CN107064892A - MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary - Google Patents

MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary Download PDF

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CN107064892A
CN107064892A CN201611003187.6A CN201611003187A CN107064892A CN 107064892 A CN107064892 A CN 107064892A CN 201611003187 A CN201611003187 A CN 201611003187A CN 107064892 A CN107064892 A CN 107064892A
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tensor
subspace
angle estimation
matrix
mimo radar
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CN107064892B (en
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文方青
陈伟国
李修权
盛冠群
李飞涛
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Yangtze University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

Abstract

The invention discloses a kind of MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary, it receives three rank tensor models of data by building, and then the high-order covariance tensor model of tensor data is built, fully excavate the inside dependency structure of array signal；Then HOSVD is carried out to tensor data, and builds new signal subspace, so as to obtain high-precision noise subspace；The invariable rotary characteristic of array data is finally utilized, the DOD and DOA of pairing are obtained by the method and method of Lagrange multipliers of constrained optimization, without further carrying out pairing calculating.MIMO radar angle estimation algorithm of the present invention, it utilizes the inside dependency structure for receiving signal, angle estimation precision is higher, so as to obtain more accurate target DOD and DOA, more reasonably referred to further to provide the relevant treatment for detecting target, and without spectrum peak search, computation complexity is relatively low.

Description

MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary
Technical field
The present invention relates to a kind of Radar Signal Processing Technology, more particularly to one kind is based on tensor subspace and rotates not The MIMO radar angle estimation algorithm of change.
Background technology
Multiple-input and multiple-output (Multiple-input Multiple-output, MIMO) radar is a kind of brand-new system Radar system, it synchronously launches and received signal using multiple array elements.Compared to traditional phased array radar system, MIMO radar exists There is potential advantage in terms of resolution ratio, anti-fading property, identifiability and suppression noise.Array element is received and dispatched according to MIMO radar Position distribution difference, MIMO radar can be divided into two classes：Count MIMO radar and co-located MIMO radar.Wherein, unite The transmitting-receiving array element configuration of MIMO radar sample distribution formula is counted, it can effectively suppress the scintillation effect of target；Co-located MIMO radar In transmitting array element and receive array element often at a distance of relatively near, this radar can obtain high-precision angle on target estimation.This hair Bright to be primarily upon bistatic MIMO radar, it is the important class in co-located radar.
Joint ripple digression (Direction of Departure, DOD) and direction of arrival (Direction of Arrival) Estimation is one of task of bistatic MIMO radar target positioning, and this problem has been widely studied at present.There is crowd at present Many DOD and DOA estimations, typical represent has multiple spectral peak classification (Multiple Signal Classification, MUSIC) Algorithm, parameter Estimation (the Estimation Method of Signal Parameters via based on ESPRIT Rotational, ESPRIT) algorithm, propagation operator (Propagator Method) algorithm, high-order Subspace Decomposition (Higher Order Singular Value Decomposition, HOSVD) algorithm, parallel factor (Parallel Factor, PARAFAC) algorithm, algorithm for estimating based on rarefaction representation etc..But above-mentioned algorithm is only applicable to MIMO under the conditions of ideal array Radar angular is estimated, in Practical Project, inconsistent due to each array element amplifier gain, and array received signal, which can exist, to be increased Benefit-phase error (Gain-Phase Error, GPE).Under the influence of GPE, traditional angle estimation algorithm performance can decline, It is even entirely ineffective when serious.GPE problems in MIMO radar have caused the attention of some scholars, have there is one at present Scholar is divided to propose related solution annual reporting law.Small jasmine of Liu et al. proposes a kind of MUSIC-Like algorithms, and (Liu little Li, Liao Gui life are biradical Ground MIMO radar Multi-target position and amplitude phase error estimation [J] electronic letters, vols, 2011,39 (3):596-601), but the algorithm only The related data of first transmitting-receiving array element is make use of, angle estimation aperture is not utilized effectively.And the side of the calculation down-sampling iteration Method and MUSIC thoughts carry out angle estimation, and computation complexity is high；Li et al. proposes a kind of dimensionality reduction MUSIC (RD-MUSIC) algorithm (J.Li,X.Zhang,R.Cao,et al.Reduced-dimension music for angle and array gain- phase error estimation in bistatic MIMO radar[J],IEEE Communications Letters, 2013,17(3):443-446), the algorithm is insensitive to the position of calibrated array element, and is applied to nonuniform noise, but the calculation Method needs to carry out spectrum peak search, thus its computation complexity is high, and can have grid mismatch problem；Guo et al. proposes a kind of ESPRIT-Like algorithms (Y.D.Guo, Y.S.Zhang, N.N.Tong.Esprit-like angle estimation for bistatic MIMO radar with gain and phase uncertainties[J],Electronics Letters, 2011,47(17):996-997), it uses the rotational invariance of array to carry out angle estimation, and computation complexity is low；RD-MUSIC Algorithm and ESPRIT algorithms carry out parameter Estimation using the subspace for receiving signal, and it needs to carry out characteristic value to receiving data Decompose (Eigenvalue Decomposition, EVD), computation complexity is higher, Chen et al. proposes a kind of calculation without EVD Method --- PM-Like algorithms (C.Chen, X.F.Zhang.Joint angle and array gain-phase errors estimation using PM-like algorithm for bistatic MIMO radar[J],Circuits System Signal Process,2013,32(3):1293-1311), it is lower compared to ESPRIT-Like algorithm computation complexities；Li etc. People proposes a kind of improved ESPRIT (I-ESPRIT) algorithm (J.Li, M.Jin, Y.Zheng, G.Liao, Transmit and receive array gain phase error estimation in bistatic MIMO radar[J],IEEE Antennas and Wireless Propagation Letters,2015,14:32-35), the algorithm to GPE without carrying out Estimation, computation complexity is relatively low.But I-ESPRIT only make use of two calibrated transmittings and receive the reception data of array element, its Angle estimation estimation procedure is to noise-sensitive, and the algorithm needs the parameter estimated by extra pairing；To utilize number of arrays According to inside Multi-attributes, Li et al. proposes a kind of PARAFAC-Like algorithms (J.Li, X.F.Zhang, X.Gao.A joint scheme for angle and array gain phase error estimation in bistatic MIMO radar [J],IEEE Geoscience and Remote Sensing Letters.2013,10(6):1478-1482), but the algorithm Firstly the need of the GPE of estimation array, and estimate that GPE process errors have accumulative effect, cause GPE estimations often inaccurate, from And influence the precision of its angle estimation.
The content of the invention
For these reasons, it is necessary to provide a kind of angle estimation precision higher and without spectrum peak search, computation complexity The relatively low MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary.
The present invention provides a kind of MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary, described to be based on The MIMO radar angle estimation algorithm of tensor subspace and invariable rotary comprises the following steps：
S1, the three rank tensor models for building target echo signal, the high-order for receiving signal is built by tensor model structure Covariance tensor model；
S2, Higher-order Singular value decomposition is carried out to high-order covariance tensor model, and build new signal subspace, obtain high The noise subspace of precision；
S3, the invariable rotary model for constructing array data, estimate according to the method for constrained optimization and method of Lagrange multipliers Go out GPE relevant information, obtain the DOD and DOA of pairing；
Wherein, the function of invariable rotary characteristic is as follows：
In formula,Bt1=At1⊙(CrAr), Bt2=At2⊙(CrAr), Br1=(CtAt)⊙Ar1And Br2=(CtAt)⊙Ar2, and At1And At2A is represented respectivelytPreceding M-1 rows with after M-1 rows, Ar1And Ar2A is represented respectivelyrPreceding N-1 rows and rear N-1 rows.
MIMO radar angle estimation algorithm of the present invention based on tensor subspace and invariable rotary, it is connect by building Three rank tensor models of data are received, and then build the high-order covariance tensor model of tensor data, array signal is fully excavated Internal dependency structure；Then HOSVD is carried out to tensor data, and builds new signal subspace, so as to obtain high-precision make an uproar Phonon space；The invariable rotary characteristic of array data is finally utilized, is obtained by the method and method of Lagrange multipliers of constrained optimization The DOD and DOA of pairing are taken, without further carrying out pairing calculating.MIMO radar angle estimation algorithm of the present invention, it is utilized The inside dependency structure of signal is received, angle estimation precision is higher, so that more accurate target DOD and DOA is obtained, to enter one Walk to provide the relevant treatment for detecting target and more reasonably refer to, and without spectrum peak search, computation complexity is relatively low.
Brief description of the drawings
Fig. 1 is bistatic MIMO radar angle estimation schematic diagram；
Fig. 2 is the MIMO radar angle estimation algorithm of the present invention based on tensor subspace and invariable rotary in SNR= Angle estimation scatter diagram during 5dB；
Fig. 3 is the MIMO radar angle estimation algorithm of the present invention based on tensor subspace and invariable rotary in SNR= The scatter diagram of angle estimation during 15dB；
Fig. 4 is that the MIMO radar angle estimation algorithm of the present invention based on tensor subspace and invariable rotary is calculated with other The RMSE of method compares；
Fig. 5 is that the MIMO radar angle estimation algorithm of the present invention based on tensor subspace and invariable rotary is calculated with other The PSD contrasts of method；
Fig. 6 is the MIMO radar angle estimation algorithm of the present invention based on tensor subspace and invariable rotary in difference RMSE performances under the conditions of SNR and L；
Fig. 7 is the MIMO radar angle estimation algorithm of the present invention based on tensor subspace and invariable rotary in difference PSD performances under the conditions of SNR and L.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples The present invention is further elaborated, it will be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and It is not used in the restriction present invention.
The present invention provides a kind of MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary, described to be based on The MIMO radar angle estimation algorithm of tensor subspace and invariable rotary comprises the following steps：
S1, the three rank tensor models for building target echo signal, the high-order for receiving signal is built by tensor model structure Covariance tensor model；
S2, Higher-order Singular value decomposition is carried out to high-order covariance tensor model, and build new signal subspace, obtain high The noise subspace of precision；
S3, the invariable rotary model for constructing array data, estimate according to the method for constrained optimization and method of Lagrange multipliers Go out GPE relevant information, obtain the DOD and DOA of pairing.
Specifically, being firstly introduced into three Operation Definitions on tensor model：
Define 1 (tensor expansion)：OrderFor a N rank tensor, X mould-n (n=1 ..., N) matrix expansion table It is shown as [X]n.Wherein, positioned at tensor X (i1,…,in) position element turn into be located at matrix [X]n(in, the j) element at place,And
Define 2 (mould-n tensors and matrix products)：Define N rank tensorsWith matrixMould-n products For YX=X×nA, whereinAnd
Define 3 (tensor modular multiplication properties)：N rank tensorsModular multiplication property mainly have following two：
X×n·A×mB=X×m·B×n·A,m≠n
X×n·A×mB=X×n(BA) expression formula 1
The model that bistatic MIMO radar joint DOD and DOA involved in the present invention estimates is as shown in Figure 1.Assuming that day Linear system system is made up of M transmitting array element and N number of reception array element, both at linear array, and receive and dispatch the spacing of array element be λ/ 2, λ be the wavelength of transmitting carrier wave.Assuming that there is GPE, m-th (m=1,2 ..., M) transmitting battle array with receiving array in emission array Member GPE beThe GPE that n-th (n=1,2 ..., N) receives array element isWithout loss of generality, it is assumed that before emission array mtIndividual (1≤mt≤ M) individual array element and receiving array preceding nrIndividual (1≤nr≤ N) individual array element is calibrated, i.e.,If K incoherent point targets are located at radar array far-field position, and k-th (1 ≤ k≤K) orientation of point target isWhereinFor the DOD of target relative transmission aerial array, θkFor target relative to The DOA of receiving array.In addition, it is assumed that the baseband waveform of transmitting array element is mutually orthogonal encoded signal, then receiving array is matched Filtered data signal is represented by
X=[CtAt⊙CrAr]ST+ N=AST+ N expression formulas 3
In above formula,For direction of the launch matrix,For transmitting steering vector, its m (m=1 ..., M) individual element is To receive direction matrix,To receive steering vector, its n-th (n=1 ..., N) individual element isCt=Diag { ctTo launch GPE matrixes, Diag { } is that diagonalization is operated,For transmitting GPE vectors；Cr=Diag { ctTo receive GPE matrixes, To receive GPE vectors；For target RCS coefficients, and assume the RCS of all targets in L reception Swerling-II (fast to rise and fall) model is met in snap；N is the noise matrix received, and assumes to meet Gaussian noise model；The virtual direction matrix that dimension is MN × K can be considered as, wherein ⊙ is Khatri-Rao products (press lek Kronecker product),Virtual steering vector can be considered as,Table Show Kronecker product.Expression formula 3 can be counted as receiving the matrix model of signal, can be by using Tucker tensor models The column signal re of reception is into the tensor X that an exponent number is that 3, order is K, the element of its (m, n, l) individual position
In above formula, At(m, k) represents AtIn (m, k) individual element, other method for expressing are similar.
Make R to receive the covariance matrix of signal, in actual engineering, it can estimate R ≈ with reception sample XXH/L.Because R is a Hermitian matrix, therefore Eigenvalues Decomposition (Eigenvalue can be carried out to it Decomposition, EVD)
Wherein, Σ=Diag (λ1,...,λMN), and by λ1≥…≥λK＞ λK+1=...=λMNArrangement, ΣsRepresent by preceding K Individual big eigenvalue cluster into diagonal matrix, UsFor the corresponding characteristic vector of corresponding characteristic value, it is considered signal Subspace；ΣnRepresent by remaining MN-K less eigenvalue clusters into diagonal matrix, UnIt is corresponding for corresponding characteristic value Characteristic vector, it can be considered as noise subspace.RD-MUSIC algorithms and ESPRIT algorithms are exactly on the basis of subspace Progress parameter Estimation, but the subspace limited precision that the Subspace Decomposition based on matrix model is obtained, therefore parameter Estimation Performance can be further elevated.The present invention obtains corresponding subspace using the method for tensor covariance, and specific principle is as follows. The tensor covariance model of the reception signal of 4 ranks is built first, and its (m, n, p, q) individual element is
Similarly, R is a Hermitian tensor, and its HOSVD process can be expressed as
R=G×1·U1×1·U2×2·U3×3·U4Expression formula 7
In above formulaFor core tensor,WithFor 4 Individual unitary matrice, it is respectively the left singular matrix of R n- moulds (n ∈ { 1,2,3,4 }) expansion, i.e.,Due to R's Order is K, therefore a new covariance tensor R can be built with the HOSVD of truncations
Rs=Gs×1·U1s×1·U2s×2·U3s×3·U4sExpression formula 8
Wherein,For the component of signal of core tensor, UnsFor UnK in (n ∈ { 1,2,3,4 }) The corresponding characteristic vector of big characteristic value.By GsBring expression formula 8 into, according to defining 2, can obtain
According to defining 3, while the same R of matrix R in expression formula 5sRelation, a new signal subspace can be built empty Between matrix Rs, its building method is
Because R can often be approached by K principal component amount, i.e.,Expression formula 10 is carried it into, can be obtained
Because R is Hermitian tensors, therefore is hadSo, to RsEVD decomposition is carried out, can be obtained Obtain a new signal subspace Es, it is
Due to UsIdentical subspace is opened into virtual direction matrix A, therefore is caused in the presence of a non-singular matrix T
Es=AT=[CtAt⊙CrAr] T expression formulas 13
That is EsIdentical subspace is opened into A.
Consider the invariable rotary characteristic of uniform linear array, angle estimation is carried out using the special construction of array.Make At1 And At2A is represented respectivelytPreceding M-1 rows and rear M-1 rows, Ar1And Ar2A is represented respectivelyrPreceding N-1 rows and rear N-1 rows.Define Bt1= At1⊙(CrAr), Bt2=At2⊙(CrAr), Br1=(CtAt)⊙Ar1And Br2=(CtAt)⊙Ar2, from ESPRIT principle, There is following invariable rotary characteristic in array
WhereinSimilarly, E is madet1、Et2、Et1 And Et2Respectively use similar Bt1、Bt2、Br1And Br2Method from EsThe matrix of middle extraction, then its meet following relation
C in above formulat1=Diag (ct1), Ct2=Diag (ct2), Cr1=Diag (cr1), Cr2=Diag (cr2), wherein ct1、 ct2Respectively ctPreceding M-1 rows and rear M-1 rows, cr1、cr2Respectively crPreceding N-1 rows and rear N-1 rows, INRepresentation dimension is N × N Tie up unit matrix.Similar to Bt1With Bt2、Br1With Br2Invariable rotary relation, E can be obtainedt1With Et2、Et1With Et2Rotation not Change relation
Wherein, Ψt=T-1ΦtT, Ψr=T-1ΦrT.Wherein ΨtWith ΨrDOD containing target and DOA information, but due to expression formula 15 respectively Middle Ct12, Cr12, ΨtWith ΨrIt is unknown, thus expression formula 15 is without specific solution.But the solution of expression formula 15 can be converted into as Next constrained optimization problem
Wherein, e1=[1,01×(M-1)N]T, e2=[1,01×M(N-1)]T, 01×(M-1)NFor row that dimension is 1 × (M-1) N-dimensional to Amount.The least square solution of expression formula 16 is
Wherein,Represent pseudo-inverse operation.Bring expression formula 17 into expression formula 16, p can be obtainedtAnd ptEstimation
In formula,Due to
In above formula, tr { } is to ask mark computing,Accumulated for Hadamard.OrderAnd bring expression formula 19 into expression formula 18, it can obtain
Using method of Lagrange multipliers, it can obtain
Work as ptAnd prAfter being estimated, expression formula 17 is carried it into, you can obtain ΨtAnd ΨrEstimation.Due to ΨtWith ΨrIt is diagonal matrix, therefore, by carrying out Eigenvalues Decomposition to it, by taking phase, and sine of negating to characteristic value, you can Obtain the DOD and DOA of target.Due to ΨtAnd ΨrThere is identical characteristic vector, therefore the DOD obtained and DOA is automatic matching 's.
The present invention is carried out to the MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary proposed Substantial amounts of emulation experiment, Fig. 1 is bistatic MIMO radar angle estimation schematic diagram.
Assume that K=3 target is in far field in emulation, its DOA and DOD are respectivelyWithLaunch the number M=8 of array element in emulation experiment, receive array element Several number N=8, both at uniform linear array, array element spacing is λ 2, and L is snap number.Launch GPE vectors ct= [1,1,1,1.21ej0.12,1.10ej1.35,0.89ej0.98,1.35ej2.65,0.92ej1.97], it is c to receive GPE vectorsr=[1,1, 0.94ej1.12,1.23ej2.35,1.49ej0.58,0.75ej0.65,0.52ej1.22,2.10ej0.89].Signal to noise ratio in emulation (signal-to-noise ratio, SNR) is defined as SNR=10log10(||X-N||2/||N||2) [dB], to all algorithms Carry out 200 Monte Carlo simulations.The algorithm for proposing algorithm contrast with the present invention has ESPRIT-Like algorithms, PM-Like to calculate Method, PARAFAC-Like algorithms, I-ESPRIT algorithms and Cramér-Rao lower bound (Cram é r-Rao Bound, CRB).
Accompanying drawing 2 and accompanying drawing 3 carry estimation scatter diagram of the algorithm in SNR=5dB and SNR=15dB, wherein L for the present invention =200.In figure, ' X ' represents the true bearing of target, and ' ' represents the estimate of inventive algorithm.Can from simulation result Go out, the DOD and DOA of target can effectively be estimated by carrying algorithm, and can accurately match estimated angle, and SNR is higher, Estimated accuracy is higher.
For comparison of the carried algorithm relatively more of the invention compared with algorithm estimated accuracy, the precision of angle estimation is missed with root mean square Poor (root mean squared error, RMSE) and success detection probability (Probability of Successful Detection, PSD) evaluate, wherein RMSE is defined as：
In formulaWithRespectively obtained in ith Monte Carlo simulation to θkWithEstimation；W is the number of times that correctly detects, if in a Monte Carlo simulation DOD and DOA of each target with truly DOD and the DOA absolute value of difference be both less than 0.5 °, then record this emulation and successfully detect.101
Accompanying drawing 4 and accompanying drawing 5 sets forth carried algorithm with the RMSE performances of other algorithms and the comparison of PSD performances, its Middle L=200.From simulation result, with SNR increase, the estimated accuracy of all algorithms has all been lifted.But carried algorithm Estimated accuracy, which is substantially better than, carries other algorithms, because the tensor subspace method that the present invention is carried can effectively suppress Noise in subspace, therefore compared to conventional subspace method, more accurate subspace estimation, therefore institute can be obtained by carrying algorithm Put forward algorithm angle estimation effect more excellent.Although PARAFAC-Like algorithms also utilize the multidimensional structure for receiving signal, it is estimated There is deviation accumulation effect in meter GPE processes, the GPE of the estimation error under Low SNR is larger, therefore can have a strong impact on angle Spend the precision of estimation.
Accompanying drawing 6 sets forth the property that the present invention puies forward algorithm parameter Estimation under the conditions of different L and SNR from accompanying drawing 7 Energy.From simulation result, SNR and L are bigger, and the effect of angle estimation is better, because SNR is bigger, L is bigger, subspace estimation Precision it is higher, accordingly, angle estimation will be more accurate.
MIMO radar angle estimation algorithm of the present invention based on tensor subspace and invariable rotary, it is connect by building Three rank tensor models of data are received, and then build the high-order covariance tensor model of tensor data, array signal is fully excavated Internal dependency structure；Then HOSVD is carried out to tensor data, and builds new signal subspace, so as to obtain high-precision make an uproar Phonon space；The invariable rotary characteristic of array data is finally utilized, is obtained by the method and method of Lagrange multipliers of constrained optimization The DOD and DOA of pairing are taken, without further carrying out pairing calculating.MIMO radar angle estimation algorithm of the present invention, it is utilized The inside dependency structure of signal is received, angle estimation precision is higher, so that more accurate target DOD and DOA is obtained, to enter one Walk to provide the relevant treatment for detecting target and more reasonably refer to, and without spectrum peak search, computation complexity is relatively low.
The foregoing is only presently preferred embodiments of the present invention, be not intended to limit the invention, it is all the present invention spirit and Within principle, any modification, equivalent substitution and improvements made etc. should be included in the scope of the protection.

Claims (5)

1. a kind of MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary, it is characterised in that described to be based on The MIMO radar angle estimation algorithm of tensor subspace and invariable rotary comprises the following steps：
S1, the three rank tensor models for building target echo signal, the high-order association side for receiving signal is built by tensor model structure Poor tensor model；
S2, Higher-order Singular value decomposition is carried out to high-order covariance tensor model, and build new signal subspace, obtain high accuracy Noise subspace；
S3, the invariable rotary model for constructing array data, GPE is estimated according to the method and method of Lagrange multipliers of constrained optimization Relevant information, obtain pairing DOD and DOA；
Wherein, the function of invariable rotary characteristic is as follows：
In formula,Bt1=At1⊙(CrAr), Bt2= At2⊙(CrAr), Br1=(CtAt)⊙Ar1And Br2=(CtAt)⊙Ar2, and At1And At2A is represented respectivelytPreceding M-1 rows and rear M-1 OK, Ar1And Ar2A is represented respectivelyrPreceding N-1 rows and rear N-1 rows.
2. the MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary, its feature according to claim 1 It is, the step S2 is included as follows step by step：
S21, the tensor covariance model R for receiving signal for building 4 ranks；
S22, according to tensor covariance model R with the HOSVD truncated build a signal subspace matrix Rs；
S23, to signal subspace matrix RsCarry out EVD and decompose one new signal subspace E of acquisitions, EsWith virtual direction matrix A opens into identical subspace.
3. the MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary, its feature according to claim 1 Be, the tensor model include three below Operation Definition：
Define the expansion of 1, tensor：OrderFor a N rank tensor, X mould-n matrix expansion is expressed as [X]n, wherein, position In tensor X inThe element of position, which turns into, is located at matrix [X]n(in, the j) element at place,And
Define 2, mould-n tensors and matrix product：Define N rank tensorsWith matrixMould-n products be YX =X×nA, whereinAnd
Define 3, tensor modular multiplication property：N rank tensorsModular multiplication property mainly have following two：
X×n·A×mB=X×m·B×n·A,m≠n
X×n·A×mB=X×n·(B·A)
4. the MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary, its feature according to claim 3 It is, when the baseband waveform for launching array element is mutually orthogonal encoded signal, then the matrix model of target echo signal is represented For：
X=[CtAt⊙CrAr]ST+ N=AST+N；
In above formula, M is the number of transmitting array element；N is receives the number of array element, and λ is the wavelength of transmitting carrier wave,For m-th of hair The GPE of array element is penetrated,For n-th reception array element GPE, and It is relative for target The DOD of transmitting antenna array, θkDOA for target relative to receiving array；For launch party To matrix,For transmitting steering vector, its m (m=1 ..., M) individual element is To receive direction matrix,To receive steering vector, its n-th (n=1 ..., N) individual element isCt=Diag { ctTo launch GPE matrixes, Diag { } is that diagonalization is operated,For transmitting GPE vectors；Cr=Diag { ctTo receive GPE matrixes, To receive GPE vectors；RCS for target RCS coefficients, and all targets receives snap at L Inside meet Swerling-II models；N is the noise matrix received, and meets Gaussian noise model.
5. the MIMO radar angle estimation algorithm based on tensor subspace and invariable rotary, its feature according to claim 4 It is, the three ranks tensor model is expressed as：
(m=1 ..., M；N=1 ..., N；L=1 ..., L)
In above formula, At(m, k) represents AtIn (m, k) individual element.
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