CN102279387B - Method for estimating target arrival angle of multiple input multiple output (MIMO) radar - Google Patents

Abstract

The invention discloses a method for estimating target arrival angle of a multiple input multiple output (MIMO) radar, which mainly solves the problem of large signal processing capacity in the target positioning process of MIMI radar. The method comprises the following steps of: 1) obtaining a virtual array of echo of each receiving antenna by a matched filter bank; 2) constructing a data conversion matrix and a dimension reduction array according to position of transmitting and receiving array; (3) reducing dimension of the virtual array data by the dimension reduction array to obtain an effective array after dimension reduction; 4) constructing two sub-arrays by rotational variance of effective array, and deriving covariance matrix of data; 5) decomposing eigenvalue of covariance matrix to obtain signal sub-spaces corresponding to two sub-arrays; 6) deriving rotational invariant relationship matrix by least square method to obtain arrival angle of target. The dimension reduction matrix form constructed by the method has versatility; the computation quantity is reduced by the dimension reduction of data and the ESPRIT (estimating signal parameter via rotational invariance techniques) algorithm; the computation speed of MIMO radar is increased; and the real-time signal processing of the MIMO radar is made easier.

Description

The target angle of arrival method of estimation of MIMO radar

Technical field

The invention belongs to the Radar Technology field, relate to the angle of arrival estimation of radar, a kind of MIMO radar target angle of arrival method of estimation based on dimensionality reduction ESPRIT algorithm can be used for target localization and tracking specifically.

Background technology

For overcoming the impact of traditional Radar Target Scatter sectional area RCS flicker etc., reference has more into many output MIMO communication systems, the people such as Fishler Eran in 2003 have proposed the concept of MIMO radar, because it in the advantage of the aspects such as target detection, parameter estimation, has obtained various countries scholars' extensive concern.The MIMO radar system of research can be divided into two large classes substantially at present, and a class is the distributed MIMO radar, take the Fishler Eran of New Jersey research institute and the Blum Rick of the U.S. Lehigh of Bethlehem university etc. as representative.The emitting antenna interval of this class MIMO radar is very wide, so that target presents relatively independent reflection characteristic for each emitting antenna, ipsilateral observed object never namely, and then so that the echoed signal of the signal of different transmit antennas emission after the target reflection is incoherent, the flicker of spatial spread RCS of target be can effectively resist like this, thereby detection and the parameter estimation performance of radar improved.It can also be used to estimate to process the microinching target and realize high resolution target location etc. from the Doppler of a plurality of directions in addition.

Another kind of is centralized MIMO radar, is also referred to as relevant MIMO radar.The researcher is mainly take the Stoica Petre of the Li Jian of U.S. Florida university and Sweden Uppsala university as representative, it transmits and receives array and traditional array is similar, antenna spacing is less, can obtain higher resolution and better parameter estimation performance, the microinching target is had higher detection sensitivity, and direct application self-adapting array technique.The waveform optimization of MIMO radar system also presents unique characteristics in addition, can obtain flexibly transmit beam direction figure design.

For emission array and accept the relevant MIMO radar that array is linear array, have higher degree of freedom, higher resolution and the better advantage such as parameter estimation performance, but it has also increased the complexity of system-computed greatly simultaneously.The MIMO radar system of receiving as send out N for a M, the array number of the equivalent virtual array that forms after the process Signal Pretreatment is MN, is M times of traditional phased-array radar, its calculated amount also just increases greatly.Therefore how to reduce its calculated amount and just become the important subject that the MIMO radar is pushed practicality to.Present existing technology mainly contains following several:

Zhang Juan has proposed a kind of signal subspace reconstruct SSR algorithm 531 pages to 533 pages of the 7th phase of the 46th volume in 2010 of Electronics Letters periodical, the method is at first utilized partial data to obtain emission, is received covariance matrix, extract signal phasor, then utilize kronecker to amass to construct total covariance matrix, thereby reduce computation complexity.

Zhang Xiaofei has proposed emission angle and the acceptance angle that a kind of dimensionality reduction Capon method is estimated bistatic MIMO radar 860 pages to 861 pages of the 12nd phase of the 46th volume in 2010 of Electronics Letters periodical, and this method is to pass through restrictive condition

So that just utilized the data of part array element when processing at every turn.

Zhao Yongbo and Xie Rong are these overlapping characteristics for many Virtual arrays position of MIMO, transmitting-receiving is the situation of average line linear array, constructed the dimensionality reduction matrix, adopt respectively again multiple signal classification MUSIC algorithm and polynomial rooting algorithm to estimate DOA, propose in the meeting of Institute of Electrical and Electronics Engineers.

But said method all is the MIMO radar that is even linear array for transmitting-receiving, though and said method reduced to a certain extent operand, but its operand is still unacceptable.

Summary of the invention

The object of the invention is to overcome the deficiency of above-mentioned prior art, a kind of target angle of arrival method of estimation of MIMO radar is proposed, to realize emission or to be accepted as the MIMO radar of Nonuniform Linear Array to the estimation of target DOA, and further computation reduction, the computing velocity of estimating to improve MIMO radar DOA.

For achieving the above object, technical thought of the present invention is: one that limits in emission, the receiving array is even linear array, and another one is random array, and the spacing between any two adjacent array elements is not more than the aperture of even linear array; According to element position structure general data-switching matrix and dimensionality reduction matrix, make the array data behind the dimensionality reduction have rotational invariance; Recycle at last least square signal subspace invariable rotary LS-ESPRIT algorithm and try to achieve the DOA of target.The specific implementation step comprises as follows:

1) with the echoed signal of each receiving antenna by a matched filter banks, isolate the signal of corresponding each transmission channel, the receive data X (t) of the virtual array that to obtain an array number be MN, wherein M, N are respectively emission, reception array number;

2) according to the emission, receiving array the position, construction data transition matrix E and dimensionality reduction matrix Q:

$E={[e_{u_1},e_{u_2},...,e_{u_{\mathrm{MN}}}]}_{\mathrm{MN}\×N_e}^T---1)$

Q＝E(E ^HE) ^-1 2）

Wherein, N _eThe effective array number of expression MIMO radar virtual array,

Represent u _kIndividual element is 1 N _eThe vector of unit length of * 1 dimension, u _k=u _{R, n}+ u _{T, m}-1, m=1,2 ..., M, n=1,2 ..., N, k=1,2 ..., MN, u _{T, m}And u _{R, n}The position coordinates that represents respectively m emitting antenna and n receiving antenna, T, H is representing matrix transposition and conjugate transpose respectively;

3) utilize dimensionality reduction matrix Q that virtual array data X (t) is carried out dimension-reduction treatment, obtain the effective array data behind the dimensionality reduction: $\stackrel{\‾}{X}\left(t\right)=Q^{H}X\left(t\right);$

4) calculate effective array data

Covariance matrix:

Front N by effective array _e-1 array element and rear N _e-1 array element consists of two submatrixs;

5) covariance matrix R is carried out Eigenvalues Decomposition and try to achieve signal subspace U _s, and try to achieve two submatrix respective signal subspace U _S1And U _S2, both satisfy invariable rotary relation: U _S2=U _S1Ψ, wherein the invariable rotary relational matrix of Ψ for finding the solution;

6) utilize least square method to find the solution,

Then Ψ is carried out feature decomposition, by P eigenwert

Obtain the DOA of P corresponding signal, wherein, P is the single interior target number of same distance, k=1 ..., P.

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

(1) method of existing MIMO radar computation reduction all is to study for launching, receive the situation that is even linear array, and mode is fairly simple, and when the arrangement mode of array changed, the form of dimensionality reduction matrix was no longer applicable, and method can lose efficacy; And array format of the present invention is relatively loose, only need to launch, in the receiving array one gets final product for even linear array, the form of dimensionality reduction matrix is along with array shape and array number is different, the structure expression formula is constant, has certain versatility, and the transmitting-receiving array is the situation of random array, the data transformation matrix is applicable too.

(2) the dimension-reduction treatment method of existing MIMO radar MUSIC, CAPON super-resolution algorithms of adopting behind dimensionality reduction still need to carry out the search of angle dimension more, and operand is still very large.And disposal route of the present invention adopts the ESPRIT algorithm behind Data Dimensionality Reduction, does not need to carry out angle searching, and operand reduces greatly, and then has improved arithmetic speed.

Description of drawings

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

Fig. 2 is emission array number M=5 among the present invention, receives MIMO radar array position, Virtual array position and the effective element position schematic diagram of array number N=4;

Fig. 3 is with the present invention and other three kinds of DOA algorithm for estimating performance comparison diagram to the target DOA estimation of MIMO radar;

Fig. 4 is that transmitting-receiving array element is 10 MIMO radar array position, Virtual array position and effective element position schematic diagram among the present invention.

Embodiment

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

Step 1 is carried out matched filtering to received signal, obtains virtual receiving array data.

MIMO radar system of the present invention is comprised of M emitting antenna, a N receiving antenna, wherein in emission, the receiving array is even linear array, another one is the aperture that the spacing between random array and any two adjacent array elements is not more than even linear array, during the present invention realizes, provided M=5, N=4 and M=10, two examples of N=10.The position coordinates of m emitting antenna and n receiving antenna is respectively l _{T, m}=u _{T, m}D, m=1,2 ..., M and l _{R, n}=u _{R, n}D, n=1,2 ..., N), u wherein _{T, m}And u _{R, n}Be integer, d is that array element distance is made as half-wavelength, and M antenna launched a plurality of arrowbands orthogonal signal simultaneously, can extract signal corresponding to each transmission channel at each receiving cable by matched filter banks, thereby the virtual array that to obtain an array number be MN, its element position is:

{l _k}＝{l _T,m+l _R,n|m＝1,2,...,M;n＝1，2,…,N} <1>

K=1 wherein, 2 ..., MN;

Suppose in same range unit, to have P incoherent target, wherein the arrival θ of k target _k, k=1 ..., P represents, the output x of m the matched filter corresponding with m transmission channel in n receiving cable _Mn, m=1 ... M, n=1 ..., N represents, the output of matched filter banks can be expressed as in all receiving cables like this:

$X\left(t\right)=\mathrm{As}\left(t\right)+N\left(t\right)=\underset{k=1}{\overset{P}{\mathrm{\&Sigma;}}}{a}_r\left({\mathrm{\&theta;}}_k\right)\&CircleTimes;a_t\left({\mathrm{\&theta;}}_k\right)s_k\left(t\right)+N\left(t\right)---<2>$

Wherein

Be the array manifold matrix of NM * P dimension, a _r(θ _k)=[exp (j π u _{R, 1}Sin θ _k) ..., exp (j π u _{R, N}Sin θ _k)] ^TFor receiving steering vector, a _t(θ _k)=[exp (j π u _{T, 1}Sin θ _k) ..., exp (j π u _{T, M}Sin θ _k)] ^TBe the emission steering vector. Be that Kronecker is long-pending, T represents matrix transpose operation.S (t)=[s ₁(t), s ₂(t) .., s _P(t)] represent to transmit vector, N (t) is the zero-mean of NM * 1 dimension, and covariance matrix is σ ²The white complex gaussian noise of I.

Step 2, structure array transition matrix and Data Dimensionality Reduction matrix.

Virtual array for most of MIMO radars, the position of many equivalent array elements all overlaps, as shown in Figure 4, when the transmitting-receiving array is the even linear array of 10 array elements, effectively element position only is M+N-1=19, only be about Virtual array and count 1/5 of MN=100, the Virtual array data that therefore will be positioned at same position are carried out suitable merging, can greatly reduce the computation complexity of MIMO radar.

Suppose the effective array number N of MIMO radar virtual array _eRepresent, then can construct a MN * N _eThe transition matrix of dimension

$E={[e_{u_1},e_{u_2},...,e_{u_{\mathrm{MN}}}]}_{\mathrm{MN}\&times;N_e}^T---<3>$

U wherein _k=u _{R, n}+ u _{T, m}-1, m=1,2 ..., M, n=1,2 ..., N, k=1,2 ..., MN, and U _kIndividual element is 1 N _eThe vector of unit length of * 1 dimension, then MIMO radar vectoring vector a (θ _k) can be expressed as:

$a\left({\mathrm{\&theta;}}_k\right)=a_r\left({\mathrm{\&theta;}}_k\right)\&CircleTimes;a_t\left({\mathrm{\&theta;}}_k\right)=\mathrm{Eb}\left({\mathrm{\&theta;}}_k\right)---<4>$

Wherein, b (θ _k)=[exp (j π sin θ _k) ..., exp (j π 2sin θ _k), exp (j π N _eSin θ _k)] ^T, according to＜4〉and formula structure dimensionality reduction matrix Q=E (E ^HE) ^-1So that MIMO radar vectoring vector a (θ _k) be converted to:

Q ^H·a(θ _k)＝(E ^HE) ^-1E ^HEb(θ _k)＝b(θ _k) <5>

From＜5〉can find out that the data transformation of the virtual array of MIMO radar is a N the formula _eThe data vector of * 1 dimension, and the array data after the conversion keeps rotational invariance.

Step 3 is carried out dimension-reduction treatment to receive data.

With Q substitution＜2〉Shi Kede

$\stackrel{\&OverBar;}{X}\left(t\right)=Q^{H}X\left(t\right)=\underset{k=1}{\overset{P}{\mathrm{\&Sigma;}}}{Q}^H\mathrm{Eb}\left({\mathrm{\&theta;}}_k\right)s_k\left(t\right)+Q^{H}N\left(t\right)$ $---<6>$

$=\underset{k=1}{\overset{P}{\mathrm{\&Sigma;}}}b\left({\mathrm{\&theta;}}_k\right)s_k\left(t\right)+\stackrel{\&OverBar;}{N}\left(t\right)$

Wherein,

For the noise behind the dimensionality reduction, from＜6〉formula as seen, be that an array number is N through the data equivalence after the dimension-reduction treatment _eReceiving array.

Step 4 is divided into two submatrixs with the data behind the dimensionality reduction, and utilizes two submatrix data to ask covariance matrix.

Because it is even linear array that the front has been limited in emission, the receiving array one, can guarantee that so the effective array after the dimension-reduction treatment is even linear array, then utilizes the front N of effective array _e-1 array element data

With rear N _e-1 array element data

Form two submatrixs, try to achieve the covariance matrix R of data.

Step 5 is found the solution signal subspace corresponding to two submatrixs.

Covariance matrix R is carried out Eigenvalues Decomposition try to achieve signal subspace U _s, and get respectively the corresponding signal subspace U of row acquisition corresponding to two submatrixs _S1And U _S2, specifically realize according to the following procedure: covariance matrix R is carried out Eigenvalues Decomposition obtain N _eIndividual eigenwert and N _eIndividual eigenwert characteristic of correspondence vector is got N _eP eigenwert and this P eigenwert characteristic of correspondence vector maximum in the individual eigenwert form matrix U _s, get U _sIn front N _e-1 row consists of submatrix signal subspace U _S1, get U _sIn rear N _e-1 row consists of submatrix signal subspace U _S2Both satisfy invariable rotary relation: U _S2=U _S1Ψ, wherein the invariable rotary relational matrix of Ψ for finding the solution.

Step 6 utilizes least square method to find the solution the angle of arrival of signal.

Utilize least square method to find the solution the invariable rotary relational matrix

Then it is carried out feature decomposition, obtain P eigenwert K=1 ..., P just can obtain the angle of arrival of P corresponding target

Wherein

Representative

Phase place, k=1 ..., P.

Effect of the present invention further specifies by following Calculation Simulation:

Emulation content 1: the structure of transition matrix and dimensionality reduction matrix;

Simulated conditions: suppose that the MIMO radar array is 54 arrays of receiving, minimum array element distance

The coordinate of emission, receiving array is respectively u _{T, m}={ 1,2,4,7,9} and u _{R, n}={ 1,2,3,4}.

Simulation result: obtain virtual array position and effective element position as shown in Figure 2, effectively array number is 12 as seen from Figure 2, and 20 * 12 dimension matrixes of conversion are as follows:

And then must the dimensionality reduction matrix be:

From Fig. 2 and formula＜7 and formula＜8 can find out, the structure practicability and effectiveness of transition matrix provided by the invention and dimensionality reduction matrix, can guarantee that the data matrix behind the dimensionality reduction keeps rotational invariance, and utilize the dimensionality reduction matrix of Zhao Yong ripple and Xie Rong method construct, the data behind the dimensionality reduction no longer have rotational invariance.

Emulation content 2: Performance Ratio is than emulation;

Simulated conditions: suppose that the MIMO radar array is 54 and receives array, three incoherent targets are arranged, the angle of arrival is respectively-20 °, and 5 ° and 30 °, fast umber of beats L=100, the root-mean-square error that definition DOA estimates is

Angle value for the estimation of the target angle of arrival.Utilize respectively the SSR algorithm of the inventive method, Zhang Juan, the dimensionality reduction CAPON algorithm of Zhang Xiaofei, the MUSIC algorithm that is designated as RD CAPON algorithm and full degree of freedom carries out emulation relatively, does 500 Monte Carlo experiments.

Simulation result: the result that target angle of arrival estimated performance changes with signal to noise ratio (S/N ratio) as shown in Figure 3.As can be seen from Figure 3, performance of the present invention is better than RD CAPON algorithm, at SNR〉suitable with the SSR algorithm performance during high s/n ratio of 5dB, but the SSR algorithm lost efficacy during low signal-to-noise ratio.As seen the present invention is in computation reduction, and estimated performance there is no decline.Although the RMSE of full degree of freedom MUSIC algorithm is minimum, estimated performance is best, and its complexity is higher than the present invention.

Emulation content 3: computation complexity relatively;

Simulated conditions: suppose that MIMO radar system transmitting-receiving array number is 10, as shown in Figure 4, target number P=3 is when fast umber of beats L=100 and angle searching number n=500.

Simulation result: table 1 has been listed the present invention and existing SSR, RD CAPON, and the computation complexity of the MUSIC algorithm of the full degree of freedom of MIMO radar.

The computation complexity of table 1 the present invention and existing algorithm

As can be seen from Table 1, complexity of the present invention is O{4.0 * 10 ⁴, and the complexity of other three kinds of algorithms is all in O{2.2 * 10 ⁵About, the present invention and other three kinds of algorithms compare, and computation complexity is minimum, reduces near an order of magnitude than other three kinds of algorithms.And M, N are larger, and overlapping Virtual array number is more, and algorithm complex reduces more.As seen the present invention can reduce the operand of MIMO Radar Signal Processing greatly, improves the computing velocity that the target angle of arrival is estimated.

Claims (3)

1. the target angle of arrival method of estimation of a MIMO radar comprises following process:

1) with the echoed signal of each receiving antenna by a matched filter banks, isolate the signal of corresponding each transmission channel, the receive data X (t) of the virtual array that to obtain an array number be MN, wherein M, N are respectively emission, reception array number;

2) according to the emission, receiving array the position, construction data transition matrix E and dimensionality reduction matrix Q:

Q＝E(E ^HE) ^-1 2）

Wherein, N _eThe effective array number of expression MIMO radar virtual array,

Represent u _kIndividual element is 1 N _eThe vector of unit length of * 1 dimension, u _k=u _{R, n}+ u _{T, m}-1,, m=1,2 ..., M, n=1,2 ..., N,, k=1,2 ..., MN, u _{T, m}And u _{R, n}The position coordinates that represents respectively m emitting antenna and n receiving antenna, T, H is representing matrix transposition and conjugate transpose respectively;

3) utilize dimensionality reduction matrix Q that virtual array data X (t) is carried out dimension-reduction treatment, obtain the effective array data behind the dimensionality reduction:

4) calculate effective array data

Covariance matrix:

Front N by effective array _e-1 array element and rear N _e-1 array element consists of two submatrixs;

5) covariance matrix R is carried out Eigenvalues Decomposition and try to achieve signal subspace U _s, and try to achieve two submatrix respective signal subspace U _S1And U _S2, both satisfy invariable rotary relation: U _S2=U _S1Ψ, wherein the invariable rotary relational matrix of Ψ for finding the solution;

6) utilize least square method to find the solution,

Then Ψ is carried out feature decomposition, by P eigenwert

Obtain the DOA of P corresponding signal, wherein, P is the single interior target number of same distance, k=1 ..., P.

2. the target angle of arrival method of estimation of MIMO radar according to claim 1, wherein the described dimensionality reduction matrix Q that utilizes of step 3) carries out dimension-reduction treatment to virtual array data X (t), carries out as follows:

3.1) virtual array data X (t) is launched

Wherein,

Be the array manifold matrix of NM * P dimension,

a _r(θ _k)=[exp (j π u _{R, 1}Sin θ _k) ..., exp (j π u _{R, N}Sin θ _k)] ^TBe the reception steering vector,

a _t(θ _k)=[exp (j π u _{T, 1}Sin θ _k) ..., exp (j π u _{T, M}Sin θ _k)] ^TBe emission steering vector, θ _kBe the angle of arrival of k target,

That Kronecker is long-pending, s (t)=[s ₁(t), s ₂(t) ..., s _P(t)] represent to transmit vector, s _k(t) k of expression transmits, and N (t) is the zero-mean of NM * 1 dimension, and covariance matrix is σ ²The white complex gaussian noise of I;

3.2) according to data-switching matrix E MIMO radar vectoring vector a (θ _k) be expressed as

Wherein, b (θ _k)=[exp (j π sin θ _k), exp (j π 2sin θ _k) ..., exp (j π N _eSin θ _k)] ^T

3.3) dimensionality reduction matrix Q substitution formula 3) and the receive data of effective array

Wherein,

Represent respectively the noise after the dimension-reduction treatment.

3. the target angle of arrival method of estimation of MIMO radar according to claim 1, the wherein described two submatrix respective signal subspace U that try to achieve of step 5) _S1And U _S2, carry out as follows:

5.1) covariance matrix R is carried out Eigenvalues Decomposition obtain N _eIndividual eigenwert and N _eIndividual eigenwert characteristic of correspondence vector;

5.2) get N _eP eigenwert and this P eigenwert characteristic of correspondence vector maximum in the individual eigenwert form matrix U _s

5.3) get U _sIn front N _e-1 row consists of submatrix signal subspace U _S1, get U _sIn rear N _e-1 row consists of submatrix signal subspace U _S2

Images