CN103913732A - Multicarrier frequency MIMO radar high-speed target angle estimation method - Google Patents

Abstract

The invention discloses a multicarrier frequency MIMO radar high-speed target angle estimation method which mainly solves the problem that in the prior art, the angle estimation accuracy of high-seed coherent and incoherent mixed targets is poor. The multicarrier frequency MIMO radar high-speed target angle estimation method includes the steps that (1) a high-speed target echo signal is obtained through multicarrier frequency MIMO radar; (2) channel separation is conducted on the high-speed target echo signal, so that a signal processed through channel separation is obtained; (3) DFT is conducted on the signal processed through channel separation, so that a high-speed target signal is obtained; (4) focus transformation is conducted on the high-speed target signal through the bilateral related transformation TCT algorithm, so that a high-speed target signal processed through focusing is obtained; (5) the high-speed target angle of the high-speed target signal processed through focusing is estimated through the ESPRIT algorithm. By means of the multicarrier frequency MIMO radar high-speed target angle estimation method, accurate estimation on the angles of high-speed coherent and incoherent mixed targets can be achieved and the method can be applied to high-speed target detection.

Description

Multi-carrier frequency MIMO radar high-speed target angle estimating method

Technical field

Invention belongs to Radar Technology field, is specifically related to the angle estimating method of radar for high-speed target, can be used for estimating with incoherent target relevant at a high speed, improves multi-carrier frequency multiple-input and multiple-output MIMO radar high-speed target is detected to performance.

Background technology

MIMO radar is a kind of new system radar growing up in recent years, the MIMO radar system of research is divided into two large classes substantially at present, one class is distributed MIMO radar, this class MIMO transmitting radar antenna interval is very wide, make target present relatively independent reflection characteristic for each emitting antenna, and the echoed signal of the signal of different transmit antennas transmitting after target scattering is incoherent, the angle scintillations of spatial spread target be can effectively resist, thereby detection and the parameter estimation performance of radar promoted.Another kind of is centralized MIMO radar, and this radar antenna spacing is less, is similar to traditional array, has higher resolution and parameter estimation performance.

It is the study hotspot in Estimation of Spatial Spectrum field that direction of arrival DOA estimates always, and a lot of scholars have proposed numerous algorithms in this field.People such as the Schmidt R O of the U.S. 1986 New Times that the multiple signal classification MUSIC algorithm to 280 pages of propositions has been started spatial spectral estimation algorithm research the 276th page of the 34th the 3rd phase of volume of IEEE Transaction on Antenna and Propagation periodical, the rise and development that has promoted proper subspace class algorithm, has become the significant algorithm in Estimation of Spatial Spectrum theoretical system.But the necessary spectrum peak search of MUSIC algorithm has increased the operand of algorithm greatly.People such as the Roy R of the U.S. 1986 are at IEEE Transaction on Acostics, the 1340th page of the 34th the 10th phase of volume of Speech and Signal Processing periodical ESPRIT algorithm to 1342 pages of propositions obtains signal DOA by numerical solution, and generally Billy is low with the MUSIC method operand of angle searching.

Along with the proposition of MIMO radar, the direction of arrival of MIMO radar estimates to have caused numerous scholars' very big interest.If people such as Chen Duofang 2008 are at the 44th the 12nd phase of volume of Electronics Letters periodical the 770th page of bistatic MIMO radar ESPRIT algorithm to 771 pages of propositions, estimating there is good performance on the bistatic MIMO radar angle of arrival.The people such as X.Zhang realize MIMO radar angle estimation at the 14th the 12nd phase of volume of IEEE Communications Letters periodical the 1161st page of bistatic MIMO radar dimensionality reduction MUSIC algorithm to 1163 pages of propositions with less operand in 2010.

Multi-carrier frequency MIMO radar, is the one in MIMO radar, and this radar is launched multiple-frequency signal by cell site, receives signal by receiving station.While adopting multi-carrier frequency MIMO radar to carry out angle estimation to high-speed target, due to receiving station receive signal after channel separation, the Doppler frequency of each passage is not in same Doppler unit, can not directly carry out angle estimation, for this problem, the people such as Qin Guodong utilize Keystone conversion to proofread and correct Doppler unit and walk about the 2763rd page to 2768 pages of the 38th the 12nd phases of volume of electronic letters, vol for 2010, and utilize MUSIC algorithm to carry out angle estimation, there is good angle estimation performance.But when there is high speed Coherent Targets in above-mentioned existing method, cannot correctly estimate angle, can reduce the detection performance of radar to high-speed target.

Summary of the invention

The object of the invention is to the deficiency for multi-carrier frequency MIMO radar high-speed target angle estimation, propose a kind of multi-carrier frequency MIMO radar high-speed target angle estimating method, to improve the angle estimation precision of high speed Coherent Targets.

Technical scheme of the present invention is achieved in that

The array that transmits and receives that the present invention adopts is even linear array, and the adjacent array element distance of array is half-wavelength, based on the feature of multi-carrier frequency MIMO radar, in conjunction with broadband signal algorithm for estimating, by focusing transform, the data of the different frequent points after channel separation are focused on same frequency, recycle invariable rotary at the tenth of the twelve Earthly Branches subspace ESPRIT method high-speed target angle is estimated, specific implementation step comprises as follows:

(1) utilize multi-carrier frequency MIMO radar to obtain high-speed target echoed signal, and this echoed signal is carried out to channel separation and discrete Fourier transformation DFT, obtain high-speed target signal X;

(2) utilize two-sided correlation matrices transformation TCT algorithm to focus on high-speed target signal X, the high-speed target signal X after being focused on _fTwith focus signal frequency f _γ;

(3) according to the high-speed target signal X after focusing on _fT, utilize invariable rotary at tenth of the twelve Earthly Branches subspace ESPRIT algorithm to estimate high-speed target angle:

3a) utilize the high-speed target signal X after focusing on _fT, structure signal reconstruction matrix Z: $Z=\left[\begin{array}{cc}{X}_{\mathrm{FT}}& J_{N_r}{X}_{\mathrm{FT}}^{*}{J}_M\end{array}\right]$

Wherein, that dimension is N _r× N _rswitching matrix, J _mbe that dimension is the switching matrix of M × M, subscript * represents matrix to carry out conjugate operation, N _rthe number that represents multi-carrier frequency MIMO radar receiving antenna, M represents multi-carrier frequency MIMO radar transmitted pulse number;

3b) signal reconstruction matrix Z is carried out to real unitary transformation, obtains real unitary transformation matrix T (Z):

$T\left(Z\right)=Q_{N_r}^H{\mathrm{ZQ}}_{2M}$

Wherein, that dimension is N _r× N _rsparse matrix, Q _2Mbe that dimension is the sparse matrix of 2M × 2M, subscript H represents matrix to carry out conjugate transpose;

3c) calculate the covariance matrix of real unitary transformation matrix T (Z): and to this covariance matrix R _tcarry out Eigenvalues Decomposition, obtain signal subspace matrix E _s;

3d) utilize signal subspace matrix E _sconstruct respectively real and signal subspace matrix U _s1, and empty difference signal subspace matrix U _s2:

U _s1＝H ₁E _s

U _s2＝H ₂E _s

Wherein, H ₁for reality and transformation matrix: h ₂for the poor transformation matrix of void: $H_2=Q_{N_r-1}^{H}j(\left[\begin{array}{cc}{I}_{N_r-1}& 0\end{array}\right]-\left[\begin{array}{cc}0& I_{N_r-1}\end{array}\right])Q_{N_r},$ that dimension is (N _r-1) × (N _r-1) sparse matrix, that dimension is (N _r-1) × (N _r-1) unit matrix of dimension, the 0th, dimension is (N _r-1) × 1 null matrix, that dimension is N _r× N _rsparse matrix, j represents imaginary unit;

3e) utilize real and signal subspace matrix U _s1with empty difference signal subspace matrix U _s2, structure total least square matrix G:

$G=\left[\begin{array}{c}{U}_{s1}^H\\ U_{s2}^H\end{array}\right]\left[\begin{array}{cc}{U}_{s1}& U_{s2}\end{array}\right]$

3f) total least square matrix G is carried out to Eigenvalues Decomposition and obtain eigenvectors matrix V _g, then by this eigenvectors matrix V _gresolve into the matrix that four dimensions are P × P, that is:

$V_G=\left[\begin{array}{cc}{V}_{11}& V_{12}\\ V_{21}& V_{22}\end{array}\right],$ Wherein V ₁₁upper left submatrix, V ₁₂upper right submatrix, V ₂₁lower-left submatrix and V ₂₂bottom right submatrix, wherein, P represents the number of high-speed target;

3g) utilize upper right submatrix V ₁₂with bottom right submatrix V ₂₂calculate invariable rotary matrix Ψ ':

${\mathrm{\Ψ}}^{\′}=-V_{12}{V}_{22}^{-1}$

Wherein, subscript-1 represents matrix inversion matrix;

3h) invariable rotary matrix Ψ ' is carried out to Eigenvalues Decomposition, obtain P eigenvalue λ _q, q=1,2 ..., P, recycles this P eigenwert and obtains P invariable rotary angle:

β _q＝2arctanλ _q，q＝1,2,…,P；

3i) utilize this P invariable rotary angle, try to achieve the angle estimation value of P high-speed target:

${\widehat{\mathrm{\θ}}}_q=\arcsin \left[\frac{c{\mathrm{\β}}_q{f}_{\mathrm{\γ}}}{2\mathrm{\π}{d}_r}\right],q=\mathrm{1,2},...,P$

Wherein, c represents electromagnetic wave propagation speed, d _rrepresent the spacing of receiving antenna.

The present invention compared with prior art has the following advantages:

Prior art is carried out angle estimation mainly for the incoherent target of high speed of multi-carrier frequency MIMO radar, and the high speed Coherent Targets of multi-carrier frequency MIMO radar and the angle estimation that incoherent target is mixed are seldom discussed.The present invention has been owing to having adopted two-sided correlation matrices transformation TCT algorithm and invariable rotary at tenth of the twelve Earthly Branches subspace ESPRIT method, can realize the angle that high speed Coherent Targets to multi-carrier frequency MIMO radar and incoherent target mix and estimate.

Emulation shows, the angle estimation precision that the present invention mixes for high speed Coherent Targets and the incoherent target of multi-carrier frequency MIMO radar is better than the existing MUSIC method based on Keystone conversion.

Accompanying drawing explanation

Fig. 1 is realization flow figure of the present invention.

Fig. 2 utilizes the present invention to carry out the angle estimation result that 100 emulation experiments obtain.

Fig. 3 utilizes the existing MUSIC method based on Keystone conversion to carry out the angle estimation result that 100 emulation experiments obtain.

Fig. 4 is the curve that utilizes respectively the square error of the angle estimation that the present invention and existing MUSIC method based on Keystone conversion obtain to change with signal to noise ratio (S/N ratio).

Embodiment

With reference to Fig. 1, specific implementation step of the present invention is as follows:

Step 1, carries out channel separation and discrete Fourier transformation DFT to multi-carrier frequency MIMO radar high-speed target echoed signal, obtains high-speed target signal X.

Multi-carrier frequency MIMO radar of the present invention obtains high-speed target echoed signal, and the cell site of this radar and receiving station are respectively by N _e, N _rthe even linear array of individual antenna composition, adjacent antenna spacing is d _r, implementation step is as follows:

1a), in the time there is the different high-speed target of P direction in same range unit, the high-speed target echoed signal that receiving station's receiving antenna receives is:

$S_n^b\left(t\right)=\underset{k=1}{\overset{N_e}{\mathrm{\&Sigma;}}}\underset{q=1}{\overset{P}{\mathrm{\&Sigma;}}}\mathrm{rect}(t-{\mathrm{\&tau;}}_{\mathrm{kn}}^q)e^{j2\mathrm{\&pi;}[g_k(t-{\mathrm{\&tau;}}_{\mathrm{kn}}^q)-0.5B_u{(t-{\mathrm{\&tau;}}_{\mathrm{kn}}^q)}^2/T_e]},n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N_r---<1>$

Wherein represent gate-control signal, $\mathrm{rect}(t-{\mathrm{\&tau;}}_{\mathrm{kn}}^q)=\left\{\begin{array}{cc}0& 0\&le;t-{\mathrm{\&tau;}}_{\mathrm{kn}}^q<T_e\\ 0& T_e\&le;t-{\mathrm{\&tau;}}_{\mathrm{kn}}^q\&le;T_r\end{array}\right.,$ T represents the sampling time, and q represents high-speed target sequence number, and n represents receiving antenna sequence number, and k represents emitting antenna sequence number, represent the time delay of q high-speed target with respect to k emitting antenna and n receiving antenna, ${\mathrm{\&tau;}}_{\mathrm{kn}}^q=R/c-d_k^a\sin {\mathrm{\&theta;}}_q/c-d_n^b\sin {\mathrm{\&theta;}}_q/c-v_q(m{T}_r+t)/c,$ R represents initial distance, and c represents electromagnetic wave propagation speed, represent the spacing of k emitting antenna and the 1st emitting antenna, represent the spacing of n receiving antenna and the 1st receiving antenna, θ _qrepresent the angle of q high-speed target, v _qrepresent the radial velocity of q high-speed target, T _eindicating impulse width, T _rthe indicating impulse repetition period, f _krepresent the carrier frequency of k transmission antennas transmit signal, f _k=f ₀+ c _kΔ f, f ₀centered by carrier frequency, Δ f represents frequency interval, c _kpresentation code sequence, c _k∈ { (N _e-1)/2 ..., (N _e-1)/2}, m indicating impulse sequence number, m=1,2 ..., M, M represents the pulse number of transmission antennas transmit, B _urepresent modulating bandwidth;

High-speed target echoed signal 1b) receiving station's receiving antenna being received with channel separation signal multiply each other, then carry out low-pass filtering, obtain the signal after channel separation

$r_{\mathrm{kn}}^0\left(t\right)=\underset{q=1}{\overset{P}{\mathrm{\&Sigma;}}}{e}^{j2\mathrm{\&pi;}(\mathrm{\&mu;}{\mathrm{\&tau;}}_{\mathrm{kn}}^{q}t-f_k{\mathrm{\&tau;}}_{\mathrm{kn}}^q-0.5\mathrm{\&mu;}{\left({\mathrm{\&tau;}}_{\mathrm{kn}}^q\right)}^2),k=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N_e,n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N_r<2>}$

Wherein, μ represents chirp rate, μ=B _u/ T _e;

1c) to the signal after channel separation carry out discrete Fourier transformation DFT, obtain the signal after discrete Fourier transformation:

$\begin{array}{c}{r}_{\mathrm{kn}}(\mathrm{\&tau;},m{T}_r)=\underset{q=1}{\overset{P}{\mathrm{\&Sigma;}}}{A}_r{e}^{-j2\mathrm{\&pi;}[f_k(R/c-d_k^a\sin {\mathrm{\&theta;}}_q/c-d_n^b\sin {\mathrm{\&theta;}}_q/c)}{e}^{-\mathrm{j\&pi;\&mu;}{(R/c-d_k^a\sin {\mathrm{\&theta;}}_q/c-d_n^b\sin {\mathrm{\&theta;}}_q/c)}^2{e}^{j2\mathrm{\&pi;}{f}_k{v}_q{T}_{r}m/c}}\\ k=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N_e,n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N_r,m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,M\end{array}<3>$

Wherein A _rrepresent amplitude factor, τ _mrepresent the time delay of m pulse repetition time q high-speed target, τ _m=R/c-v _qt _rm/c+f _kv _q/ c μ;

1d) get the maximal value of signal after discrete Fourier transformation, obtain range unit signal:

$\begin{array}{c}{r}_{\mathrm{kn}}({\mathrm{\&tau;}}_m,m{T}_r)=\underset{q=1}{\overset{P}{\mathrm{\&Sigma;}}}{e}^{-j2\mathrm{\&pi;}{f}_k{d}_n^b\sin {\mathrm{\&theta;}}_q/c}{e}^{-j2\mathrm{\&pi;}{f}_k(R/c-d_k^a\sin {\mathrm{\&theta;}}_q/c)}{e}^{-\mathrm{j\&pi;\&mu;}{(R/c)}^2{e}^{j2\mathrm{\&pi;}{f}_k{v}_q{T}_{r}m/c}}\\ k=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N_e,n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N_r,m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,M\end{array}<4>$

1e) utilize the definition of matrix multiplication, write range unit signal as matrix form, obtain high-speed target signal X:

X＝A(θ ₀)S+N <5>

Wherein, A (θ ₀) expression array manifold matrix, A (θ ₀)=[diag[a (θ ₀₁)] diag[a (θ ₀₂)] ... diag[a (θ _0P)]], diag represents matrix to carry out diagonalization processing, and S represents to reset signal matrix, n represents noise vector.The array manifold matrix of q high-speed target is a (θ _0q),

$a\left({\mathrm{\&theta;}}_{0q}\right)={\left[\begin{array}{ccccccccccccc}{a}_{11}& a_{12}& ...& a_{1N_e}& a_{21}& a_{22}& ...& a_{2N_e}& ...& a_{N_{r}1}& a_{N_{r}2}& ...& a_{N_r{N}_e}\end{array}\right]}^T,$ A _knrepresent the array manifold element of q high-speed target, the rearrangement signal matrix of q high-speed target is $s_q\left(m{T}_r\right),s_q\left({\mathrm{mT}}_r\right)={\left[\begin{array}{ccccccccccccc}{s}_1& s_2& ...& s_{N_e}& s_1& s_2& ...& s_{N_e}& ...& s_1& s_2& ...& s_{N_e}\end{array}\right]}^T,$ S _krepresent the rearrangement signal element of q high-speed target, q=1,2 ..., P, k=1,2 ..., N _e, n=1,2 ..., N _r, m=1,2 ..., M, subscript T representing matrix transposition.

Step 2, utilizes high-speed target signal X, adopts two-sided correlation matrices transformation TCT algorithm, carries out focusing transform, the high-speed target signal X after being focused on _fTwith the signal frequency f focusing on _γ.Being implemented as follows of this step:

2a) high-speed target signal X is adopted to two-sided correlation matrices transformation TCT algorithm, obtain focusing transform matrix D and focus signal frequency f _γ;

2b) utilize high-speed target signal X and focusing transform matrix D, the high-speed target signal X after being focused on _fT:

X _FT＝DX。<6>

Step 3, according to the high-speed target signal X after focusing on _fT, utilize invariable rotary at tenth of the twelve Earthly Branches subspace ESPRIT algorithm to estimate high-speed target angle.

3a) structure N _r× N _rthe switching matrix of dimension and the switching matrix J of M × M dimension _m,

3b) utilize the high-speed target signal X after focusing on _fT, N _r× N _rthe switching matrix of dimension and the switching matrix J of M × M dimension _m, obtain signal reconstruction matrix Z:

$Z=\left[\begin{array}{cc}{X}_{\mathrm{FT}}& J_{N_r}{X}_{\mathrm{FT}}^{*}\end{array},J_M\right],---<7>$

Wherein, subscript * represents matrix to carry out conjugate operation;

3c) structure N _r× N _rdimension sparse matrix it is expressed as follows:

Work as N _rduring for even number, $Q_{N_r}=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}{I}_{N_r/2}& j{I}_{N_r/2}\\ J_{N_r/2}& -j{J}_{N_r/2}\end{array}\right],---<8>$

Wherein, representation dimension is unit matrix, representation dimension is switching matrix,

Work as N _rduring for odd number, $Q_{N_r}=\frac{1}{\sqrt{2}}\left[\begin{array}{ccc}{I}_{(N_r-1)/2}& 0& j{I}_{(N_r-1)/2}\\ 0& \sqrt{2}& 0\\ J_{(N_r-1)/2}& 0& -j{J}_{(N_r-1)/2}\end{array}\right],---<9>$

Wherein representation dimension is unit matrix, representation dimension is switching matrix,

3d) structure 2M × 2M dimension sparse matrix Q _2M, it is expressed as:

$Q_{2M}=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}{I}_M& j{I}_M\\ J_M& -j{J}_M\end{array}\right],---<10>$

Wherein, I _mrepresentation dimension is the unit matrix of M × M.

3e) utilize N _r× N _rdimension sparse matrix and 2M × 2M dimension sparse matrix Q _2M, signal reconstruction matrix Z is carried out to real unitary transformation, obtain real unitary transformation matrix T (Z):

$T\left(Z\right)=Q_{N_r}^{H}Z{Q}_{2M},---<11>$

Wherein, subscript H represents matrix to carry out conjugate transpose;

3f) calculate the covariance matrix of real unitary transformation matrix T (Z): and to this covariance matrix R _tcarry out Eigenvalues Decomposition, obtain signal subspace matrix E _s;

3g) utilize signal subspace matrix E _sconstruct respectively real and signal subspace matrix U _s1, and empty difference signal subspace matrix U _s2:

U _s1＝H ₁E _s，<12>

U _s2=H ₂e _s, <13> wherein, H ₁for reality and transformation matrix: h ₂for the poor transformation matrix of void: $H_2=Q_{N_r-1}^{H}j(\left[\begin{array}{cc}{I}_{N_r-1}& 0\end{array}\right]-\left[\begin{array}{cc}0& I_{N_r-1}\end{array}\right])Q_{N_r},$ (N _r-1) × (N _r-1) sparse matrix of dimension, (N _r-1) × (N _r-1) unit matrix of dimension, the 0th, (N _r-1) null matrix of × 1 dimension, that dimension is N _r× N _rsparse matrix, j represents imaginary unit;

3h) utilize real and signal subspace matrix U _s1with empty difference signal subspace matrix U _s2, structure total least square matrix G:

$G=\left[\begin{array}{c}{U}_{s1}^H\\ U_{s2}^H\end{array}\right]\left[\begin{array}{cc}{U}_{s1}& U_{s2}\end{array}\right]---<14>$

3i) total least square matrix G is carried out to Eigenvalues Decomposition and obtain eigenvectors matrix V _g, then by this eigenvectors matrix V _gresolve into the matrix that four dimensions are P × P, that is:

$V_G=\left[\begin{array}{cc}{V}_{11}& V_{12}\\ V_{21}& V_{22}\end{array}\right],$ Wherein V ₁₁upper left submatrix, V ₁₂upper right submatrix, V ₂₁lower-left submatrix and V ₂₂bottom right submatrix, wherein, P represents the number of high-speed target;

3j) utilize upper right submatrix V ₁₂with bottom right submatrix V ₂₂calculate invariable rotary matrix Ψ ':

${\mathrm{\&Psi;}}^{\&prime;}=-V_{12}{V}_{22}^{-1}---<15>$

Wherein, subscript-1 represents matrix inversion matrix;

3k) invariable rotary matrix Ψ ' is carried out to Eigenvalues Decomposition, obtain P eigenvalue λ _q, q=1,2 ..., P, recycles this P eigenwert and obtains P invariable rotary angle:

β _q＝2arctanλ _q，q＝1,2,…,P<16>

3l) utilize this P invariable rotary angle, try to achieve the angle estimation value of P high-speed target:

${\widehat{\mathrm{\&theta;}}}_q=\arcsin \left[\frac{c{\mathrm{\&beta;}}_q{f}_{\mathrm{\&gamma;}}}{2\mathrm{\&pi;}{d}_r}\right],q=\mathrm{1,2},...,P---<17>$

Wherein, c represents electromagnetic wave propagation speed, d _rrepresent the spacing of receiving antenna.

So far complete multi-carrier frequency MIMO radar to high-speed target angle estimation.

Effect of the present invention further illustrates by following emulation experiment:

1. simulated conditions:

Simulation parameter is as follows: center carrier frequence f ₀=3GHz, pulse repetition time T _r=512 μ s, pulse width T _e=450 μ s, frequency interval Δ f=500KHz, modulating bandwidth B _u=500KHz, number of transmit antennas N _e=16, receiving antenna number N _r=8, transponder pulse number M=64, three high-speed target angles in same Range resolution unit are respectively-5 °, 0 °, 5 °, and speed is respectively 1000m/s, 1000m/s, 1050m/s, and the root-mean-square error RMSE of high-speed target angle estimation is: wherein, E[] expression mathematical expectation, represent the angle estimation of q high-speed target, θ _qrepresent the true angle of q high-speed target.

2. emulation content:

1. adopt the inventive method, under the condition that is 0dB, carry out angle estimation 100 times in signal to noise ratio (S/N ratio), result is as Fig. 2.

2. adopt the existing MUSIC method based on Keystone conversion, under the condition that is 0dB, carry out angle estimation 100 times in signal to noise ratio (S/N ratio), result as shown in Figure 3.

3. under the condition of different signal to noise ratio (S/N ratio)s, adopt the present invention and the existing MUSIC method converting based on Keystone to carry out angle estimation to the high-speed target under simulated conditions, obtain the root-mean-square error result of high-speed target angle estimation, as shown in Figure 4.

3. simulation analysis

Can find out from Fig. 2 Fig. 3, compared with the existing MUSIC method based on Keystone conversion, adopt the present invention to estimate the high speed Coherent Targets of multi-carrier frequency MIMO radar and the angle of incoherent compound target;

As can be seen from Figure 4, adopt the square error of the angle estimation of the high speed Coherent Targets of the present invention to multi-carrier frequency MIMO radar and incoherent compound target to increase and reduce with signal to noise ratio (S/N ratio), show that the present invention is practicable, and the angular properties that the high speed Coherent Targets of the present invention to multi-carrier frequency MIMO radar and incoherent target are mixed is obviously better than the MUSIC algorithm based on Keystone conversion.

Claims (3)

1. a multi-carrier frequency MIMO radar high-speed target angle estimating method, comprises the steps:

(1) utilize multi-carrier frequency MIMO radar to obtain high-speed target echoed signal, and this echoed signal is carried out to channel separation and discrete Fourier transformation DFT, obtain high-speed target signal X;

(2) utilize two-sided correlation matrices transformation TCT algorithm to focus on high-speed target signal X, the high-speed target signal X after being focused on _fTwith focus signal frequency f _γ;

(3) according to the high-speed target signal X after focusing on _fT, utilize invariable rotary at tenth of the twelve Earthly Branches subspace ESPRIT algorithm to estimate high-speed target angle:

3a) utilize the high-speed target signal X after focusing on _fT, structure signal reconstruction matrix Z:

$Z=\left[\begin{array}{cc}{X}_{\mathrm{FT}}& J_{N_r}{X}_{\mathrm{FT}}^{*}{J}_M\end{array}\right]$

Wherein, that dimension is N _r× N _rswitching matrix, J _mbe that dimension is the switching matrix of M × M, subscript * represents matrix to carry out conjugate operation, N _rthe number that represents multi-carrier frequency MIMO radar receiving antenna, M represents multi-carrier frequency MIMO radar transmitted pulse number;

3b) signal reconstruction matrix Z is carried out to real unitary transformation, obtains real unitary transformation matrix T (Z):

$T\left(Z\right)=Q_{N_r}^H{\mathrm{ZQ}}_{2M}$

Wherein, that dimension is N _r× N _rsparse matrix, Q _2Mbe that dimension is the sparse matrix of 2M × 2M, subscript H represents matrix to carry out conjugate transpose;

3c) calculate the covariance matrix of real unitary transformation matrix T (Z): and to this covariance matrix R _tcarry out Eigenvalues Decomposition, obtain signal subspace matrix E _s;

3d) utilize signal subspace matrix E _sconstruct respectively real and signal subspace matrix U _s1, and empty difference signal subspace matrix U _s2:

U _s1＝H ₁E _s

U _s2＝H ₂E _s

Wherein, H ₁for reality and transformation matrix: h ₂for the poor transformation matrix of void: that dimension is (N _r-1) × (N _r-1) sparse matrix, that dimension is (N _r-1) × (N _r-1) unit matrix of dimension, the 0th, dimension is (N _r-1) × 1 null matrix, that dimension is N _r× N _rsparse matrix, j represents imaginary unit;

3e) utilize real and signal subspace matrix U _s1with empty difference signal subspace matrix U _s2, structure total least square matrix G:

$G=\left[\begin{array}{c}{U}_{s1}^H\\ U_{s2}^H\end{array}\right]\left[\begin{array}{cc}{U}_{s1}& U_{s2}\end{array}\right]$

3f) total least square matrix G is carried out to Eigenvalues Decomposition and obtain eigenvectors matrix V _g, then by this eigenvectors matrix V _gresolve into the matrix that four dimensions are P × P, that is:

$V_G=\left[\begin{array}{cc}{V}_{11}& V_{12}\\ V_{21}& V_{22}\end{array}\right],$ Wherein V ₁₁upper left submatrix, V ₁₂upper right submatrix, V ₂₁lower-left submatrix and V ₂₂bottom right submatrix, wherein, P represents the number of high-speed target;

3g) utilize upper right submatrix V ₁₂with bottom right submatrix V ₂₂calculate invariable rotary matrix Ψ ':

${\mathrm{\&Psi;}}^{\&prime;}=-V_{12}{V}_{22}^{-1}$

Wherein, subscript-1 represents matrix inversion matrix;

3h) invariable rotary matrix Ψ ' is carried out to Eigenvalues Decomposition, obtain P eigenvalue λ _q, q=1,2 ..., P, recycles this P eigenwert and obtains P invariable rotary angle:

β _q＝2arctanλ _q，q＝1,2,…,P；

3i) utilize this P invariable rotary angle, try to achieve the angle estimation value of P high-speed target:

${\widehat{\mathrm{\&theta;}}}_q=\arcsin \left[\frac{c{\mathrm{\&beta;}}_q{f}_{\mathrm{\&gamma;}}}{2\mathrm{\&pi;}{d}_r}\right],q=\mathrm{1,2},...,P$

Wherein, c represents electromagnetic wave propagation speed, d _rrepresent the spacing of receiving antenna.

2. a kind of multi-carrier frequency MIMO radar high-speed target angle estimating method according to claim 1, wherein step 3b) in N _r× N _rdimension sparse matrix it is expressed as follows:

Work as N _rduring for even number, $Q_{N_r}=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}{I}_{N_r/2}& j{I}_{N_r/2}\\ J_{N_r/2}& -j{J}_{N_r/2}\end{array}\right],$ Wherein, representation dimension is unit matrix, representation dimension is switching matrix;

Work as N _rduring for odd number, $Q_{N_r}=\frac{1}{\sqrt{2}}\left[\begin{array}{ccc}{I}_{(N_r-1)/2}& 0& j{I}_{(N_r-1)/2}\\ 0& \sqrt{2}& 0\\ J_{(N_r-1)/2}& 0& -j{J}_{(N_r-1)/2}\end{array}\right],$ Wherein representation dimension is unit matrix, representation dimension is switching matrix.

3. a kind of multi-carrier frequency MIMO radar high-speed target angle estimating method according to claim 1, wherein step 3b) in 2M × 2M dimension sparse matrix Q _2M, it is expressed as:

$Q_{2M}=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}{I}_M& j{I}_M\\ J_M& -j{J}_M\end{array}\right]$

Wherein, I _mrepresentation dimension is the unit matrix of M × M, J _mrepresentation dimension is the switching matrix of M × M.