CN105974370A - MUSIC spatial spectrum estimation method based on smooth mutual coupling correction of virtual array element space - Google Patents

Abstract

The invention relates to a MUSIC spatial spectrum estimation method based on smooth mutual coupling correction of a virtual array element space. The method aims to overcome the defects that the existing uniform linear array mutual coupling correction algorithm based on virtual array elements has poor estimation capability on low signal-to-noise ratio signals and cannot estimate coherent source signals. The MUSIC spatial spectrum estimation method based on smooth mutual coupling correction of a virtual array element space specifically comprises the following steps: 1, truncating an original array using a virtual array element method to obtain truncated radar array received signals; 2, performing spatial smoothing preprocessing on the truncated radar array received signals to obtain a smooth covariance matrix; and 3, performing MUSIC spatial spectrum estimation on the smooth covariance matrix. The method is applied in the field of radar signal processing.

Description

A kind of MUSIC Estimation of Spatial Spectrum based on Virtual array space smoothing mutual coupling calibration Method

Technical field

The present invention relates to the MUSIC Estimation of Spatial Spectrum method of Virtual array space smoothing mutual coupling calibration.

Background technology

In the ideal case, MUSIC spatial spectral estimation algorithm to the estimation of sense close to carat Metro lower bound.But Under non-ideal condition, during as there is the situation of array mutual coupling, MUSIC Estimation of Spatial Spectrum performance will decline, and the most also can go out The inestimable situation in existing direction.

At present, conventional even linear array mutual coupling calibration algorithm is even linear array mutual coupling calibration algorithm based on Virtual array. This algorithm is without estimating the mutual coupling coefficient, and has the advantages such as calculating is simple, be easily achieved.Then, this algorithm exist right Low SNR signal estimated capacity is poor, and the shortcoming cannot estimated coherent source signal.

Summary of the invention

The invention aims to solve existing even linear array mutual coupling calibration algorithm based on Virtual array to low noise Ratio Signal estimation ability, and shortcoming coherent source signal cannot estimated, and propose a kind of based on virtual array The even linear array mutual coupling calibration method of unit's Space planar angle.

A kind of MUSIC Estimation of Spatial Spectrum method based on Virtual array space smoothing mutual coupling calibration concretely comprises the following steps:

Step one, utilizing Virtual array method to block original array, the radar array after being blocked receives signal

Step 2, to after blocking radar array receive signalCarry out space smoothing process, obtain smoothed covariance Matrix；

Step 3, smoothed covariance matrix is done MUSIC Estimation of Spatial Spectrum.

The invention have the benefit that

The present invention can improve the target direction estimated capacity under low signal-to-noise ratio, mutual compared with even linear array based on Virtual array It is high that coupling correcting algorithm is estimated power, fast convergence rate.Secondly, coherent source signal can be estimated by the present invention, with as The Space planar angle with decorrelation LMS ability compares, and the estimation of the present invention has higher success rate；Such as Fig. 9 a, 9b, 9c, 9d, 9e, 9f Give signal source and be coherent source and six kinds of method space spectrograms time signal to noise ratio is 10dB.Owing to space smoothing processes permissible The problem efficiently solving signal source decorrelation LMS, so coherent source signal is to have employed two kinds of methods (d) that space smoothing processes (f) impact is not the most produced.Review (a), (b), (c) and (e) not using space smoothing to process and all occur in that different journey The false-alarm phenomenon of degree, even and if in the case of signal to noise ratio is the highest, space spectrum is the lowest.This also show institute herein Virtual-the Space planar angle proposed has the strongest robustness to Estimation of Spatial Spectrum；

Present invention robustness under different signal to noise ratios is more preferable.Meanwhile, the present invention has been also equipped with single signal side taken soon To estimated capacity.The method of invention, it is possible to improve the sense under low signal-to-noise ratio and estimate, and coherent source can be believed Number travel direction is estimated, is also equipped with single sense estimated capacity taken soon simultaneously.

As Figure 10 and Figure 11 sets forth direction estimation success rate and the RMSE analysis that six kinds of methods change with signal to noise ratio Figure.Arranging test 3 senses of stochastic generation every time in emulation, between 3 directions, interval is all higher than 10 degree of (resolving power foots Enough), and give identical signal to noise ratio (X-axis).Each signal to noise ratio is 100 tests, statistics success rate and RMSE.Signal source is Incoherent source, fast umber of beats is 50.Wherein, spatial spectrum search precision is 0.25 degree, and spacing spectrum peak detection threshold is set to 5dB；When failing to identify, RMSE gives the punishment of 5 degree.Result shows, listed method discrimination is all with signal to noise ratio Increasing and increase, RMSE has reduced with the increase of signal to noise ratio.But, direct MUSIC method and Space planar angle be not to Equidirectional random combine, success rate presents fluctuation status.This mutual coupling effect shadow to different directions of being the most indirectly recruited Sound is to have optionally, illustrates to study the necessity of mutual coupling calibration algorithm the most simultaneously.It addition, it is permissible from RMSE analysis chart Finding, MUSIC algorithm ideally can approach CRB curve, Virtual array method and virtual-Space planar angle well Along with the increase of signal to noise ratio also is able to converge to CRB curve, and the MUSIC that performance is also possible to be better than known the mutual coupling coefficient calculates Method.

Figure 14 and Figure 15 give several method under coherent source with fast umber of beats change direction be estimated power curve and RMSE curve.Owing to have employed coherent source, MUSIC algorithm complete failure, and instead MUSIC algorithm has in the case of having mutual coupling There is certain estimated capacity.This explanation, mutual symplectic information source has certain decorrelation LMS ability, and concrete conclusion also needs to mutually Coupling model launches more research and just can obtain.

Show that the method that the present invention proposes has the strongest robustness；Either under low signal-to-noise ratio, or in coherent source Under RST, even also target signal direction can there be is certain estimated capacity single taking soon.

Accompanying drawing explanation

Fig. 1 is space smoothing schematic diagram；

Fig. 2 is Virtual array schematic diagram；

When Fig. 3 a is signal source signal to noise ratio for (0,0,0) dB, the spatial spectrum of ideal conditions MUSIC algorithm compares schematic diagram；

When Fig. 3 b is signal source signal to noise ratio for (0,0,0) dB, the spatial spectrum of mutual coupling direct MUSIC algorithm is had to compare signal Figure；

When Fig. 3 c is signal source signal to noise ratio for (0,0,0) dB, it is known that the spatial spectrum of mutual coupling MUSIC algorithm compares schematic diagram；

When Fig. 3 d is signal source signal to noise ratio for (0,0,0) dB, the spatial spectrum of space smoothing MUSIC algorithm compares schematic diagram；

When Fig. 3 e is signal source signal to noise ratio for (0,0,0) dB, the spatial spectrum of Virtual array MUSIC algorithm compares schematic diagram；

When Fig. 3 f is signal source signal to noise ratio for (0,0,0) dB, the spatial spectrum of virtual-space smoothing MUSIC algorithm compares and shows It is intended to；

When Fig. 4 a is signal source signal to noise ratio for (3,3,3) dB, the spatial spectrum of ideal conditions MUSIC algorithm compares schematic diagram；

When Fig. 4 b is signal source signal to noise ratio for (3,3,3) dB, the spatial spectrum of mutual coupling direct MUSIC algorithm is had to compare signal Figure；

When Fig. 4 c is signal source signal to noise ratio for (3,3,3) dB, it is known that the spatial spectrum of mutual coupling MUSIC algorithm compares schematic diagram；

When Fig. 4 d is signal source signal to noise ratio for (3,3,3) dB, the spatial spectrum of space smoothing MUSIC algorithm compares schematic diagram；

When Fig. 4 e is signal source signal to noise ratio for (3,3,3) dB, the spatial spectrum of Virtual array MUSIC algorithm compares schematic diagram；

When Fig. 4 f is signal source signal to noise ratio for (3,3,3) dB, the spatial spectrum of virtual-space smoothing MUSIC algorithm compares and shows It is intended to；

When Fig. 5 a is signal source signal to noise ratio for (6,6,6) dB, the spatial spectrum of ideal conditions MUSIC algorithm compares schematic diagram；

When Fig. 5 b is signal source signal to noise ratio for (6,6,6) dB, the spatial spectrum of mutual coupling direct MUSIC algorithm is had to compare signal Figure；

When Fig. 5 c is signal source signal to noise ratio for (6,6,6) dB, it is known that the spatial spectrum of mutual coupling MUSIC algorithm compares schematic diagram；

When Fig. 5 d is signal source signal to noise ratio for (6,6,6) dB, the spatial spectrum of space smoothing MUSIC algorithm compares schematic diagram；

When Fig. 5 e is signal source signal to noise ratio for (6,6,6) dB, the spatial spectrum of Virtual array MUSIC algorithm compares schematic diagram；

When Fig. 5 f is signal source signal to noise ratio for (6,6,6) dB, the spatial spectrum of virtual-space smoothing MUSIC algorithm compares and shows It is intended to；

When Fig. 6 a is signal source signal to noise ratio for (10,10,10) dB, the spatial spectrum of ideal conditions MUSIC algorithm compares signal Figure；

When Fig. 6 b is signal source signal to noise ratio for (10,10,10) dB, there is the spatial spectrum of mutual coupling direct MUSIC algorithm to compare and show It is intended to；

When Fig. 6 c is signal source signal to noise ratio for (10,10,10) dB, it is known that the spatial spectrum of mutual coupling MUSIC algorithm compares signal Figure；

When Fig. 6 d is signal source signal to noise ratio for (10,10,10) dB, the spatial spectrum of space smoothing MUSIC algorithm compares signal Figure；

When Fig. 6 e is signal source signal to noise ratio for (10,10,10) dB, the spatial spectrum of Virtual array MUSIC algorithm compares signal Figure；

When Fig. 6 f is signal source signal to noise ratio for (10,10,10) dB, the spatial spectrum of virtual-space smoothing MUSIC algorithm compares Schematic diagram；

When Fig. 7 a is signal source signal to noise ratio for (20,5,5) dB, the spatial spectrum of ideal conditions MUSIC algorithm compares schematic diagram；

When Fig. 7 b is signal source signal to noise ratio for (20,5,5) dB, the spatial spectrum of mutual coupling direct MUSIC algorithm is had to compare signal Figure；

When Fig. 7 c is signal source signal to noise ratio for (20,5,5) dB, it is known that the spatial spectrum of mutual coupling MUSIC algorithm compares schematic diagram；

When Fig. 7 d is signal source signal to noise ratio for (20,5,5) dB, the spatial spectrum of space smoothing MUSIC algorithm compares schematic diagram；

When Fig. 7 e is signal source signal to noise ratio for (20,5,5) dB, the spatial spectrum of Virtual array MUSIC algorithm compares schematic diagram；

When Fig. 7 f is signal source signal to noise ratio for (20,5,5) dB, the spatial spectrum of virtual-space smoothing MUSIC algorithm compares and shows It is intended to；

When Fig. 8 a is signal source signal to noise ratio for (30,10,10) dB, the spatial spectrum of ideal conditions MUSIC algorithm compares signal Figure；

When Fig. 8 b is signal source signal to noise ratio for (30,10,10) dB, there is the spatial spectrum of mutual coupling direct MUSIC algorithm to compare and show It is intended to；

When Fig. 8 c is signal source signal to noise ratio for (30,10,10) dB, it is known that the spatial spectrum of mutual coupling MUSIC algorithm compares signal Figure；

When Fig. 8 d is signal source signal to noise ratio for (30,10,10) dB, the spatial spectrum of space smoothing MUSIC algorithm compares signal Figure；

When Fig. 8 e is signal source signal to noise ratio for (30,10,10) dB, the spatial spectrum of Virtual array MUSIC algorithm compares signal Figure；

When Fig. 8 f is signal source signal to noise ratio for (30,10,10) dB, the spatial spectrum of virtual-space smoothing MUSIC algorithm compares Schematic diagram；

Fig. 9 a be signal source be coherent source, when signal to noise ratio is (10,10,10) dB, the spatial spectrum of ideal conditions MUSIC algorithm Relatively schematic diagram；

Fig. 9 b be signal source be coherent source, when signal to noise ratio is (10,10,10) dB, have the space of mutual coupling direct MUSIC algorithm Spectrum compares schematic diagram；

Fig. 9 c be signal source be coherent source, when signal to noise ratio is (10,10,10) dB, it is known that the spatial spectrum of mutual coupling MUSIC algorithm Relatively schematic diagram；

Fig. 9 d be signal source be coherent source, when signal to noise ratio is (10,10,10) dB, the spatial spectrum of space smoothing MUSIC algorithm Relatively schematic diagram；

Fig. 9 e be signal source be coherent source, when signal to noise ratio is (10,10,10) dB, the spatial spectrum of Virtual array MUSIC algorithm Relatively schematic diagram；

Fig. 9 f be signal source be coherent source, when signal to noise ratio is (10,10,10) dB, virtual-space smoothing MUSIC algorithm Spatial spectrum compares schematic diagram；

Figure 10 is the direction estimation success rate curve synoptic diagram that several method changes with signal to noise ratio；

Figure 11 is the RMSE curve synoptic diagram that several method changes with signal to noise ratio；

Figure 12 is the several method direction estimation success rate curve synoptic diagram with some direction signal to noise ratio change；

Figure 13 is the several method RMSE curve synoptic diagram with some direction signal to noise ratio change；

Figure 14 is direction estimation success rate curve (coherent source) schematic diagram that several method changes with snap number；

Figure 15 is RMSE curve (coherent source) schematic diagram that several method changes with snap number；

Figure 16 is flow chart of the present invention.

Detailed description of the invention

Detailed description of the invention one: combine Figure 16 and present embodiment is described, the one of present embodiment is empty based on Virtual array Between the MUSIC Estimation of Spatial Spectrum method detailed process of smooth mutual coupling calibration be:

Even linear array Coupling Model is introduced

When there is mutual coupling in reception signal, radar array receives signal and will become

x_r(l)=CAs (l)+n (l), l=1,2 ..., L

WhereinFor flow pattern matrix, s (l)=[s₁(l),…,s_K(l)]^TBelieve for radar target Number source vector,For guiding vector,For the direction of kth radar target signal source, k value is k=1,2 ..., K, K For radar target number, K value is positive integer, s_kL () is kth radar target signal source, l is snap index, and n is that average is Zero, variance isRadar noise vector, L is snap number, and value is positive integer, and T is transposed matrix, and C represents mutual coupling matrix, It is a Teoplitz type matrix:

Wherein c₀=1, in formula, c_iFor the mutual coupling coefficient, i value is i=0,1 ..., p-1, p are mutual coupling degree of freedom, and p value is Positive integer, N is element number of array, and value is positive integer；For writing conveniently, Matrix C A is merged into a matrix

$\stackrel{\‾}{A}=\[{\mathrm{C\α}}_r\left({\mathrm{\φ}}_a^1\right),...,{\mathrm{C\α}}_r\left({\mathrm{\φ}}_a^K\right)\]=\[{\stackrel{\‾}{\mathrm{\α}}}_r\left({\mathrm{\φ}}_a^1\right),...,{\stackrel{\‾}{\mathrm{\α}}}_r\left({\mathrm{\φ}}_a^K\right)\]$

In formula, in formula,For mutual coupling guiding vector；

Now, receive signal covariance matrix can be written as

$R_r=\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{x}_r\left(l\right)x_r^H\left(l\right)\≈\stackrel{\‾}{A}{R}_s{\stackrel{\‾}{A}}^H+{\mathrm{\σ}}_n^2{I}_N$

L is snap index,For variance, L is snap number, and value is positive integer；

To R_rCarry out feature decomposition,

$R_r=\underset{i=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{e}_i{e}_i^H+\underset{i=K+1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\σ}}_n^2{e}_i{e}_i^H=E_s{\mathrm{\Λ}}_s{E}_s^H+{\mathrm{\σ}}_n^2{E}_n{E}_n^H$

In formula, λ_iFor ith feature value, wherein,Λ_s=diag [λ₁,λ₂,…,λ_K]；e_iFor with λ_iCharacteristic of correspondence vector；E_sFor signal subspace, E_s=[e₁,e₂,…,e_K]；E_n=[e_K+1, e_K+2,…,e_N] it is noise subspace；

Then MUSIC spatial spectrum can be written as

$P_{MUSIC}=\frac{1}{{\left|E_n^{H}C\mathrm{\α}\left({\mathrm{\φ}}_a\right)\right|}^2}$

But owing to the method needs previously known mutual coupling Matrix C, improve so needing to use other method instead.As used void Matroid unit method.

Virtual array refer to one can with normal received signal, but the data of this reception passage are not involved in subsequent treatment The array element of necessary being.It is arranged to virtual as in figure 2 it is shown, Virtual array method is the p-1 array element that will be located in linear array edges at two ends The method (solid expression) of array element.

Such result is mutual coupling guiding vector C α (φ_a) can be by the guiding vector of Virtual arraySubstituted, and AndIt is only guiding vector α (φ_a) low-dimensional represent, unrelated with the mutual coupling coefficient.The most just prove this process.

Mathematically can block matrix premultiplication in x with one simply_rL () completes, i.e.

${\tilde{x}}_r{\left(l\right)}_{N_e-2p+2}={\mathrm{Jx}}_r\left(l\right)=JCAs\left(l\right)+Jn\left(l\right)---(5-23)$

Wherein

$J={\[0,...,0,I_{N_e-2p+2},0,...,0\]}_{(N_e-2p+2)\×N_e}---(5-24)$

NoteThen (5-23) formula will become

${\tilde{x}}_r\left(l\right)=\tilde{C}As\left(l\right)+\tilde{n}\left(l\right)---(5-25)$

In formula,

And

Then have

$\begin{array}{c}\tilde{C}\mathrm{\α}\left({\mathrm{\φ}}_a\right)=\left[\begin{array}{c}{c}_{p-1}1+...+c_1{\mathrm{\β}}^{p-2}\left({\mathrm{\φ}}_a\right)+{\mathrm{\β}}^{p-1}\left({\mathrm{\φ}}_a\right)+c_1{\mathrm{\β}}^p\left({\mathrm{\φ}}_a\right)+...+c_{p-1}{\mathrm{\β}}^{2p-2}\left({\mathrm{\φ}}_a\right)\\ c_{p-1}\mathrm{\β}\left({\mathrm{\φ}}_a\right)+...+c_1{\mathrm{\β}}^{p-1}\left({\mathrm{\φ}}_a\right)+{\mathrm{\β}}^p\left({\mathrm{\φ}}_a\right)+c_1{\mathrm{\β}}^{p+1}\left({\mathrm{\φ}}_a\right)+...+c_{p-1}{\mathrm{\β}}^{2p-1}\left({\mathrm{\φ}}_a\right)\\ .\\ .\\ .\\ c_{p-1}{\mathrm{\β}}^{N_e-2p}\left({\mathrm{\φ}}_a\right)+...+c_1{\mathrm{\β}}^{N_e-p-2}\left({\mathrm{\φ}}_a\right)+{\mathrm{\β}}^{N_e-p-1}\left({\mathrm{\φ}}_a\right)+c_1{\mathrm{\β}}^{N_e-p}\left({\mathrm{\φ}}_a\right)+...+c_{p-1}{\mathrm{\β}}^{N_e-2}\left({\mathrm{\φ}}_a\right)\\ c_{p-1}{\mathrm{\β}}^{N_e-2p+1}\left({\mathrm{\φ}}_a\right)+...+c_1{\mathrm{\β}}^{N_e-p-1}\left({\mathrm{\φ}}_a\right)+{\mathrm{\β}}^{N_e-p}\left({\mathrm{\φ}}_a\right)+c_1{\mathrm{\β}}^{N_e-p+1}\left({\mathrm{\φ}}_a\right)+...+c_{p-1}{\mathrm{\β}}^{N_e-1}\left({\mathrm{\φ}}_a\right)\end{array}\right]\\ =(c_{p-1}\mathrm{\β}{\left({\mathrm{\φ}}_a\right)}^{1-p}+...+c_1\mathrm{\β}{\left({\mathrm{\φ}}_a\right)}^{-1}+1+c_1\mathrm{\β}({\mathrm{\φ}}_a)+...+c_{p-1}\mathrm{\β}{\left({\mathrm{\φ}}_a\right)}^{p-1})\left[\begin{array}{c}1\\ \mathrm{\β}\left({\mathrm{\φ}}_a\right)\\ .\\ .\\ .\\ {\mathrm{\β}}^{N_e-2p+1}\left({\mathrm{\φ}}_a\right)\end{array}\right]\\ =c\left({\mathrm{\φ}}_a\right)\widetilde{\mathrm{\α}}\left({\mathrm{\φ}}_a\right)\end{array}$

$\mathrm{\β}\left({\mathrm{\φ}}_a\right)=e^{-j2\mathrm{\π}\frac{d}{\mathrm{\λ}}{\mathrm{sin\φ}}_a}$

Then, can be in the hope of the covariance matrix of Virtual array method

${\tilde{R}}_r=E\[{\tilde{x}}_r\left(l\right){\tilde{x}}_r^H\left(l\right)\]=\tilde{C}{\mathrm{AR}}_s{A}^H{\tilde{C}}^H+{\mathrm{\σ}}_n^2{\tilde{I}}_N---(5-28)$

And have feature decomposition

${\tilde{R}}_r=\underset{i=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{\tilde{e}}_i{\tilde{e}}_i^H+\underset{i=K+1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\σ}}_n^2{\tilde{e}}_i{\tilde{e}}_i^H={\tilde{E}}_s{\widetilde{\mathrm{\Λ}}}_s{\tilde{E}}_s^H+{\mathrm{\σ}}_n^2{\tilde{E}}_n{\tilde{E}}_n^H---(5-29)$

Then, MUSIC spatial spectrum is

$P_{MUSIC}=\frac{1}{{\left|{\tilde{E}}_n^H\tilde{C}\mathrm{\α}\left({\mathrm{\φ}}_a\right)\right|}^2}---(5-30)$

Becausec(φ_a) it is a scalar value.So, byUnderstandThen MUSIC spatial spectrum becomes

Step one, utilizing Virtual array method to block original array, the radar array after being blocked receives signal

Space smoothing algorithm

As it is shown in figure 1, by an even linear array containing N number of array element, be divided into G submatrix, each submatrix all comprise M (M < N) individual array element.Use x_g(l=1,2 ..., G) represent the received signal vector of g submatrix.Wherein the g submatrix is by original battle array The g array element to the g+M-1 array element in row forms.

The G submatrix, should be made up of to last array element the G array element in original array, therefore should have

G+M-1=N, G=N-M+1

Assume space exists the signal of K different directions, and useRepresent these direction, then The reception signal of the 1st forward direction space smoothing submatrix can be expressed as

x₁(l)=A₁s(l)+n₁(l)

Wherein x₁L () is a M dimensional vector；Be by K different directions guide to M × K that amount is constituted ties up flow pattern matrix；n₁T () represents that M dimension average is zero, variance isGaussian noise vector；Submatrix guide to Amount α₁(θ) be

${\mathrm{\&alpha;}}_1\left({\mathrm{\&phi;}}_a\right)={\&lsqb;1,e^{-j2\mathrm{\&pi;}\frac{d}{\mathrm{\&lambda;}}{\mathrm{sin\&phi;}}_a},...,e^{-j2\mathrm{\&pi;}\frac{d}{\mathrm{\&lambda;}}(M-1){\mathrm{sin\&phi;}}_a}\&rsqb;}^T$

The received signal vector of the 2nd forward direction space smoothing submatrix can also be similar to and be expressed as

x₂(l)=A₂s(l)+n₂(l)

Wherein

$A_2=\&lsqb;{\mathrm{\&alpha;}}_2\left({\mathrm{\&phi;}}_a^1\right),{\mathrm{\&alpha;}}_2\left({\mathrm{\&phi;}}_a^2\right),...,{\mathrm{\&alpha;}}_2\left({\mathrm{\&phi;}}_a^K\right)\&rsqb;$

${\mathrm{\&alpha;}}_2\left({\mathrm{\&phi;}}_a\right)={\&lsqb;e^{-j2\mathrm{\&pi;}\frac{d}{\mathrm{\&lambda;}}{\mathrm{sin\&phi;}}_a},e^{-j2\mathrm{\&pi;}\frac{d}{\mathrm{\&lambda;}}\&CenterDot;2{\mathrm{sin\&phi;}}_a},...,e^{-j2\mathrm{\&pi;}\frac{d}{\mathrm{\&lambda;}}{\mathrm{Msin\&phi;}}_a}\&rsqb;}^T=e^{-j2\mathrm{\&pi;}\frac{d}{\mathrm{\&lambda;}}{\mathrm{sin\&phi;}}_a}{\mathrm{\&alpha;}}_1\left({\mathrm{\&phi;}}_a\right)$

Thus it is possible to by x₂L () is rewritten as

x₂(l)=A₂s(l)+n₂(l)=A₁Ds(l)+n₂(l)

Wherein D is the diagonal matrix on K rank

In formula, d is array element distance, and λ is radar work step-length；

In like manner can obtain the received signal vector of g submatrix

x_g(l)=A_gs(l)+n_g(l)=A₁D^g-1s(l)+n_g(l)

After having obtained the received signal vector of each submatrix, can be in the hope of the reception signal covariance square of each submatrix Battle array, i.e.

$\begin{array}{c}{R}_g^f=E\&lsqb;x_g\left(l\right)x_g^H\left(l\right)\&rsqb;\\ =E\{\&lsqb;A_1{D}^{g-1}s\left(l\right)+n_g\left(l\right)\&rsqb;{\&lsqb;A_1{D}^{g-1}s\left(l\right)+n_g\left(l\right)\&rsqb;}^H\}\\ =A_1{D}^{g-1}E\&lsqb;s\left(l\right)s^H\left(l\right)\&rsqb;{\left(D^{g-1}\right)}^H{A}_1^H+{\mathrm{\&sigma;}}_n^2{I}_M\\ =A_1{D}^{g-1}{R}_s{\left(D^{g-1}\right)}^H{A}_1^H+{\mathrm{\&sigma;}}_n^2{I}_M\end{array}$

R_s=E [s (l) s^H(l)]；

Finally G the submatrix tried to achieve is received signal covariance matrix and seek arithmetic average, it is possible to the association after being smoothed Variance matrix

$\begin{array}{c}{R}_f=\frac{1}{G}\underset{g=1}{\overset{G}{\mathrm{\&Sigma;}}}{R}_l=\frac{1}{G}\underset{g=1}{\overset{G}{\mathrm{\&Sigma;}}}{A}_1{D}^{g-1}{R}_s{\left(D^{g-1}\right)}^H{A}_1^H+{\mathrm{\&sigma;}}_n^2{I}_M\\ =A_1\&lsqb;\frac{1}{G}\underset{g=1}{\overset{G}{\mathrm{\&Sigma;}}}{D}^{g-1}{R}_s{\left(D^{g-1}\right)}^H\&rsqb;A_1^H+{\mathrm{\&sigma;}}_n^2{I}_M\end{array}$

Said process is known as forward direction smoothing processing.Similarly, it is also possible to carry out backward smoothing processing.We use y (t) Represent backward smooth submatrix；

1st backward space smoothing submatrix is y₁, its received signal vector can be expressed as

$y_1\left(l\right)={\&lsqb;x_{N_e}\left(l\right),x_{N_e-1}\left(l\right),...,x_{N_e-M+1}\left(l\right)\&rsqb;}^T\stackrel{\mathrm{\&Delta;}}{=}{\mathrm{Bx}}_G$

Wherein matrix B is backward battle array,

The g submatrix is y_g, its received signal vector is

y_g(l)=Bx_G-g+1

Then, the covariance matrix of g submatrix is

$\begin{array}{c}{R}_g^b=\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{y}_g\left(l\right)y_g^H\left(l\right)\\ ={\mathrm{BA}}_1{D}^{G-g}{R}_s{\left(D^{G-g}\right)}^H{A}_1^{H}B+{\mathrm{\&sigma;}}_n^2{I}_M\end{array}$

Finally G the submatrix tried to achieve is received signal covariance matrix and seek arithmetic average, it is possible to the association after being smoothed Variance matrix

$\begin{array}{c}{R}_b=\frac{1}{G}\underset{g=1}{\overset{G}{\mathrm{\&Sigma;}}}{R}_g^b=\frac{1}{G}\underset{g=1}{\overset{G}{\mathrm{\&Sigma;}}}{\mathrm{BA}}_1{D}^{G-g}{R}_s{\left(D^{G-g}\right)}^H{A}_1^{H}B+{\mathrm{\&sigma;}}_n^2{I}_M\\ ={\mathrm{BA}}_1\&lsqb;\frac{1}{G}\underset{g=1}{\overset{G}{\mathrm{\&Sigma;}}}{D}^{G-g}{R}_s{\left(D^{G-g}\right)}^H\&rsqb;A_1^{H}B+{\mathrm{\&sigma;}}_n^2{I}_M\end{array}$

Then, the covariance matrix after space smoothing processes just can be written as

$R_{fb}=\frac{1}{2}(R_f+R_b)$

Step 2, to after blocking radar array receive signalCarry out space smoothing process, obtain smoothed covariance Matrix；

Step 3, smoothed covariance matrix is done MUSIC Estimation of Spatial Spectrum.

Detailed description of the invention two: present embodiment is unlike detailed description of the invention one: utilize void in described step one Matroid unit method arranges Virtual array to original array；Detailed process is:

1) receiving signal without radar array under array mutual-coupling condition is: x_r(l)=As (l)+n (l), l=1,2 ..., L

WhereinFor flow pattern matrix, s (l)=[s₁(l),…,s_K(l)]^TBelieve for radar target Number source vector,For guiding vector,For the direction of kth radar target signal source, k value is k=1,2 ..., K, K For radar target number, usually require that K is less than element number of array, s_kL () is kth radar target signal source, l is snap index, n For average be zero, variance beRadar noise vector, L is snap number, and value is L=1,2 ..., 2048, T is transposition square Battle array；

2) in the case of having mutual coupling, radar array reception signal is: x_r(l)=CAs (l)+n (l), l=1,2 ..., L

Wherein, C is mutual coupling matrix, is a Teoplitz type matrix；

Matrix C A is merged into a matrix

$\stackrel{\&OverBar;}{A}=CA=\&lsqb;{\mathrm{C\&alpha;}}_r\left({\mathrm{\&phi;}}_a^1\right),...,{\mathrm{C\&alpha;}}_r\left({\mathrm{\&phi;}}_a^K\right)\&rsqb;=\&lsqb;{\stackrel{\&OverBar;}{\mathrm{\&alpha;}}}_r\left({\mathrm{\&phi;}}_a^1\right),...,{\stackrel{\&OverBar;}{\mathrm{\&alpha;}}}_r\left({\mathrm{\&phi;}}_a^K\right)\&rsqb;$

In formula,For mutual coupling guiding vector；

Employing is blocked matrix and radar array in the case of having mutual coupling is received signal x_rL ()=As (l)+n (l) blocks, Obtain

Wherein, N is element number of array, and value is N=8,9 ..., 256；P is mutual coupling degree of freedom, and p value is p=1,2 ..., N,Signal is received for the radar array after blocking；I is unit battle array；Signal is received for the radar array after blocking.

Other step and parameter are identical with detailed description of the invention one.

Detailed description of the invention three: present embodiment is unlike detailed description of the invention one or two: described C is:

In formula, c_iFor the mutual coupling coefficient, i value is i=0,1 ..., p-1, p are mutual coupling degree of freedom, and p value of the present invention is 0 < p < 25, wherein c₀=1；N is element number of array, and value of the present invention is 25.

Other step and parameter are identical with detailed description of the invention one or two.

Detailed description of the invention four: present embodiment is unlike one of detailed description of the invention one to three: described in block square Battle array is

Wherein, I is unit battle array.

Other step and parameter are identical with one of detailed description of the invention one to three.

Detailed description of the invention five: present embodiment is unlike one of detailed description of the invention one to four: described step 2 In to after blocking radar array receive signalCarry out space smoothing process, obtain space smoothing covariance matrix；Specifically Process is:

1) setForThe g forward direction space smoothing submatrix radar array receive signal, g=p, p+1 ..., N-p+1,Being M dimensional vector, M is submatrix element number of array, M < N-2p+2；

Then the covariance matrix of the g forward direction space smoothing submatrix is:

In formula, H is conjugate transpose；

And then obtain forward direction space smoothing covariance matrix R_f；

2) setForThe radar array of g backward space smoothing submatrix receive signal, g=p, p+1 ..., N-p+1,Being M dimensional vector, M is submatrix element number of array, and value is M=2,3 ..., N-2p+2；

Then the covariance matrix of g backward space smoothing submatrix is:

And then obtain backward space smoothing covariance matrix R_b；

Then space smoothing covariance matrix is:

$R_{fb}=\frac{1}{2}(R_f+R_b).$

Other step and parameter are identical with one of detailed description of the invention one to four.

Detailed description of the invention six: present embodiment is unlike one of detailed description of the invention one to five: described forward direction is empty Between smoothed covariance matrix R_fFor:

$R_f=\frac{1}{N-2p+1}\underset{g=p}{\overset{N-p+1}{\mathrm{\&Sigma;}}}{R}_g^f.$

Other step and parameter are identical with one of detailed description of the invention one to five.

Detailed description of the invention seven: present embodiment is unlike one of detailed description of the invention one to six: described backward sky Between smoothed covariance matrix R_bFor:

Other step and parameter are identical with one of detailed description of the invention one to six.

Detailed description of the invention eight: present embodiment is unlike one of detailed description of the invention one to seven: described step 3 In space smoothing covariance matrix is done MUSIC Estimation of Spatial Spectrum；Detailed process is:

To space smoothing covariance matrix R_fbCarry out feature decomposition,

$R_{fb}=\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_i{e}_i{e}_i^H+\underset{i=K+1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_i{e}_i{e}_i^H\&ap;E_s{\mathrm{\&Lambda;}}_s{E}_s^H+{\mathrm{\&sigma;}}_n^2{E}_n{E}_n^H$

In formula, δ_jFor jth eigenvalue, wherein,e_jFor with δ_jRight The characteristic vector answered；E_sFor signal subspace；E_s=[e₁,e₂,…,e_K]

Λ_s=diag [δ₁,δ₂,…,δ_K]；E_n=[e_K+1,e_K+2,…,e_N] it is noise subspace；J value is 1≤j≤N；

Then MUSIC Estimation of Spatial Spectrum is written as:

$P_{MUSIC}=\frac{1}{{\left|E_n^H{\widetilde{\mathrm{\&alpha;}}}_r\left({\mathrm{\&phi;}}_a\right)\right|}^2}$

In formula,Smooth guiding vector for Virtual Space, be the even linear array guiding vector of a M dimension.

Other step and parameter are identical with one of detailed description of the invention one to seven.

Employing following example checking beneficial effects of the present invention:

Embodiment one: a kind of MUSIC Estimation of Spatial Spectrum side based on Virtual array space smoothing mutual coupling calibration of the present embodiment Method is specifically prepared according to following steps:

Investigate signal to noise ratio, the coherence of signal source and the snap number shadow to even linear array MUSIC mutual coupling calibration algorithm Ring.Emulation compared for MUSIC algorithm under ideal conditions, MUSIC algorithm when having a mutual coupling, known the mutual coupling coefficient time MUSIC Six kinds of algorithms such as algorithm, Space planar angle, Virtual array method and proposed virtual-Space planar angle.

Fundamental simulation parameter is as follows: element number of array N_eIt it is 25；Spacing wave number K is 3, direction be respectively (70 degree, 40 degree, 30 degree)；Mutual coupling degree of freedom p is 3, and the mutual coupling coefficient is (1,0.5-0.14j ,-0.2+0.24j)；Space smoothing submatrix group number G is 3 groups.

(1) 3 signal sources of setting in this emulation that affect of noise alignment algorithm are incoherent source, and snap number L is 50.

Fig. 3 a, 3b, 3c, 3d, 3e, 3f give space spectrogram when 3 signal source signal to noise ratios are 0dB.Simulation result Showing, the MUSIC algorithm under ideal conditions can successfully estimate all directions, but its spectral peak height but outline is less than existing mutually Situation during coupling.And the signal in 30 degree and 40 degree directions all can be estimated in other the five kinds of methods having mutual coupling, but But 70 degree of directions effectively could not be estimated.This phenomenon explanation mutual coupling effect changes the column space in 70 degree of directions.Right Than 3b and 3c it is found that under this low signal-to-noise ratio the most known the mutual coupling coefficient result to estimating have and produce the biggest shadow Ring.3e and 3f of employing Virtual array method spectrum outline between 30 degree and 40 degree is higher than other algorithm.This is because it is virtual Array element method needs to carry out original array dimensionality reduction computing in processing procedure, thus causes the loss of array resolving power, result in The spectrum of transitional region improves.It addition, from 3d and 3f it is found that after have employed space smoothing process, spectral peak height all has Raising in various degree.

Fig. 4 a, 4b, 4c, 4d, 4e, 4f give space spectrogram when 3 signal source signal to noise ratios are 3dB.Along with noise More sharply, spectral peak height the most correspondingly increases the spectral peak of MUSIC algorithm under ideal conditions that increases of ratio.Virtual- Space planar angle Fig. 4 f also begins to estimate the signal in 70 degree of directions under this signal to noise ratio, and in 30 degree and 40 degree of directions On spectral peak be also higher than MUSIC algorithm under ideal conditions.It addition, can be seen that from Fig. 4 c, it is known that also exist during the mutual coupling coefficient 70 degree of directions occur in that spectral peak, but spectrum is relatively low.This shows the increase along with signal to noise ratio, and mutual coupling effect is to 70 degree of direction row skies Between impact the most slowly disappear.

As shown in Fig. 5 a, 5b, 5c, 5d, 5e, 5f, after three signal source signal to noise ratios increase to 6dB, Virtual array method is also It has been formed about spectral peak in 70 degree of directions.It addition, comparison diagram 5c and Fig. 5 f is it is found that adopt in the case of unknown the mutual coupling coefficient It is higher than the MUSIC algorithm of known the mutual coupling coefficient with the spatial spectrum peak value of virtual-Space planar angle, this also illustrates and set forth herein Method be highly effective.

As shown in Fig. 6 a, 6b, 6c, 6d, 6e, 6f, after the signal to noise ratio of three signal sources increases 10dB further, The performance of Virtual array method has had bigger improvement, the effect of virtual-space smoothing to approach the MUSIC algorithm under ideal conditions. Review mutual coupling direct MUSIC algorithm and Space planar angle along with the increase of signal to noise ratio, only carried on spatial spectrum peak value Height, overall estimation effect does not has the biggest change.

Above simulation result shows, in the case of signal to noise ratio is relatively low (SNR < 3dB), employing Space planar angle can be effectively Improve the spectral peak of spatial spectrum, but several method all occurs in that missing inspection on 70 degree of directions.This shows in the case of low signal-to-noise ratio, Mutual coupling effect can affect the column space on some direction so that it is no longer mutually orthogonal with noise subspace.And at low signal-to-noise ratio Under the most known the mutual coupling coefficient the result of Estimation of Spatial Spectrum is affected and little.

And after signal to noise ratio is more than 3dB, virtual-Space planar angle starts to estimate the signal in 70 degree of directions.Separately Outer discovery from the spatial spectrum of known the mutual coupling coefficient MUSIC algorithm, after signal to noise ratio improves, the mutual coupling effect impact on column space The most slowly disappear.After signal to noise ratio is more than 6dB, the effect of Virtual array method also begins to take a turn for the better.To sum up analyze, Space planar angle Under low signal-to-noise ratio and high s/n ratio, good performance is shown respectively, so combining the void of the two advantage with Virtual array method Plan-space smoothing algorithm, has not only surmounted the two, MUSIC algorithm when even effect is also better than known the mutual coupling coefficient in performance. But, the shortcoming of this algorithm is also apparent from.Need to experience the dimensionality reduction computing of twice, the loss to direction resolving power in processing procedure It is more, so it is relatively low or have in the system of more array element to can be only applied to resolving power requirement.

More than only discuss and be identical situation without the Signal-to-Noise in direction.Analyze signal to noise ratio below the most multiple The performance of six kinds of methods in the case of miscellaneous.Fig. 7 a, 7b, 7c, 7d, 7e, 7f give three direction signal to noise ratios be respectively (20,5, 5) six kinds of method space spectrograms during dB.Wherein ideal conditions MUSIC algorithm pattern 7a, known mutual coupling MUSIC algorithm pattern 7c, virtual Array element method Fig. 7 e, virtual-Space planar angle Fig. 7 f show good effect.But there is mutual coupling direct MUSIC algorithm, even if It is in the case of 70 degree of direction signal to noise ratios are the highest, the most not can recognize that it comes.It addition, Space planar angle entirety Space spectrum is considerably reduced.

Fig. 8 a, 8b, 8c, 8d, 8e, 8f give six kinds of methods during three direction signal to noise ratios respectively (30,10,10) dB Space spectrogram.Now, Space planar angle occurs in that missing inspection on 30 degree of directions, and defines spectral peak in the wrong direction.And have Mutual coupling direct MUSIC algorithm the most not can recognize that 70 degree of directions are come.

By analyzing it is found that mutual coupling effect and direction are relevant above.Have mutual coupling direct MUSIC algorithm and Space smoothing algorithm is do not do the step corrected for mutual coupling effect, but they still can under some signal to noise ratio Part direction is made and identifies accurately, turned out mutual coupling effect and there is directional characteristic.Review known mutual coupling MUSIC algorithm and Virtual array metaclass algorithm all has the algorithm steps of mutual coupling calibration, so, these methods can estimate sense effectively.

(2) simulation parameter of the present invention that affects of algorithm is set essentially identical, only with the next item up emulation by signal source coherence Change signal source is coherent source.

Fig. 9 a, 9b, 9c, 9d, 9e, 9f give signal source and are coherent source and six kinds of method skies time signal to noise ratio is 10dB Between spectrogram.Owing to space smoothing process can efficiently solve the problem of signal source decorrelation LMS, so coherent source signal is to employing Two kinds of methods (d) and (f) that space smoothing processes the most do not produce impact.Review do not use space smoothing to process (a), B (), (c) and (e) all occurs in that false-alarm phenomenon in various degree, even and if in the case of signal to noise ratio is the highest, spatial spectrum It is worth the lowest.This also show proposed virtual-Space planar angle and has the strongest robustness to Estimation of Spatial Spectrum.

(3) discrimination of algorithms of different and root-mean-square error analysis

Figure 10 and Figure 11 sets forth direction estimation success rate and the RMSE analysis chart that six kinds of methods change with signal to noise ratio. Arranging test 3 senses of stochastic generation every time in emulation, between 3 directions, interval is all higher than 10 degree (resolving power is enough), And give identical signal to noise ratio (X-axis).Each signal to noise ratio is 100 tests, statistics success rate and RMSE.Signal source is non-phase Dry source, fast umber of beats is 50.Wherein, spatial spectrum search precision is 0.25 degree, and spacing spectrum peak detection threshold is set to 5dB；Right In fail identify situation, RMSE gives the punishment of 5 degree.Result shows, listed method discrimination all with signal to noise ratio increase and Increasing, RMSE has reduced with the increase of signal to noise ratio.But, direct MUSIC method and Space planar angle are to different directions Random combine, success rate presents fluctuation status.This mutual coupling effect of being the most indirectly recruited is tool on the impact of different directions Selectively, illustrate to study the necessity of mutual coupling calibration algorithm the most simultaneously.It addition, from RMSE analysis chart it is found that MUSIC algorithm ideally can approach well CRB curve, Virtual array method and virtual-Space planar angle along with The increase of signal to noise ratio also is able to converge to CRB curve, and performance is also possible to be better than the MUSIC algorithm of known the mutual coupling coefficient.

In order to study the listed method adaptability to increasingly complex situation further, we have done following emulation, as Figure 12, Figure 13.Basic parameter is identical with a upper emulation, tests still three directions of stochastic generation each time, but to wherein two Individual direction gives fixing signal to noise ratio 5dB, investigate listed method with the direction estimation success rate of the 3rd direction signal to noise ratio change and RMSE。

Simulation result shows, the performance of several method all occurs in that decline in various degree, especially Space planar angle Can deteriorate serious.From the point of view of the performance curve of spatial smoothing method, its smoothing process makes big noise analogy in signal subspace To signal accumulated, and the signal in little signal to noise ratio direction is submerged in noise subspace.This also illustrates space to put down Sliding method is poor to the robustness of complex situations.Additionally different from a upper simulation result, the most known the mutual coupling coefficient The performance of MUSIC algorithm increases, and result is better than Virtual array method and virtual-Space planar angle.If so having one Plant effective estimation of mutual coupling coefficient algorithm, and this estimated result is used in MUSIC spatial spectrum search formula, it is also possible to obtain one Plant new mutual coupling calibration algorithm, and its robustness may also be better than method in this paper.

Figure 14 and Figure 15 give several method under coherent source with fast umber of beats change direction be estimated power curve and RMSE curve.Owing to have employed coherent source, the MUSIC algorithm complete failure under ideal conditions, and in the case of having mutual coupling Instead MUSIC algorithm has certain estimated capacity.This explanation, mutual symplectic information source has certain decorrelation LMS ability.Due to, this The algorithm that patent proposes applies space smoothing and processes, and space smoothing processes and has decorrelation LMS ability, so this algorithm just table Reveal good performance.From the point of view of overall simulation result, method in this paper has the strongest robustness.Either exist Under low signal-to-noise ratio, or under coherent source RST, even also target signal direction can be had one single taking soon Fixed estimated capacity.The present invention also can have other various embodiments, in the case of without departing substantially from present invention spirit and essence thereof, this Skilled person is when making various corresponding change and deformation according to the present invention, but these change accordingly and deformation is all answered Belong to the protection domain of appended claims of the invention.

Claims (8)

1. a MUSIC Estimation of Spatial Spectrum method based on Virtual array space smoothing mutual coupling calibration, it is characterised in that: Yi Zhongji MUSIC Estimation of Spatial Spectrum method in Virtual array space smoothing mutual coupling calibration concretely comprises the following steps:

Step one, utilizing Virtual array method to block original array, the radar array after being blocked receives signal

Step 2, to after blocking radar array receive signalCarry out space smoothing process, obtain smoothed covariance matrix；

Step 3, smoothed covariance matrix is made MUSIC Estimation of Spatial Spectrum.

A kind of MUSIC Estimation of Spatial Spectrum method based on Virtual array space smoothing mutual coupling calibration, It is characterized in that: described step one utilizes Virtual array method original array is arranged Virtual array；Detailed process is:

1) receiving signal without radar array under array mutual-coupling condition is: x_r(l)=As (l)+n (l), l=1,2 ..., L

Wherein,For flow pattern matrix, s (l)=[s₁(l),…,s_K(l)]^TFor radar target signal source Vector,For guiding vector,For the direction of kth radar target signal source, k value is k=1,2 ..., K, K are thunder Reaching target number, K is less than element number of array, s_kL () is kth radar target signal source, l is snap index, n be average be zero, Variance isRadar noise vector, L is snap number, and value is L=1,2 ..., 2048, T is transposed matrix；

2) in the case of having mutual coupling, radar array reception signal is: x_r(l)=CAs (l)+n (l), l=1,2 ..., L

Wherein, C is mutual coupling matrix, is a Teoplitz type matrix；

Matrix C A is merged into a matrix

$\stackrel{\&OverBar;}{A}=CA=\&lsqb;{\mathrm{C\&alpha;}}_r\left({\mathrm{\&phi;}}_a^1\right),...,{\mathrm{C\&alpha;}}_r\left({\mathrm{\&phi;}}_a^K\right)\&rsqb;=\&lsqb;{\stackrel{\&OverBar;}{\mathrm{\&alpha;}}}_r\left({\mathrm{\&phi;}}_a^1\right),...,{\stackrel{\&OverBar;}{\mathrm{\&alpha;}}}_r\left({\mathrm{\&phi;}}_a^K\right)\&rsqb;$

In formula,For mutual coupling guiding vector；

Employing is blocked matrix and radar array in the case of having mutual coupling is received signal x_rL ()=CAs (l)+n (l) blocks, obtain

Wherein, N is element number of array, and value is N=8,9 ..., 256；P is mutual coupling degree of freedom, and p value is p=1,2 ..., N,Signal is received for the radar array after blocking.

A kind of MUSIC Estimation of Spatial Spectrum method based on Virtual array space smoothing mutual coupling calibration, It is characterized in that: described C is:

In formula, c_iFor the mutual coupling coefficient, i value is i=0,1 ..., p-1, wherein c₀=1.

A kind of MUSIC Estimation of Spatial Spectrum method based on Virtual array space smoothing mutual coupling calibration, It is characterized in that: described in block matrix and be

Wherein, I is unit battle array.

A kind of MUSIC Estimation of Spatial Spectrum method based on Virtual array space smoothing mutual coupling calibration, It is characterized in that: described step 2 receives signal to the radar array after blockingCarry out space smoothing process, obtain sky Between smoothed covariance matrix；Detailed process is:

1) setFor x_rThe radar array reception signal of the g forward direction space smoothing submatrix of (l), g=p, p+1 ..., N-p+ 1,Being M dimensional vector, M is submatrix element number of array, and value is M=2,3 ..., N-2p+2；

Then the covariance matrix of the g forward direction space smoothing submatrix is:

In formula, H is conjugate transpose；

And then obtain forward direction space smoothing covariance matrix R_f；

2) setFor x_rThe radar array reception signal of the g of (l) backward space smoothing submatrix, g=p, p+1 ..., N-p + 1,Being M dimensional vector, M is submatrix element number of array, and value is M=2,3 ..., N-2p+2；

Then the covariance matrix of g backward space smoothing submatrix is:

And then obtain backward space smoothing covariance matrix R_b；

Then space smoothing covariance matrix is:

$R_{fb}=\frac{1}{2}(R_f+R_b).$

A kind of MUSIC Estimation of Spatial Spectrum method based on Virtual array space smoothing mutual coupling calibration, It is characterized in that: described forward direction space smoothing covariance matrix R_fFor:

$R_f=\frac{1}{N-2p+1}\underset{g=p}{\overset{N-p+1}{\&Sigma;}}{R}_g^f.$

A kind of MUSIC Estimation of Spatial Spectrum method based on Virtual array space smoothing mutual coupling calibration, It is characterized in that: described backward space smoothing covariance matrix R_bFor:

$R_b=\frac{1}{N-2p+1}\underset{g=p}{\overset{N-p+1}{\&Sigma;}}{R}_g^b.$

A kind of MUSIC Estimation of Spatial Spectrum method based on Virtual array space smoothing mutual coupling calibration, It is characterized in that: space smoothing covariance matrix is done MUSIC Estimation of Spatial Spectrum by described step 3；Detailed process is:

To space smoothing covariance matrix R_fbCarry out feature decomposition,

$R_{fb}=\underset{j=1}{\overset{K}{\&Sigma;}}{\mathrm{\&delta;}}_j{e}_j{e}_j^H+\underset{j=K+1}{\overset{N}{\&Sigma;}}{\mathrm{\&delta;}}_j{e}_j{e}_j^H\&ap;E_s{\mathrm{\&Lambda;}}_s{E}_s^H+{\mathrm{\&sigma;}}_n^2{E}_n{E}_n^H$

In formula, δ_jFor jth eigenvalue, wherein,e_jFor with δ_jCorresponding Characteristic vector；E_sFor signal subspace；E_s=[e₁,e₂,…,e_K]

Λ_s=diag [δ₁,δ₂,…,δ_K]；E_n=[e_K+1,e_K+2,…,e_N] it is noise subspace；J value is 1≤j≤N；

Then MUSIC Estimation of Spatial Spectrum is written as:

$P_{MUSIC}=\frac{1}{{\left|E_n^H{\widetilde{\mathrm{\&alpha;}}}_r\left({\mathrm{\&phi;}}_a\right)\right|}^2}$

In formula,Smooth guiding vector for Virtual Space, be the even linear array guiding vector of a M dimension.