array}\right.---\left(2\right)$

Pairing process

Namely estimate the angle α of target and linear array X, Y respectively, β, due to α _k, β _kbe respectively by linear array X, Y independent estimations, therefore its order is difficult to guarantee is one to one, and the object of pairing obtains this corresponding relation exactly, is then obtained the azimuth angle theta of target by following formula _kand the angle of pitch

Draw θ _kafterwards according to cos α _k, cos β _kpositive and negatively determine θ _kin the position of four quadrants, adjustment θ _ksize.

The present invention proposes PMLS algorithm, and PMLS is the abbreviation of Pair-matching method based on Maximum Likelihoodusing Source covariance matrix, realizes the pairing that two groups of one-dimensional waves reach angle.

Under white Gaussian noise background, first information source covariance matrix estimated by the present invention maximal possibility estimation can be expressed as

${\hat{R}}_s=E\left\{{\hat{s}\hat{s}}^H\right\}=E\{{\hat{A}}_y^{+}\·{\mathrm{YY}}^H\·{\left({\hat{A}}_y^H\right)}^{+}\}={\hat{A}}_y^{+}{R}_{\mathrm{yy}}{\left({\hat{A}}_y^H\right)}^{+}---\left(4\right)$

Wherein for estimated by the linear array Y the array manifold of structure, in the order of each angle any, for moore-Penrose inverse, R _yyfor linear array Y receives the covariance matrix of data

$R_{\mathrm{yy}}=E\left\{{\mathrm{YY}}^H\right\}=A_y\·E\left\{{\mathrm{ss}}^H\right\}\·A_y^H+{\mathrm{\σ}}^{2}I=A_y{R}_s{A}_y^H+{\mathrm{\σ}}^{2}I---\left(5\right)$

To linear array X, note with the array manifold of corresponding linear array X is if for rear N capable, the present invention's second information source covariance matrix is

$\begin{array}{c}{R}_s^{\′}={\hat{A}}_x^{+}\·E\left\{{\mathrm{XY}}^H\right\}\·{\left({\hat{A}}_y^{\′H}\right)}^{+}\\ ={\hat{A}}_x^{+}{R}_{\mathrm{xy}}{\left({\hat{A}}_y^{\′H}\right)}^{+}\end{array}---\left(6\right)$

Wherein a ' _y, Y ' is respectively A _y, Y rear N capable.

Define a K × K and tie up permutation matrix T, if T _ijfor the i-th row j column element of matrix T, then

$\left\{\begin{array}{cc}\∀T_{\mathrm{ij}}\∈\left\{\mathrm{0,1}\right\}& \\ \underset{i=1}{\overset{K}{\mathrm{\Σ}}}{T}_{\mathrm{ij}}=1& j=\mathrm{1,2},\·\·\·,K\\ \underset{j=1}{\overset{K}{\mathrm{\Σ}}}{T}_{\mathrm{ij}}=1& i=\mathrm{1,2},\·\·\·,K\end{array}\right.---\left(7\right)$

If keep order constant, the angle of corresponding incoming wave and array X is [α ₁, α ₂..., α _k] T, then the array manifold that two linear arrays are corresponding is ${\hat{A}}_y,{\hat{A}}_{x}T.$ If ${\hat{A}}_{x}T\≈A_x,$ Then ${\hat{A}}_x^{+}\≈T{A}_x^{+},$ Formula (6) can turn to

$R_s^{\′}={\hat{A}}_x^{+}{R}_{\mathrm{xy}}{\left({\hat{A}}_y^{\′H}\right)}^{+}\≈{\mathrm{TA}}_x^{+}\left(A_x{R}_s{A}_y^{\′H}\right){\left({\hat{A}}_y^{\′H}\right)}^{+}\≈{\mathrm{TR}}_s\≈{T\hat{R}}_s---\left(8\right)$

When information source independence, can directly by draw T, then T is revised the form shown in an accepted way of doing sth (7), can draw corresponding relation.But matrix inversion operation amount is comparatively large when information source is more, and if there is coherent source, now be irreversible, said method will be no longer applicable.

The present invention, in conjunction with the special construction of T, proposes a kind of simple and effective method for solving, note

$J_{\mathrm{PMLS}}=\underset{T}{\min }{\left|\right|R_s^{\′}-{T\hat{R}}_s\left|\right|}_F^2=\underset{T}{\min }{\left|\right|\left({\hat{A}}_x^{+}{R}_{\mathrm{xy}}{\left({\hat{A}}_y^{\′H}\right)}^{+}\right)-T\·\left({\hat{A}}_y^{+}{R}_{\mathrm{yy}}{\left({\hat{A}}_y^H\right)}^{+}\right)\left|\right|}_F^2---\left(9\right)$

An above formula demand once moore-Penrose inverse, because of can exist at most K! Kind possible pairing situation, therefore need to carry out K! Secondary computing.When information source number K is larger, the operand of formula (9) increases greatly, the further dimensionality reduction optimization (MPMLS) of the present invention, if i-th row of note T is designated as T _i, R ' _sthe i-th row be designated as R ' _si, then

$J_{\mathrm{MPMLS}}=\underset{T_i}{\min }{\left|\right|R_{\mathrm{si}}^{\′}{-T}_i{\hat{R}}_s\left|\right|}_F^2---\left(10\right)$

T _isolution be e ₁=[1 0 ... 0], e ₂=[0 1 ... 0] ..., e _k=[0 0 ... 1] one in, and the solution that T often goes is different, therefore only needs to calculate (K-1) (K+2)/2 time formula (10) and can draw T.

Algorithm performance simulation analysis

In order to verify performance of the present invention, carry out following emulation.

The present invention devises five emulation experiments, emulation 1 checking the present invention can realize the object of pairing deblurring under two target conditions, emulation 2, emulation 3 verify that independent source and lower of coherent source situation carry algorithm performance with signal to noise ratio (S/N ratio) situation of change respectively, emulate 4 verification algorithm performances in fixing low signal-to-noise ratio situation with fast umber of beats situation of change, emulate 5 verification algorithms under multi-target condition, match performance.

Simulated conditions: linear array array number M=N=10, array element distance d _x=d _y=λ/2, white Gaussian noise background, the one dimension DOA estimate of incoming wave and two linear arrays adopts LS-ESPRIT algorithm, CCM method refers to the method applying cross-correlation matrix pairing, the matching method of " signal covariance matrix " that Hermite method refers to estimate whether be Hermite matrix be decision criteria, and simulation times is 500, emulation 1 ~ emulation 3 is incident direction and is (30 °, 40 °), the two equal strength information sources of (50 °, 45 °).

Emulation 1: two incoming signal is independent source, fast umber of beats is 200, signal to noise ratio (S/N ratio) is 5dB, Monte Carlo simulation times is 500, the planisphere of pairing front and back parallactic angle and the angle of pitch as shown in Figure 2, by generation two false fuzzy objects when can find out pairing not yet in effect from Fig. 2 a, the object reaching deblurring after employing PMLS method of the present invention is matched can be found out from Fig. 2 b.

Emulation 2: two incoming signals are independent source, fast umber of beats is 200, signal to noise ratio (S/N ratio) increases to 10dB from-10dB, each method be paired into power as shown in Figure 3, therefrom can find out the present invention carry algorithm and innovatory algorithm compares CCM method and Hermite method has higher robustness when low signal-to-noise ratio, the MPMLS method that operand is less can slightly be inferior to PMLS method when low noise.

Emulation 3: when two incoming signals are coherent source, fast umber of beats is still 200, each method be paired into power as shown in Figure 4, when therefrom can find out simulation result and independent source almost, Algorithm robustness that the present invention carries is still higher when low signal-to-noise ratio.

Emulation 4: when signal to noise ratio (S/N ratio) is fixed as-5dB, fast umber of beats increases to 200 from 10, each method be paired into power as shown in Figure 5, therefrom can find out the present invention carry pairing algorithm owing to have employed maximum-likelihood criterion, in fewer snapshots situation, still there is higher robustness.

Emulation 5: array structure is constant, when signal to noise ratio (S/N ratio) is 10dB, fast umber of beats is that the incident angle of 500,4 targets is respectively (30 °, 48 °), (50 °, 49 °), (70 °, 44 °), (85 °, 30 °), latter two target bit coherent source, after adopting the present invention to propose the pairing of PMLS algorithm, pitching-orientation diagram as shown in Figure 6, there is not blooming, describe the practicality of put forward algorithm to multi-target condition after therefrom can finding out pairing.

Claims (1)

1. a signal processing method for L battle array position angle and angle of pitch pairing, is characterized in that:

The basic step of this signal processing method is:

According to existing one dimensional linear array direction of arrival estimation method, step one: pre-service, show that two groups of one-dimensional waves of target and two linear arrays reach angle; If two linear array X, Y intersect at initial point, array number is respectively M+1, N+1, and total array number is M+N+1; The far field narrow band signal being provided with K concentricity frequency is received by this L battle array, and λ is carrier frequency wavelength, θ _kwith represent position angle and the angle of pitch of a kth incoming wave signal respectively if information source can be divided in two linear arrays, now the two-dimentional DOA estimate problem of L battle array is broken down into two one dimension DOA estimate;

Note a _x, a _yfor the steering vector of linear array X, Y, x _mfor m array element in X-axis to initial point distance (m=1,2 ... M), y _nfor the n-th array element in Y-axis to initial point distance (n=1,2 ..., N), then the steering vector of information source k can be expressed as:

$\left\{\begin{array}{c}{a}_x\left({\mathrm{\α}}_k\right)={[1,e^{-j\frac{2\mathrm{\π}{x}_1}{\mathrm{\λ}}\cos {\mathrm{\α}}_k},e^{-j\frac{2\mathrm{\π}{x}_2}{\mathrm{\λ}}\cos {\mathrm{\α}}_k},\·\·\·,e^{-j\frac{2\mathrm{\π}{x}_M}{\mathrm{\λ}}\cos {\mathrm{\α}}_k}]}^{T}k=\mathrm{1,2},\·\·\·,K\\ a_y\left({\mathrm{\β}}_k\right)={[1,e^{-j\frac{2\mathrm{\π}{y}_1}{\mathrm{\λ}}\cos {\mathrm{\β}}_k},e^{-j\frac{2\mathrm{\π}{y}_2}{\mathrm{\λ}}\cos {\mathrm{\β}}_k},\·\·\·,e^{-j\frac{2\mathrm{\π}{y}_N}{\mathrm{\λ}}\cos {\mathrm{\β}}_k}]}^{T}k=\mathrm{1,2},\·\·\·,K\end{array}\right.---\left(1\right)$

Wherein, note A _x, A _ybe respectively the array manifold of linear array X and linear array Y, A _x(α)=[a _x(α ₁), a _x(α ₂) ..., a _x(α _k)], A _y(β)=[a _y(β ₁), a _y(β ₂) ..., a _y(β _k)]; s _kfor the complex envelope of a kth information source, then echoed signal can be expressed as s (t)=[s ₁(t), s ₂(t) ..., s _k(t)] ^t;

Note n _x, n _yfor white Gaussian noise, then the reception data of linear array X and linear array Y are respectively:

$\left\{\begin{array}{c}X\left(t\right)=A_x\left(\mathrm{\α}\right)s+n_x=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{a}_x\left({\mathrm{\α}}_k\right)s_k\left(t\right)+n_x\left(t\right)\\ Y\left(t\right)=A_y\left(\mathrm{\β}\right)s+n_y=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{a}_y\left({\mathrm{\β}}_k\right)s_k\left(t\right)+n_y\left(t\right)\end{array}\right.---\left(2\right)$

One dimension direction of arrival estimation method is adopted to estimate the angle of target and two linear array X, Y respectively with

Step 2: reach angle by the reception data of one of them linear array with the one-dimensional wave estimated by this linear array and obtain an information source covariance matrix; Under white Gaussian noise background, first information source covariance matrix maximal possibility estimation be expressed as:

${\hat{R}}_s=E\left\{{\hat{s}\hat{s}}^H\right\}=E\{{\hat{A}}_y^{+}\·{\mathrm{YY}}^H\·{\left({\hat{A}}_y^H\right)}^{+}\}={\hat{A}}_y^{+}{R}_{\mathrm{yy}}{\left({\hat{A}}_y^H\right)}^{+}---\left(4\right)$

Wherein for estimated by the linear array Y the array manifold of structure, in the order of each angle any, for moore-Penrose inverse, R _yyfor linear array Y receives the covariance matrix of data:

$R_{\mathrm{yy}=}E\left\{{\mathrm{YY}}^H\right\}=A_y\·E\left\{{\mathrm{ss}}^H\right\}\·A_y^H+{\mathrm{\σ}}^{2}I=A_y{R}_s{A}_y^H+{\mathrm{\σ}}^{2}I---\left(5\right)$

Step 3: reach angle with the reception data of two linear arrays and estimated two groups of one-dimensional waves simultaneously and obtain second information source covariance matrix; To linear array X, note with the array manifold of corresponding linear array X is if for rear N capable, second information source covariance matrix is:

$\begin{array}{c}{R}_s^{\′}={\hat{A}}_x^{+}\·E\left\{{\mathrm{XY}}^H\right\}\·{\left({\hat{A}}_y^{\′H}\right)}^{+}\\ ={\hat{A}}_x^{+}{R}_{\mathrm{xy}}{\left({\hat{A}}_y^{\′H}\right)}^{+}\end{array}---\left(6\right)$

Wherein a ' _y, Y ' is respectively A _y, Y rear N capable;

By optimization method, step 4: utilize a permutation matrix two information source covariance matrix equivalences to be coupled together, show that two groups of one-dimensional waves reach angle one to one; Define a K × K and tie up permutation matrix T, if T _ijfor the i-th row j column element of matrix T, then

$\left\{\begin{array}{cc}\∀T_{\mathrm{ij}}\∈\left\{\mathrm{0,1}\right\}& \\ \underset{i=1}{\overset{K}{\mathrm{\Σ}}}{T}_{\mathrm{ij}}=1& j=\mathrm{1,2},\·\·\·,K\\ \underset{j=1}{\overset{K}{\mathrm{\Σ}}}{T}_{\mathrm{ij}}=1& i=\mathrm{1,2},\·\·\·,K\end{array}\right.---\left(7\right)$

If keep order constant, corresponding incoming wave and the angle of linear array X are [α ₁, α ₂..., α _k] T, then the array manifold that two linear arrays are corresponding is ${\hat{A}}_y,{\hat{A}}_{x}T;$ If ${\hat{A}}_{x}T\≈A_x,$ Then ${\hat{A}}_x^{+}\≈T{A}_x^{+},$ Formula (6) can turn to

$R_s^{\′}={\hat{A}}_x^{+}{R}_{\mathrm{xy}}{\left({\hat{A}}_y^{\′H}\right)}^{+}\≈{\mathrm{TA}}_x^{+}\left(A_x{R}_s{A}_y^{\′H}\right){\left({\hat{A}}_y^{\′H}\right)}^{+}\≈{\mathrm{TA}}_s\≈{T\hat{R}}_s---\left(8\right)$

When information source independence, can directly by draw T, then T is revised the form shown in an accepted way of doing sth (7), can draw corresponding relation; Note

$J_{\mathrm{PMLS}}=\underset{T}{\min }{\left|\right|R_s^{\′}-{T\hat{R}}_s\left|\right|}_F^2=\underset{T}{\min }{\left|\right|\left({\hat{A}}_x^{+}{R}_{\mathrm{xy}}{\left({\hat{A}}_y^{\′H}\right)}^{+}\right)-T\·\left({\hat{A}}_y^{+}{R}_{\mathrm{yy}}{\left({\hat{A}}_y^H\right)}^{+}\right)\left|\right|}_F^2---\left(9\right)$

An above formula demand once moore-Penrose inverse, because of can exist at most K! Kind possible pairing situation, therefore need to carry out K! Secondary computing; When information source number K is larger, the operand of formula (9) increases, further dimensionality reduction optimization, if i-th row of note T is designated as T _i, R ' _sthe i-th row be designated as R ' _si, then

$J_{\mathrm{MPMLS}}=\underset{T_i}{\min }{\left|\right|R_{\mathrm{si}}^{\′}-T_i{\hat{R}}_s\left|\right|}_F^2---\left(10\right)$

T _isolution be e ₁=[1 0 ... 0], e ₂=[0 1 ... 0] ..., e _k=[0 0 ... 1] one in, and the solution that T often goes is different, therefore only needs to calculate (K-1) (K+2)/2 time formula (10) and can draw T;

Step 5: the space geometry relation reaching angle according to two groups of one-dimensional waves draws position angle and the angle of pitch of target; The azimuth angle theta of target _kand the angle of pitch

Draw θ _kafterwards according to cos α _k, cos β _kpositive and negatively determine θ _kin the position of four quadrants, adjustment θ _ksize.