CN108303683A - Single not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT - Google Patents
Single not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT Download PDFInfo
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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
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Abstract
The invention belongs to Radar Technology fields, disclose a kind of list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT, and array element is received data carries out matched filtering with transmitting signal respectively, obtains observation data vector；Dimensionality reduction pretreatment is carried out to observation data, lower dimensional space is obtained and receives data vector；Data vector is received using the real value that the not rounded characteristic and Euler formula construction array apertures of signal double；Construct the invariable rotary relationship of the virtual array of aperture extension；The covariance matrix that extension receives data is calculated, Eigenvalues Decomposition is carried out to it, estimation obtains real-valued signal subspace；New real-valued signal subspace is defined, the invariable rotary equation of new real-valued signal subspace is solved；The DOA estimated values of target are calculated.The computation complexity of ESPRIT algorithms can be greatly lowered in the present invention while significantly improving DOA estimated accuracies, be suitable for low signal-to-noise ratio and low number of snapshots occasion.
Description
Technical field
The invention belongs to Radar Technology field more particularly to a kind of single base not rounded signal angles MIMO radar real value ESPRIT
Spend method of estimation.
Background technology
Currently, the prior art commonly used in the trade is such：Multiple-input and multiple-output (multiple input multiple
Output, MIMO) radar is a kind of new system radar to be got up based on MIMO development communication technologies.MIMO radar utilizes waveform point
The thought of collection emits mutually orthogonal waveform using multiple transmitting antennas, while receiving target using multiple reception antennas simultaneously
Reflect signal.Compared with traditional phased-array radar, MIMO radar has higher angular resolution and more degree of freedom, tool
There is better angle estimation performance.Direction of arrival (direction of arrival, DOA) estimation is MIMO radar parameter Estimation
An important research content.Invariable rotary sub-space technique (Estimate signal parameters via
Rotational invariance technique, ESPRIT) it is a kind of subspace class high resolution DOA estimation algorithm of classics.
By being utilized respectively the invariable rotary structure of MIMO radar emission array and receiving array, ESPRIT algorithms can apply to MIMO
In radar target DOA estimations.Studies have shown that using the not rounded characteristic of signal, the precision of radar parameter estimation can be significantly improved,
Improve estimation performance.Nearly ten years, numerous scholars are around the expansion further investigation of ESPRIT algorithms, it is proposed that various to be suitable for MIMO
The ESPRIT innovatory algorithms of radar.U-ESPRIT algorithms (Electronics Letters, 2012,48 (3):179-181) exist
Data covariance matrix real value will be received by unitary transformation on the basis of ESPRIT, reduce the computational complexity of algorithm, and
And improve the angle estimation performance under the conditions of low signal-to-noise ratio and low number of snapshots.But this method does not utilize the spy of transmitting signal
Point, therefore its asymptotic estimates performance is identical as ESPRIT algorithms.C-ESPRIT algorithms (Electronics Letters, 2010,
46(25):The virtual array that the characteristics of not rounded signal 1692-1694) is utilized construction array aperture doubles, can significantly improve
Angle estimation precision, but computation complexity is dramatically increased also with doubling for matrix dimensionality, is unfavorable for the real-time of algorithm for estimating
It realizes.RV-ESPRIT algorithms (Journal of Applied Remote Sensing, 2016,10 (2):025003) it is a kind of
The real value ESPRIT algorithms for the characteristics of not rounded signal is utilized, although it uses real value processing means, it calculates complicated
Degree is as the increase of array number is in a cube time growth, and when MIMO port numbers are larger, calculation amount is still considerable.
In conclusion problem of the existing technology is：
(1) existing majority ESPRIT algorithms do not make full use of the not rounded characteristic of transmitting signal, in low signal-to-noise ratio and low fast
Under the conditions of umber of beats, since the inaccuracy of subspace estimation can cause angle estimation precision low or even fail；(2) emit to utilize
The not rounded characteristic of signal, existing ESPRIT algorithms typically directly construct the virtual array that aperture doubles to improve target angle estimation
Precision, this certainly will cause the computation complexity of algorithm to steeply rise, and be unfavorable for the real-time implementation of algorithm.
Solve the meaning of above-mentioned technical problem：The present invention makes full use of the not rounded characteristic of transmitting signal, can improve
The angle estimation precision of ESPRIT algorithms solves ESPRIT algorithms performance severe exacerbation under the conditions of low signal-to-noise ratio and low number of snapshots
The problem of, it is its practical application based theoretical.The present invention can reduce the complexity of existing not rounded signal ESPRIT algorithms,
It provides efficient MIMO radar not rounded angle estimating method, accelerates the speed of target direction estimation, be conducive to ESPRIT algorithms
Real-time implementation promotes the practical application of DOA algorithm for estimating.
Invention content
In view of the problems of the existing technology, the present invention provides a kind of list not rounded letters of base MIMO radar real value ESPRIT
Number angle estimating method.
The invention is realized in this way a kind of list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT,
Array element is received data and is carried out with transmitted waveform by the list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT
Matched filtering obtains observation data vector, carries out dimensionality reduction pretreatment to observation data, obtains lower dimensional space and receive data vector；Profit
Data vector is received with the real value that the not rounded characteristic of signal and Euler formula construction array apertures double, the extension of construction aperture
The invariable rotary relationship of virtual array calculates the covariance matrix for receiving data, carries out Eigenvalues Decomposition, and estimation obtains signal subspace
Space；New real-valued signal subspace is defined, the invariable rotary equation of the real-valued signal subspace is solved, target is calculated
DOA。
Further, the list not rounded signal direction of arrival methods of base MIMO radar real value ESPRIT include the following steps：
Each reception data for receiving array element are carried out matched filtering with transmitted waveform respectively, obtain matching filter by step 1
Observation data vector x (t) after wave；
Step 2 selects dimensionality reduction transformation matrix U, carries out dimensionality reduction to observation data vector x (t), obtains the observation after dimensionality reduction
Data vector y (t)=Ux (t)；
Observation data vector y (t) is decomposed into real part y by step 3 using Euler formulac(t) and imaginary part ys(t), it utilizes
The not rounded characteristic of signal connects the real and imaginary parts for observing data, and the real value that construction array aperture doubles receives data vector
yr(t)；
Step 4 defines two selection matrix J1And J2, the invariable rotary relationship J of construction extension virtual array2Gr=J1Gr
Ω；
Step 5 calculates yr(t) data covariance matrix Ry, Eigenvalues Decomposition is carried out to it, estimation obtains real-valued signal
Subspace Us；
Step 6 defines new signal subspaceNew reality is solved using total least square method
The invariable rotary equation of value signal subspaceReal value matrix Ψ is calculated；
Step 7 carries out Eigenvalues Decomposition to real value matrix Ψ, obtains P characteristic value, and then the wave for obtaining P target reaches
Direction estimation.
Further, data vector is observed in the step 1 is：
X (t)=As (t)+n (t)；
Wherein,Combine steering vector matrix for send-receive,
θ1,θ2,…,θPFor the direction of arrival of P target,It is oriented to and swears for emission array
Amount, M are transmitting antenna number,For receiving array steering vector, N is to receive
Antenna number,Operator is accumulated for Kronecker；S (t)=[s1(t),s2(t),…,sP(t)]TFor signal phasor；n(t)∈
CMN×1It is zero-mean, covariance matrix σ2The white complex gaussian noise vector of I.Under not rounded signal conditioning, s (t) can be indicated
For：
S (t)=Λ r (t)；
Wherein, r (t) is not rounded signal and meets r (t)=r*(t),Table
Show the additional phase shift of the P signal.
Further, the observation data vector in the step 2 after dimensionality reduction is：
Y (t)=V1/2GΛr(t)+nT(t)；
Wherein, G=[g (θ1),g(θ2),…,g(θP)],Ne=M+
N-1 is the effective array number of virtual line arrays；nT=V1/2FHN (t) is the noise vector after dimensionality reduction；For diagonal matrix, diag () is indicated
Element diagonal matrixization operates, and transformation matrix F is defined as：
Further, the reception data vector y that the aperture constructed in the step 3 doublesr(t) it is：
Wherein, yc(t) and ys(t) be respectively y (t) real and imaginary parts；
Gc=[gc(θ1),...,gc(θP)], gc(θp)=[cos βp,...,cos((Ne-1)πsinθp+βp)]T, Gs=[gs(θ1),...,
gs(θP)], gs(θp)=[sin βp,...,sin((Ne-1)πsinθp+βp)]T；For expanded noise vector, ns(t)
=Im [n (t)], nc(t)=Re [n (t)].
Further, the invariable rotary equation J of virtual array steering vector matrix is extended in the step 42Gr=J1GrΩ
In, selection matrix J1And J2It is defined as；
Wherein, T1And T2It is defined as：
The invariable rotary equation J2Gr=J1GrIn Ω,It is right
Angular moment battle array, diagonal element include the DOA information of target.
Further, the reception data vector y extended in step 5r(t) covariance matrix is Ry=E { y (t)ryr(t)H,
Its Eigenvalues Decomposition is：
Ry=UsΣsUs H+UnΣnUn H；
Wherein, ΣsFor by RyThe diagonal matrix that constitute of the big characteristic value of P, UsFor corresponding signal subspace；Σn
For by residue (2Ne- 1-P) diagonal matrix that constitutes of a small characteristic value, UnFor corresponding noise subspace.
Further, real-valued signal subspace new in step 6 is defined asNew real-valued signal subspace
Invariable rotary equation be
Further, the DOA estimated values of P target described in step 7 can be calculated by following formula：
Wherein, λ1,λ2,......,λpFor the P characteristic value of real value matrix Ψ,For the DOA of P target
Estimated value.
Another object of the present invention is to provide a kind of application list not rounded signals of base MIMO radar real value ESPRIT
The MIMO radar of angle estimating method.
In conclusion advantages of the present invention and good effect are：The present invention is converted using dimensionality reduction drops observation data
Dimension pretreatment, can substantially reduce operational data dimension on the whole, ensure that subsequent calculate of algorithm carries out in lower dimensional space, so
Euler formula construction real values are utilized to receive data vector afterwards so that it is subsequent to be calculated as real-valued calculation, therefore there is lower meter
Complexity is calculated, the real-time implementation of algorithm is conducive to.The present invention utilizes the real value of the characteristics of not rounded signal construction extension to receive data
Array aperture is expanded to original twice by vector, and the DOA that target is then carried out using the invariable rotary structure of array extending is estimated
Meter, can significantly improve the angle estimation precision of ESPRIT algorithms, be suitable for low signal-to-noise ratio and low number of snapshots occasion.Therefore, originally
Invention can provide the angle estimation precision significantly improved with lower computational complexity.
Description of the drawings
Fig. 1 is the list not rounded signal angle method of estimation streams of base MIMO radar real value ESPRIT provided in an embodiment of the present invention
Cheng Tu.
Fig. 2 be it is provided in an embodiment of the present invention carried out under the conditions of M=8, N=6, L=100, SNR=10dB 100 times it is imitative
The target DOA estimation value schematic diagram that true experiment obtains.
Fig. 3 is the present invention under the conditions of M=8, N=6, L=100, the root-mean-square error of angle estimation with signal-to-noise ratio change
Change relation curve schematic diagram.
Fig. 4 be the present invention under the conditions of M=8, N=6, SNR=10dB, the root-mean-square error of angle estimation is with number of snapshots
Variation relation curve synoptic diagram.
Fig. 5 be the present invention under the conditions of M=N, L=200, P=3, computational complexity shows with array number variation relation curve
It is intended to.
Specific implementation mode
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
As shown in Figure 1, the not rounded signal angle estimations of list base MIMO radar real value ESPRIT provided in an embodiment of the present invention
Method includes the following steps：
S101：Array element is received into data and obtains observation data vector with transmitted waveform progress matched filtering；
S102：Dimensionality reduction pretreatment is carried out to observation data, lower dimensional space is obtained and receives data vector；
S103：Data vector is received using the real value that the not rounded characteristic and Euler formula construction array apertures of signal double；
S104：Construct the invariable rotary relationship of the virtual array of aperture extension；
S105：The covariance matrix for receiving data is calculated, Eigenvalues Decomposition is carried out, estimation obtains signal subspace；
S106：New real-valued signal subspace is defined, the invariable rotary equation of the real-valued signal subspace is solved；
S107：The DOA of target is calculated.
The list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT provided in an embodiment of the present invention are specifically wrapped
Include following steps：
(1) MIMO radar emits mutually orthogonal pulse code signal using M transmitting antenna, it is assumed that far field space exists
P incoherent narrowband targets receive target echo using N number of reception antenna in receiving terminal, matched filter pair are used in combination
Each reception data carry out matched filtering, obtain observation data vector；
Involved observation data vector is：
X (t)=As (t)+n (t)；
Wherein,Combine steering vector matrix for send-receive,
θ1,θ2,…,θPFor the direction of arrival of P target,It is oriented to and swears for emission array
Amount,For receiving array steering vector,Operator is accumulated for Kronecker；s
(t)=[s1(t),s2(t),…,sP(t)]TFor signal phasor；n(t)∈CMN×1It is zero-mean, covariance matrix σ2The multiple height of I
This white noise vector.Under not rounded signal conditioning, s (t) can be expressed as：
S (t)=Λ r (t)；
Wherein, r (t) is not rounded signal and meets r (t)=r*(t),Table
Show the additional phase shift of the P signal.Therefore, observation data vector can be expressed as：
X (t)=A Λ r (t)+n (t)；
(2) dimensionality reduction transformation matrix U=V is chosen-1/2FH, dimensionality reduction is carried out to observation data vector x (t), obtains the number after dimensionality reduction
According to matrix y (t)=Ux (t)；
Observation data vector after involved dimensionality reduction is：
Y (t)=V1/2GΛr(t)+nT(t)；
Wherein, G=[g (θ1),g(θ2),…,g(θP)],Ne=M+
N-1 is the effective array number of virtual line arrays；
For diagonal matrix, diag () indicates that the operation of element diagonal matrixization, transformation matrix F are defined as：
nT=V1/2FHN (t) is the noise vector after dimensionality reduction.
(3) Euler formula are utilized, observation data vector y (t) is decomposed into real part yc(t) and imaginary part ys(t), signal is utilized
Not rounded characteristic, the reception data vector y that two parts series configuration aperture is doubledr(t)；
The real part y of involved data vector y (t)c(t) and imaginary part ys(t) it is respectively：
The reception data vector y of involved extensionr(t) it is：
Wherein,To extend the steering vector matrix of virtual array, Gc=
[gc(θ1),...,gc(θP)], gc(θp)=[cos βp,...,cos((Ne-1)πsinθp+βp)]T,
Gs=[gs(θ1),...,gs(θP)], gs(θp)=[sin βp,...,sin((Ne-1)πsinθp+βp)]T；For expanded noise vector, ns(t)=Im [n (t)], nc(t)=Re [n (t)].
(4) two selection matrix J are defined1And J2, the invariable rotary equation of construction extension virtual array steering vector matrix；
Involved selection matrix J1And J2For：
Wherein, T1And T2It is defined as：
The invariable rotary equation of involved extension virtual array steering vector matrix is：
J2Gr=J1GrΩ；
Wherein,Diagonal matrix, diagonal element include target
DOA information.
(5) it calculates extension and receives data vector yr(t) autocorrelation matrix Ry, Eigenvalues Decomposition is carried out to it, estimation obtains
Signal subspace Us；
Involved yr(t) autocorrelation matrix is Ry=E { y (t)ryr(t)H, Eigenvalues Decomposition can be expressed as：
Ry=UsΣsUs H+UnΣnUn H；
Wherein, ΣsFor by RyThe diagonal matrix that constitute of the big characteristic value of P, UsFor corresponding signal subspace；Σn
For by residue (2Ne- 1-P) diagonal matrix that constitutes of a small characteristic value, UnFor corresponding noise subspace.
(6) new real-valued signal subspace is calculatedNew letter is solved using least square method or total least square method
Real value matrix Ψ is calculated in the invariable rotary equation in work song space；
Involved new signal subspace isThe invariable rotary equation of involved signal subspace
For
(7) Eigenvalues Decomposition is carried out to Ψ, obtains P eigenvalue λ1,λ2,......,λp, and then target is calculated
DOA estimates.
The DOA of P involved target can be estimated to obtain by following formula：
Wherein,For the DOA estimated values of P target.
The application effect of the present invention is explained in detail with reference to emulation.
(1) simulated conditions and content
Consider the single base MIMO radar system being made of even linear array, emit array number M=8, receives array number N=6,
Each array element spacing is half-wavelength.Assuming that far field space, there are 3 incoherent narrowband targets, the azimuth of each target is respectively
θ1=100,θ2=150,θ3=200.To verify effectiveness of the invention, the present invention and U-ESPRIT algorithms, RV-ESPRIT are calculated
Method and C-ESPRIT algorithms are compared.The root-mean-square error of angle estimation is defined as：
Wherein, K is total Monte-Carlo experiment numbers,Indicate p-th of mesh in kth time Monte-Carlo experiments
Target DOA estimated values, θpFor the angle actual value of p-th of target.
(2) simulation result
1, MIMO radar target positioning performance
Fig. 2 is to carry out 100 emulation experiments under the conditions of M=8, N=6, L=100, SNR=10dB using the present invention and obtain
The target DOA estimation value arrived.From figure 2 it can be seen that multiple targets can accurately determine simultaneously using inventive algorithm
Position.
2, the root-mean-square error of MIMO radar angle estimation with signal-to-noise ratio variation relation
Fig. 3 is that the present invention carries out the angle that 500 Monte-Carlo are tested under the conditions of M=8, N=6, L=100
The root-mean-square error of estimation with signal-to-noise ratio variation relation curve.From figure 2 it can be seen that under Low SNR, this hair
The bright estimated accuracy with C-ESPRIT algorithms, RV-ESPRIT algorithms is superior to U-ESPRIT algorithms, wherein the present invention and C-
ESPRIT algorithms are apparent to the improvement of angle estimated accuracy.The estimated accuracy of each algorithm is improved with the increase of signal-to-noise ratio,
Inventive algorithm and C-ESPRIT algorithms asymptotic estimates performance having the same.
3, the root-mean-square error of MIMO radar angle estimation with number of snapshots variation relation
Fig. 4 is that the present invention carries out 500 Monte-Carlo under the conditions of M=8, N=6, SNR=10dB and tests
The root-mean-square error of angle estimation with number of snapshots variation relation curve.From figure 3, it can be seen that the present invention and C-ESPRIT are calculated
Method, the estimated accuracy of RV-ESPRIT algorithms are superior to U-ESPRIT algorithms.Since the present invention and C-ESPRIT algorithms are utilized
The angle estimation precision of the reception data that virtual aperture doubles, the two obtains large increase, and angle estimation precision is basic
It is close.
4, the computational complexity of MIMO radar angle estimation with dual-mode antenna number variation relation
From figure 5 it can be seen that the computational complexity (real value multiplication number) of each algorithm with the increase of array number and
Increase.Wherein, the computational complexity of U-ESPRIT algorithms, C-ESPRIT algorithms and RV-ESPRIT algorithms is with array number
Increase and steeply rises, and the computational complexity of inventive algorithm is slower with array number variation, and computational complexity is minimum.This
It is due to the present invention while to use dimensionality reduction transformation and real valueization operation, the operation for greatly reducing ESPRIT algorithms is complicated
Degree.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
All any modification, equivalent and improvement etc., should all be included in the protection scope of the present invention made by within refreshing and principle.
Claims (10)
1. a kind of list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT, which is characterized in that the list base
Array element is received data and is obtained with transmitted waveform progress matched filtering by the not rounded signal angle methods of estimation of MIMO radar real value ESPRIT
To observation data vector, dimensionality reduction pretreatment is carried out to observation data, lower dimensional space is obtained and receives data vector；Utilize the non-of signal
The real value that circle characteristic and Euler formula construction array apertures double receives data vector, the virtual array of structure aperture extension
Invariable rotary relationship calculates the covariance matrix for receiving data, carries out Eigenvalues Decomposition, and estimation obtains signal subspace；Definition
New real-valued signal subspace solves the invariable rotary equation of the real-valued signal subspace, the DOA of target is calculated.
2. the list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT as described in claim 1, feature exist
In the list not rounded method for estimating signal wave direction of base MIMO radar real value ESPRIT includes the following steps：
Each reception data for receiving array element are carried out matched filtering, after obtaining matched filtering by step 1 with transmitted waveform respectively
Observation data vector x (t)；
Step 2 selects dimensionality reduction transformation matrix U, carries out dimensionality reduction to observation data vector x (t), obtains the observation data after dimensionality reduction
Vector y (t)=Ux (t)；
Observation data vector y (t) is decomposed into real part y by step 3 using Euler formulac(t) and imaginary part ys(t), signal is utilized
Not rounded characteristic, the real and imaginary parts series connection of data will be observed, the real value that doubles of construction array aperture receives data vector yr
(t)；
Step 4 defines two selection matrix J1And J2, the invariable rotary relationship J of construction extension virtual array2Gr=J1GrΩ；
Step 5 calculates yr(t) data covariance matrix Ry, Eigenvalues Decomposition is carried out to it, it is empty that estimation obtains real-valued signal
Between Us；
Step 6 defines new real-valued signal subspaceNew real-valued signal subspace is solved using total least square method
Invariable rotary equationReal value matrix Ψ is calculated；
Step 7 carries out Eigenvalues Decomposition to real value matrix Ψ, obtains its P characteristic value, and then the wave for estimating P target reaches
Direction.
3. the list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT as claimed in claim 2, feature exist
In observing data vector in the step 1 is：
X (t)=As (t)+n (t)；
Wherein,Combine steering vector matrix, θ for send-receive1,
θ2,…,θPFor the direction of arrival of P target,For emission array steering vector, M
For transmitting antenna number,For receiving array steering vector, N is reception antenna
Number,Operator is accumulated for Kronecker；S (t)=[s1(t),s2(t),…,sP(t)]TFor signal phasor；n(t)∈CMN×1
It is zero-mean, covariance matrix σ2The white complex gaussian noise vector of I.Under not rounded signal conditioning, s (t) can be expressed as：
S (t)=Λ r (t)；
Wherein, r (t) is not rounded signal and satisfaction Indicate P
The additional phase shift of a reflection signal.
4. the list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT as claimed in claim 2, feature exist
In the observation data vector in the step 2 after dimensionality reduction is：
Y (t)=V1/2GΛr(t)+nT(t)；
Wherein, G=[g (θ1),g(θ2),…,g(θP)],Ne=M+N-1 is
The effective array number of virtual line arrays；nT=V1/2FHN (t) is the noise vector after dimensionality reduction；For diagonal matrix, diag () indicates member
Plain diagonal matrixization operation, transformation matrix F are defined as：
5. the list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT as claimed in claim 2, feature exist
In the reception data vector y that the aperture constructed in the step 3 doublesr(t) it is：
Wherein, yc(t) and ys(t) be respectively y (t) real and imaginary parts； Gc=
[gc(θ1),...,gc(θP)], gc(θp)=[cos βp,...,cos((Ne-1)πsinθp+βp)]T, Gs=[gs(θ1),...,gs
(θP)], gs(θp)=[sin βp,...,sin((Ne-1)πsinθp+βp)]T；For expanded noise vector, nc(t)=
Re [n (t)], ns(t)=Im [n (t)].
6. the list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT as claimed in claim 2, feature exist
In the invariable rotary equation J of extension virtual array steering vector matrix in the step 42Gr=J1GrIn Ω, selection matrix J1
And J2It is defined as：
Wherein, T1And T2It is defined as：
The invariable rotary equation J2Gr=J1GrIn Ω,For to angular moment
Battle array, diagonal element include the DOA information of target.
7. the list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT as claimed in claim 2, feature exist
In the reception data vector y extended in step 5r(t) covariance matrix is Ry=E { y (t)ryr(t)H, Eigenvalues Decomposition
For：
Ry=UsΣsUs H+UnΣnUn H；
Wherein, ΣsFor by RyThe diagonal matrix that constitute of the big characteristic value of P, UsFor corresponding signal subspace；ΣnIt serves as reasons
Residue (2Ne- 1-P) diagonal matrix that constitutes of a small characteristic value, UnFor corresponding noise subspace.
8. the list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT as claimed in claim 2, feature exist
In new real-valued signal subspace is defined as in step 6The invariable rotary side of new real-valued signal subspace
Cheng Wei
9. the list not rounded signal angle methods of estimation of base MIMO radar real value ESPRIT as claimed in claim 2, feature exist
In the DOA estimated values of P target described in step 7 can be calculated by following formula：
Wherein, λ1,λ2,......,λpFor the P characteristic value of real value matrix Ψ,For the DOA estimations of P target
Value.
10. the list not rounded signal angles of base MIMO radar real value ESPRIT described in a kind of application claim 1~9 any one are estimated
The MIMO radar of meter method.
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