CN108828551A - A kind of compressed sensing based flexible MIMO radar compound target DOA estimation method - Google Patents
A kind of compressed sensing based flexible MIMO radar compound target DOA estimation method Download PDFInfo
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Abstract
The invention discloses one kind to be based on compressed sensing (Compressed Sensing, CS flexible multiple-input and multiple-output (Multi-Input and Multi-Output), MIMO) radar compound target direction of arrival (Direction of Arrival, DOA) estimation method, it is related to array signal processing technology, the present invention focuses on solving following two problem for the design of thinned array MIMO radar structure and compound target DOA estimation：(1) a kind of flexible MIMO radar structure is designed, and is defined as flexible array element spacing Sparse Array (Sparse Array with Flexible Inter-element Spacing, SA-FIS).(2) propose a kind of two step CS algorithm of drop complexity to make full use of total Virtual array.By correcting and removing the off-diagonal element in target covariance matrix, improved CS algorithm can only identify diagonal element therein.Since traditional C/S algorithm needs to estimate all nonzero elements, the present invention can improve estimation performance by estimating less element number and reduce complexity.
Description
Technical field
The present invention relates to array signal processing technology, in particular to a kind of compressed sensing based flexible MIMO radar
Compound target DOA estimation method.
Background technique
To improve the freedom degree upper limit under the conditions of given physics array number, thinned array is carried out from " combinatorial array " angle
MIMO radar Virtual array patulous research gradually causes educational circles and payes attention to and achieve greater advance.Nested MIMO radar being capable of benefit
O (M is obtained with a array element of O (M)2) or O (M3) freedom degree, but gather submatrix keep its mutual coupling rate relatively large.Relatively prime MIMO radar
Biggish array element spacing further decreases mutual coupling rate, and the freedom degree of O (MN) can be obtained using O (M+N) a array element.But it does not open
The thinned array MIMO radar the Structural Design of exhibition system.
In recent years, compound target (including incoherent target and Coherent Targets) DOA algorithm for estimating research has caused to close extensively
Note.Under normal circumstances, since not full rank phenomenon occurs in information source covariance matrix, under conventional subspace class algorithm estimates performance sharply
Drop.Many decorrelation LMS algorithms propose and make substantial progress in succession, as space smoothing algorithm, Toeplitz matrix reconstruction method,
Maximum likelihood algorithm, CS algorithm etc..To improve target detection quantity, by establishing target information separation matrix respectively to incoherent
Target and Coherent Targets carry out two step angle estimations, as space difference method uses conventional subspace class algorithm to estimate non-phase first
Dry information source then subtracts incoherent part using spatial differentiation technique and obtains coherent information；Shadow casting technique passes through foundation
Projection matrix separates incoherent and coherent, then carries out angle estimation etc. using conventional subspace class algorithm.
Research for the virtual echo-signal DOA algorithm for estimating of thinned array MIMO radar also achieves huge progress, main
It to include space smoothing algorithm and CS algorithm.Compared to space smoothing algorithm, CS can overcome aperture caused by Subarray Smoothing to damage
It loses, and using the discrete portions in Virtual array structure.But conventional method is primarily adapted for use in incoherent target DOA estimation, into
The research of row thinned array MIMO radar compound target DOA algorithm for estimating is relatively fewer.Traditional algorithm is using CS algorithm for " and poor
DOA estimation problem under combinatorial array " structure, but due to needing the non-diagonal in the target covariance matrix after estimate vector
Element, traditional C/S algorithm have biggish operand.For example, the array element element for needing to estimate is when K target is concerned with entirely
K2, the sharply decline for estimating performance and operand will be caused to increase at this time.
Prior art disadvantage mainly has：1) not yet carry out the thinned array MIMO thunder based on freedom degree and mutual coupling combined optimization
It is designed up to structure；2) traditional C/S algorithm carries out operand with higher when thinned array MIMO radar compound target DOA estimation.
Summary of the invention
The embodiment of the invention provides a kind of compressed sensing based flexible MIMO radar compound target DOA estimation method,
To solve problems of the prior art.
A kind of compressed sensing based flexible MIMO radar compound target DOA estimation method, including：
Step 1: establishing flexible MIMO radar echo signal model：First by flexible MIMO radar (i.e. SA-FIS)
Emission array and receiving array carry out matched filtering, obtain array echo signal vector model, then according to array echo believe
Number vector model x (t) obtains the covariance matrix R and vectorization covariance matrix r of array echo signal；
Step 2: carrying out structure optimization to flexible MIMO radar echo signal model：Because in vectorization covariance matrix r
Array manifold matrix B meet " and poor combinatorial array " feature, therefore, pass through " combinatorial array " of analysis array manifold matrix B
Structure selects suitable spreading factor, to obtain the more Virtual array numbers of flexible MIMO radar；
Step 3: being calculated for the flexible MIMO radar echo signal model after structure optimization using drop two step CS of complexity
Method carries out compound target DOA estimation：Drop two step CS algorithm model of complexity is established by estimating and correcting redundant term, in conjunction with total void
Matroid identical permutation sequence removes the repetition row in vectorization covariance matrix r, can obtain signal model newly.
Preferably, the step 1 the specific steps are：
The emission array and receiving array of flexible MIMO radar (i.e. SA-FIS) are made of sparse even linear array, therefore, always
Physics array number be T=M+N；
Wherein, emission array has M array element, and array element spacing is α d；Receiving array has N number of array element, and array element spacing is β d；α
It is relatively prime spreading factor with β, d is unit array element spacing, is typically set to λ 2, λ is signal wavelength；
The element position set of emission array and receiving arrayWithFor：
Wherein, m, n are integer；
Equipped with the irrelevant and relevant compound target in K far field, information source direction integrates as θ={ θk, k=1,2 ..., K }, wherein
Incoherent target number and Coherent Targets number are respectively KuAnd Kc, i.e. K=Ku+Kc；Assuming that KcA full coherent condition of goal satisfaction；
Then the array echo signal vector model after matched filtering is：
Wherein：
Wherein,Be number of snapshots be t when k-th of target reflection coefficient；For kth0It is a
The attenuation coefficient (i.e. coherence factor) of target, for convenient for statement, it is assumed that[·]TFor matrix transposition
Operation, diag () are diagonal operation,WithIt is long-pending long-pending with Kronecker to respectively indicate Khatri-Rao；
N (t) is independent identically distributed additive gaussian white noise vector, meets CN (0, σ2)；
And
At=[at(θ1),at(θ2),…,at(θK)] (5)
Ar=[ar(θ1),at(θ2),…,ar(θK)] (6)
at(θk) and ar(θk) be respectively emission array and receiving array k-th of mesh
Target direction vector, specially：
It is according to the covariance matrix that formula (2) echo signal model can obtain array echo signal：
R=E [x (t) xH(t)]=ARsAH+σ2IMN (9)
Wherein：
Rs=E [s (t) sH(t)] (10)
For target covariance matrix, AHFor matrix A complex conjugate transposition operation, IMNUnit matrix is tieed up for MN × MN；
When number of snapshots are L (t=1 ..., L), sample covariance matrix is normally approximately：
Vectorization covariance matrix R is obtained：
R=vec (R)=Bvec (Rs)+σ2vec(IMN) (12)
Wherein,A*Representing matrix complex conjugate operation, vec () representing matrix vector quantities operation.
Preferably, the step 2 the specific steps are：Utilize the element position collection of formula (1) emission array and receiving array
It closesWith?：
" and poor combinatorial array " collection of SA-FIS is combined into：
Wherein, m0,n0For integer,
Further to analyze setFreedom degree, the Virtual array distribution situation that can obtain SA-FIS is as follows：Pass through vector
Change covariance matrix R, defines " and poor combinatorial array " set of SA-FISThen SA-FIS has following feature：
(a) relatively prime spreading factor meets：1≤α≤2N-1,1≤β≤2M-1；
(b) gatherContinuously and virtually array element range be [- c, c], wherein c=α M+ β N- α β -1；
(c)In total Virtual array number be 2g+1, g=α (M-1)+β (N-1)-(α -1) (β -1)/2；
Search Space Smoothing is only capable of utilizing continuously and virtually array element, freedom degree c+1；CS algorithm can utilize all void
Matroid member, freedom degree 2g+1；To select suitable spreading factor to obtain more Virtual array numbers, now respectively to total void
Quasi- array number and the optimization of continuously and virtually array number are as follows：
(3) total Virtual array number g
Determine spreading factor α, β and total physics array number in the optimal distribution of transmitting terminal and receiving end by Optimal Parameters g
Structure, optimization object function are as follows：
(4) continuously and virtually array number c
Similarly, it establishes and is about the objective function of optimization array number c：
Preferably, the step 3 the specific steps are：According to formula (9), the covariance matrix of array echo signal can be weighed
Newly it is expressed as：
Wherein,
It is obtained to after matrix R vectorization：
Wherein, For the signal energy of k-th of target；
By formula (17) it is found that first itemBy target covariance matrix RsDiagonal element composition, Section 2By RsOff-diagonal element composition, for the compound target of relevant and incoherent target composition, non-zero nondiagonal element
Element is made of Coherent Targets coherence factor；As can be seen that it can direct estimation target covariance matrix using first item from formula (17)
Diagonal element so that determine target angle, and Section 2 can be handled directly as redundant term；
In conjunction with above-mentioned model analysis, drop two step CS algorithm model of complexity is established by estimating and correcting redundant term, specifically
Content is as follows：
(1), for echo-signal vector model in formula (2), estimating for echo signal s (t) can be obtained using lowest mean square technology
Evaluation is：
Where it is assumed that matrix A row full rank, A+=AH(AAH)-1, then target covariance matrix is represented by：
According to formula (19), Section 2 is expressed as in formula (17)：
Using the estimated value of formula (19), formula (17) is expressed as again：
Wherein, parameter lambda1∈[0,1]；
The signal model that removes the row of the repetition in data vector r and can obtain newly that puts in order in conjunction with total Virtual array is：
Wherein, vector e is 2g+1 ranks vector, and g+1 row element is 1, remaining behavior 0；For with Virtual array position
Set corresponding (2g+1) × K dimension matrix, B0For corresponding (2g+1) × K2Tie up matrix；
Setting search vector is θ={ θj, j=1,2 ..., P }, then can establish optimization object function according to formula (22) is：
Wherein：
And noise statistics amount is it is known that η is regularization parameter；
Optimized model in formula (23) is solved using LASSO algorithm, and to illustrate convenient for step 2, solution is defined as：
(2), the Section 2 in formula (23) is calculated according to search vector θ, and since there are biggish angular errors by θ, this is extra
Item error is relatively large；For this purpose, using estimated result θ in formula (26)(1)Again Section 2 is corrected, to further increase estimation
Performance；
According to estimated result θ(1)The target covariance matrix that can be obtained newly is：
Wherein：
It can be obtained according to formula (27)：
New objective optimization function, which can be constructed, according to formula (30) is：
Wherein, parameter lambda2∈[0,1]；
Comparison expression (23) and (31) are it is found that revised Section 2It is more accurate, therefore λ1≤λ2, so the calculation
Method has lower operand and higher estimation performance；Meanwhile angle can must be reevaluated by formula (31) and be：
It is pointed out that parameter lambda1,λ2It is constant, value is influenced by echo signal model, therefore, for what is given
Signal model can determine optimal value by the method for exhaustion.
By estimating and correcting target covariance matrix, the mentioned algorithm of the present invention has lower operation than traditional C/S algorithm
Amount and higher estimation performance, inventive algorithm are also applied for incoherent target DOA estimation, by inhibiting target related coefficient to miss
Difference can be improved estimation performance, but need to carry out Optimization Solution twice.
Beneficial effect of the present invention：Biggish freedom degree is obtained by Virtual array optimization；
Array element mutual coupling is reduced by increasing emission array and receiving array array element spacing；
By estimating and inhibiting signal covariance matrix off-diagonal element to improve estimated accuracy and reduce algorithm operation quantity.
Detailed description of the invention
Fig. 1 is the compressed sensing based flexible MIMO radar compound target DOA estimation of one kind provided in an embodiment of the present invention
The flexible MIMO radar schematic diagram of method；
Fig. 2 is the compressed sensing based flexible MIMO radar compound target DOA estimation of one kind provided in an embodiment of the present invention
Flexible MIMO radar schematic diagram when the different β value of method；
Fig. 3 is the compressed sensing based flexible MIMO radar compound target DOA estimation of one kind provided in an embodiment of the present invention
The related MIMO radar Virtual array distribution schematic diagram of method；
Fig. 4 is the compressed sensing based flexible MIMO radar compound target DOA estimation of one kind provided in an embodiment of the present invention
The traditional C/S of method and two step CS algorithm operation time schematic diagrames；
Fig. 5 is the compressed sensing based flexible MIMO radar compound target DOA estimation of one kind provided in an embodiment of the present invention
The algorithms of different RMSE of method is with SNR variation relation figure；
Fig. 6 is the compressed sensing based flexible MIMO radar compound target DOA estimation of one kind provided in an embodiment of the present invention
The algorithms of different RMSE of method is with number of snapshots variation relation figure；
Fig. 7 is the compressed sensing based flexible MIMO radar compound target DOA estimation of one kind provided in an embodiment of the present invention
The different array RMSE of method are with SNR variation relation figure；
Fig. 8 is the compressed sensing based flexible MIMO radar compound target DOA estimation of one kind provided in an embodiment of the present invention
The different array RMSE of method are with number of snapshots variation relation figure；
Fig. 9 is the compressed sensing based flexible MIMO radar compound target DOA estimation of one kind provided in an embodiment of the present invention
The normalization space spectrogram of the algorithms of different of method；
Figure 10 is the compressed sensing based flexible MIMO radar compound target DOA estimation of one kind provided in an embodiment of the present invention
The normalization space spectrogram of the different sparse array structures of method.
Specific embodiment
Below with reference to the attached drawing in inventive embodiments, technical solution in the embodiment of the present invention carries out clear, complete
Description, it is to be understood that the protection scope of the present invention is not limited by the specific implementation manner.
The purpose that the present invention has is：First is that establishing a kind of more flexible thinned array MIMO radar structure to inhibit mutual coupling
And increase freedom degree, wherein current thinned array MIMO structure is its special shape；Second is that proposing that a kind of drop complexity CS is calculated
Method is estimated for compound target DOA.
It referring to Fig.1, is the compressed sensing based flexible MIMO radar compound target DOA of one kind provided in an embodiment of the present invention
The flexible MIMO radar schematic diagram of estimation method,
Step 1: establishing flexible MIMO radar echo signal model
The emission array and receiving array of flexible MIMO radar (i.e. SA-FIS) are made of sparse even linear array；Wherein, it sends out
Penetrating array has M array element, and array element spacing is α d；Receiving array has N number of array element, and array element spacing is β d；α and β be relatively prime extension because
Son, d are unit array element spacing, are typically set to λ 2, λ is signal wavelength；
Therefore, total physics array number is T=M+N；
The element position set of emission array and receiving arrayWithFor：
Wherein, m, n are integer；
Equipped with the irrelevant and relevant compound target in K far field, information source direction integrates as θ={ θk, k=1,2 ..., K }, wherein
Incoherent target number and Coherent Targets number are respectively KuAnd Kc, i.e. K=Ku+Kc；Assuming that KcA full coherent condition of goal satisfaction；
Then the array echo signal vector model after matched filtering is：
Wherein：
Wherein,Be number of snapshots be t when k-th of target reflection coefficient；For kth0It is a
The attenuation coefficient (i.e. coherence factor) of target, for convenient for statement, it is assumed that[·]TFor matrix transposition
Operation, diag () are diagonal operation,WithIt is long-pending long-pending with Kronecker to respectively indicate Khatri-Rao；
N (t) is independent identically distributed additive gaussian white noise vector, meets CN (0, σ2)；
And
At=[at(θ1),at(θ2),…,at(θK)] (5)
Ar=[ar(θ1),at(θ2),…,ar(θK)] (6)
at(θk) and ar(θk) be respectively emission array and receiving array k-th of mesh
Target direction vector, specially：
It is according to the covariance matrix that formula (2) echo signal model can obtain array echo signal：
R=E [x (t) xH(t)]=ARsAH+σ2IMN (9)
Wherein：
Rs=E [s (t) sH(t)] (10)
For target covariance matrix, AHFor matrix A complex conjugate transposition operation, IMNUnit matrix is tieed up for MN × MN；
In fact, sample covariance matrix is normally approximately when number of snapshots are L (t=1 ..., L)：
Vectorization covariance matrix R can be obtained：
R=vec (R)=Bvec (Rs)+σ2vec(IMN) (12)
Wherein,A*Representing matrix complex conjugate operation, vec () representing matrix vector quantities operation；
Step 2: carrying out Optimal Structure Designing to flexible MIMO radar echo signal model
By formula (12) it is found that therefore the array manifold matrix B of vector r, which meets " and poor combinatorial array " feature, passes through analysis
" combinatorial array " structure of matrix B explores the Virtual array spread scenarios of flexible MIMO radar；Then using formula (1) emission array and
The element position set of receiving arrayWithIt can obtain：
" and poor combinatorial array " collection of SA-FIS is combined into：
Wherein, m0,n0For integer,
Further to analyze setFreedom degree, the Virtual array distribution situation that can obtain SA-FIS is as follows：Pass through vector
Change covariance matrix R, defines " and poor combinatorial array " set of SA-FISThen SA-FIS has following feature：
(a) relatively prime spreading factor meets：1≤α≤2N-1,1≤β≤2M-1；
(b) gatherContinuously and virtually array element range be [- c, c], wherein c=α M+ β N- α β -1；
(c)In total Virtual array number be 2g+1, g=α (M-1)+β (N-1)-(α -1) (β -1)/2；
Search Space Smoothing is only capable of utilizing continuously and virtually array element, freedom degree c+1；CS algorithm can utilize all void
Matroid member, freedom degree 2g+1；
It is the suitable spreading factor of selection to obtain more Virtual array numbers, now respectively to total Virtual array number and continuous
The optimization of Virtual array number is as follows：
(1) total Virtual array number g
Determine spreading factor α, β and total physics array number in the optimal distribution of transmitting terminal and receiving end by Optimal Parameters g
Structure, optimization object function are as follows：
Followed by AM-GM inequality, the results are shown in Table 1 for formula (14)：
1 formula of table (14) solving result
(2) continuously and virtually array number c
Similarly, it establishes and is about the objective function of optimization array number c：
The solving result of formula (15) is α=2N-1, β=1 or α=1, β=2M-1；
At this point, variable c can be maximized as cmax=2MN-M-N, wherein M and N is identical as table 1 respectively；
It can be obtained according to above-mentioned optimum results and such as be drawn a conclusion：
(1) when spreading factor α (β) is maximized, total Virtual array sum is remained unchanged, that is, is equal to 2MN-M-N；
(2) convolution (14) and formula (15) optimum results are it is found that when spreading factor α (β) is maximized, with β's (α)
Increase, variable gmaxIt remains unchanged, and c increases with it and is reduced.
It is the compressed sensing based flexible MIMO radar compound target DOA of one kind provided in an embodiment of the present invention referring to Fig. 2
Flexible MIMO radar schematic diagram when the different β value of estimation method, continuously and virtually array element when giving different β value and total virtual
Array number, wherein M=N=3, α=5；Figure it is seen that total Virtual array number remains constant, value is equal to 25, and
Continuous array number increases with β and is reduced, and value is respectively 25,21,13.
(3) according to fig. 2 as can be seen that SA-FIS is without " transmitting and reception array number compared to relatively prime MIMO radar structure
It is relatively prime " this precondition, therefore, SA-FIS can satisfy any physical array number demand.In addition, working as cmax=gmaxWhen, hair
It penetrates or receiving array is close array structure (α=1 or β=1), there is biggish mutual coupling rate at this time, and then influence angle estimation
Energy.However, can achieve the purpose that inhibit mutual coupling by increasing array element spacing when carrying out DOA estimation using total Virtual array number.
Therefore, say that CS algorithm is more suitable for SA-FIS from inhibition mutual coupling angle.Finally, the array element spacing (i.e. α ≠ 1 and β ≠ 1) of variation
Also make SA-FIS actual application ability stronger.
It (4) is to illustrate that SA-FIS extends advantage, table 2 relative to traditional nested and combinatorial array MIMO radar virtual aperture
Give the Virtual array number of associated array structure, wherein assuming that M and N is relatively prime integer.From table 2 it can be seen that SA-FIS ratio
Other array structures have more high-freedom degree, and can further suppress array element mutual coupling by increasing array element spacing.
The Virtual array number of 2 associated array structure of table compares
Step 3: for the compound target DOA algorithm for estimating of the flexible MIMO radar echo signal model after optimization
Compound target DOA estimation is carried out with a kind of two step CS algorithm of drop complexity for the MIMO structure of step 2 optimization；
According to formula (9), the covariance matrix of array echo signal can be expressed as again：
Wherein,
To can be obtained after matrix R vectorization：
Wherein, For the signal energy of k-th of target；
By formula (17) it is found that first itemBy target covariance matrix RsDiagonal element composition, Section 2By RsOff-diagonal element composition, for the compound target of relevant and incoherent target composition, non-zero nondiagonal element
Element is made of Coherent Targets coherence factor；As can be seen that it can direct estimation target covariance matrix using first item from formula (17)
Diagonal element so that determine target angle, and Section 2 can be handled directly as redundant term；
In conjunction with above-mentioned model analysis, drop two step CS algorithm model of complexity is established by estimating and correcting redundant term, specifically
Content is as follows：
(1) for echo-signal vector model in formula (2), the estimation of echo signal s (t) can be obtained using lowest mean square technology
Value is：
Where it is assumed that matrix A row full rank, A+=AH(AAH)-1, then target covariance matrix is represented by：
According to formula (19), Section 2 is represented by formula (17)：
Using the estimated value of formula (19), formula (17) can be expressed as again：
Wherein, parameter lambda1∈[0,1]；
The signal model that removes the row of the repetition in data vector r and can obtain newly that puts in order in conjunction with total Virtual array is：
Wherein, vector e is 2g+1 ranks vector, and g+1 row element is 1, remaining behavior 0；For with Virtual array position
Set corresponding (2g+1) × K dimension matrix, B0For corresponding (2g+1) × K2Tie up matrix；
Setting search vector is θ={ θj, j=1,2 ..., P }, then can establish optimization object function according to formula (22) is：
Wherein：
And noise statistics amount is it is known that η is regularization parameter；
Optimized model in formula (23) is solved using LASSO algorithm, and to illustrate convenient for step 2, solution is defined as：
(2) Section 2 in formula (23) is calculated according to search vector θ, since there are biggish angular error, the redundant terms by θ
Error is relatively large；For this purpose, using estimated result θ in formula (26)(1)Again Section 2 is corrected, to further increase estimation
Energy；
According to estimated result θ(1)The target covariance matrix that can be obtained newly is：
Wherein：
It can be obtained according to formula (27)：
New objective optimization function, which can be constructed, according to formula (30) is：
Wherein, parameter lambda2∈[0,1]；
Comparison expression (23) and (31) are it is found that revised Section 2It is more accurate, therefore λ1≤λ2；Then by formula
(31) can must reevaluate angle is：
It is pointed out that parameter lambda1,λ2It is constant, value is influenced by echo signal model, therefore, for what is given
Signal model can determine optimal value, such as λ by the method for exhaustion1,λ2=0.1,0.2 ..., 1.
Embodiment 1：Establish flexible MIMO radar echo signal model
It is the compressed sensing based flexible MIMO radar compound target DOA of one kind provided in an embodiment of the present invention referring to Fig. 3
The related MIMO radar Virtual array distribution schematic diagram of estimation method, it is assumed that SA-FIS emission array and receiving array array number are
M=4, N=3.Then according to theorem 1 it is found that 1≤α≤5,1≤β≤7.In conjunction with related sparse array MIMO radar structure in table 2,
Fig. 3 gives the Virtual array distribution of each array structure, wherein flexibly relatively prime MIMO radar meetsP=2, SA-FIS
Meet α=5, β=3.From figure 3, it can be seen that nested submatrix MIMO radar transmitting or receiving array are battle array of gathering, other array junctions
Structure is made of thinned array, thus nested submatrix MIMO radar mutual coupling rate highest.In particular, SA-FIS can obtain 35
Virtual array, wherein [- 13,13] interior Virtual array is continuous；The relatively prime MIMO radar of tradition has 29 Virtual arrays, flexibly relatively prime
MIMO radar has 25 Virtual arrays, and Virtual array of the two in [- 11,11] range is continuous；Nested submatrix MIMO radar is only
There are 23 continuously and virtually array elements.Therefore, more freedom can be obtained by Optimal Parameters α, β, SA-FIS and lower array element is mutual
Coupling, thus there is preferable estimation performance.
Embodiment 2 improves CS algorithm operation time
It is the compressed sensing based flexible MIMO radar compound target DOA of one kind provided in an embodiment of the present invention referring to Fig. 4
The traditional C/S of estimation method and two step CS algorithm operation time schematic diagrames, wherein SNR 10dB, number of snapshots 200 search for model
It encloses for [0 °, 40 °], step-size in search is 1 °, and the variation range of N=3, M are [2,8].Assuming that α=5, β=3, three target directions
For θ1=10 °, θ2=20 °, θ3=30 °, wherein latter two target is relevant, corresponding coherence factor be 0.9exp (j1.1 π) and
0.8exp(j0.75π).So as shown in Figure 4, two step CS algorithms have lower operand compared to traditional C/S algorithm.
Embodiment 3 improves CS algorithm mean square error
Referring to figure 5 and figure 6, firstly, comparing traditional C/S algorithm, l1The estimation performance of-SVD and two step CS algorithms, and CRB is mentioned
For estimating performance lower bound.Assuming that target position and coherence factor are same as Example 2, and M=2, N=3, α=5, β=3, and search for
Step-length is 0.05 °.Fig. 5 gives RMSE with the variation relation of SNR, number of snapshots 200.Fig. 6 gives RMSE with number of snapshots
Variation relation, SNR 0dB.From Fig. 5-6 as can be seen that improving CS algorithm, l1- SVD and traditional C/S algorithm are with SNR, number of snapshots
Increase and increase.Wherein, the step of improving CS algorithm two can improve estimation performance by amendment target covariance matrix, because
And estimated accuracy is better than traditional C/S algorithm；But there are large error, estimations due to estimating target covariance matrix in step 1
Performance is weaker than traditional C/S algorithm, meanwhile, it is more preferable relative to traditional C/S algorithm estimation performance to improve CS algorithm steps two；l1- SVD by
In be only capable of using echo-signal " and combinatorial array " and freedom degree is lower, thus estimate performance it is worst.
Then, the estimation performance improved between CS algorithm comparison difference array structure is utilized, wherein the CRB of SA-FIS makees
To estimate that lower bound, three target directions are θ1=5 °, θ2=10 °, θ3=15 °, most latter two target is relevant, corresponding phase responsibility
Number is 0.8exp (j0.9 π) and 0.65exp (j0.85 π), and step-size in search is 0.05 °.
RMSE is described with the variation relation of SNR, number of snapshots 200 referring to Fig. 7 and Fig. 8, Fig. 7.Fig. 8 describe RMSE with
The variation relation of number of snapshots, SNR 0dB.According to Fig. 7-8 it is found that by utilizing discrete virtual array element, flexible relatively prime MIMO radar
It is more preferable than nested submatrix MIMO radar estimation performance；Similarly, the relatively prime MIMO of tradition due to more discrete virtual array elements and
Better than flexible relatively prime structure.By optimizing spreading factor α, β, SA-FIS can obtain more Virtual arrays, thus the property estimated
It can be more preferable.
Embodiment 4：Improve CS algorithm angular resolution
Referring to Fig. 9 and Figure 10, compare between algorithms of different first (including traditional C/S algorithm, l1- SVD and two step CS algorithms)
Angular resolution, it is assumed that there are three adjacent objects, position θ1=20 °, θ2=23 °, θ2=26 °, most latter two target phase
Dry, corresponding coherence factor is respectively 0.9exp (j1.1 π) and 0.8exp (j0.75 π), and dotted line indicates real angle direction.Fig. 9
Provide CS spatial spectrum of two kinds of algorithms under SA-FIS structure, SNR 20dB, number of snapshots 200, M=4, N=3, α=5, β=
6, search range is [0 °, 90 °], and step-size in search is 0.5 °.From fig. 9, it can be seen that two step CS algorithms can differentiate three neighbouring mesh
Mark, but two step CS algorithms and l1- SVD method can not identify intermediate objective.
Then, the angular resolution improved between CS algorithm comparison difference array structure is utilized, wherein three adjacent objects
Position is θ1=20 °, θ2=24 °, θ3=28 °, latter two target is relevant, and coherence factor is identical as Fig. 9, and dotted line indicates true angle
Spend direction.Figure 10 gives the CS spatial spectrum under different MIMO structures, SNR 10dB, number of snapshots 200, M=4, and N=3, α=
5, β=3, search range is [0 °, 90 °], and step-size in search is 0.5 °.As shown in Figure 10, it is neighbouring to differentiate above three by SA-FIS
Target, and the relatively prime MIMO of tradition, flexibly relatively prime MIMO can not differentiate second target with nested submatrix MIMO.Meanwhile relative to
The relatively prime MIMO radar of tradition, SA-FIS has higher estimated accuracy, particularly with first aim.
In conclusion the present invention is focused on solving for the design of thinned array MIMO radar structure and compound target DOA estimation
Following two problem：
(1) a kind of flexible MIMO radar structure is designed, and is defined as flexible array element spacing Sparse Array, i.e. SA-FIS.Specifically
Say that SA-FIS can utilize the array element spacing of two relatively prime spreading factor increase transmittings and receiving array, theory analysis explanation in ground
Traditional nested and relatively prime MIMO radar is its special construction.According to " and poor combinatorial array " concept, system has derived relatively prime extension
The closed solutions of the factor, continuously and virtually array element and total Virtual array.Optimization structure proves that SA-FIS can inhibit the phenomenon that mutual coupling
It is lower to obtain more Virtual arrays.
(2) propose a kind of two step CS algorithm of drop complexity to make full use of total Virtual array.By correcting and removing target
Off-diagonal element in covariance matrix, improved CS algorithm can only identify diagonal element therein.Due to traditional C/S algorithm
Need to estimate that all nonzero elements, innovatory algorithm of the present invention can be by estimating that less element number improves estimation performance simultaneously
Reduce complexity.
Disclosed above is only a specific embodiment of the invention, and still, the embodiment of the present invention is not limited to this, is appointed
What what those skilled in the art can think variation should all fall into protection scope of the present invention.
Claims (4)
1. a kind of compressed sensing based flexible MIMO radar compound target DOA estimation method, which is characterized in that including：
Step 1: establishing flexible MIMO radar echo signal model：It by emission array to flexible MIMO radar and connects first
It receives array and carries out matched filtering, array echo signal vector model is obtained, then according to array echo signal vector model x (t)
Obtain the covariance matrix R and vectorization covariance matrix r of array echo signal；
Step 2: carrying out structure optimization to flexible MIMO radar echo signal model：Because of the battle array in vectorization covariance matrix r
Column flow pattern matrix B meets " and poor combinatorial array " feature, therefore, by analyzing " combinatorial array " structure of array manifold matrix B,
Suitable spreading factor is selected, to obtain the more Virtual array numbers of flexible MIMO radar；
Step 3: for the flexible MIMO radar echo signal model after structure optimization, using drop two step CS algorithm of complexity into
Row compound target DOA estimation：Drop two step CS algorithm model of complexity is established by estimating and correcting redundant term, in conjunction with total virtual array
Identical permutation sequence removes the repetition row in vectorization covariance matrix r, can obtain signal model newly.
2. the method as described in claim 1, which is characterized in that the step 1 the specific steps are：
The emission array and receiving array of flexible MIMO radar are made of sparse even linear array, and therefore, total physics array number is T
=M+N；
Wherein, emission array has M array element, and array element spacing is α d；Receiving array has N number of array element, and array element spacing is β d；α and β are
Relatively prime spreading factor, d are unit array element spacing, are typically set to λ/2, λ is signal wavelength；
The element position set of emission array and receiving arrayWithFor：
Wherein, m, n are integer；
Equipped with the irrelevant and relevant compound target in K far field, information source direction integrates as θ={ θk, k=1,2 ..., K }, wherein non-phase
Dry target number and Coherent Targets number are respectively KuAnd Kc, i.e. K=Ku+Kc；Assuming that KcA full coherent condition of goal satisfaction；Then
It is with filtered array echo signal vector model：
Wherein：
Wherein,Be number of snapshots be t when k-th of target reflection coefficient；For kth0A target
Attenuation coefficient, for convenient for statement, it is assumed that[·]TFor matrix transposition operation, diag () is
Diagonal operation,WithIt is long-pending long-pending with Kronecker to respectively indicate Khatri-Rao；
N (t) is independent identically distributed additive gaussian white noise vector, meets CN (0, σ2)；
And
At=[at(θ1),at(θ2),…,at(θK)] (5)
Ar=[ar(θ1),at(θ2),…,ar(θK)] (6)
at(θk) and ar(θk) be respectively emission array and receiving array k-th of target
Direction vector, specially：
It is according to the covariance matrix that formula (2) echo signal model can obtain array echo signal：
R=E [x (t) xH(t)]=ARsAH+σ2IMN (9)
Wherein：
Rs=E [s (t) sH(t)] (10)
For target covariance matrix, AHFor matrix A complex conjugate transposition operation, IMNUnit matrix is tieed up for MN × MN；
When number of snapshots are L, when t=1 ..., L, sample covariance matrix is normally approximately：
Vectorization covariance matrix R is obtained：
R=vec (R)=Bvec (Rs)+σ2vec(IMN) (12)
Wherein,A*Representing matrix complex conjugate operation, vec () representing matrix vector quantities operation.
3. the method as described in claim 1, which is characterized in that the step 2 the specific steps are：Emit battle array using formula (1)
The element position set of column and receiving arrayWith?：
" and poor combinatorial array " collection of SA-FIS is combined into：
Wherein, m0,n0For integer,
Further to analyze setFreedom degree, the Virtual array distribution situation that can obtain SA-FIS is as follows：Pass through vectorization association side
Poor matrix R defines " and poor combinatorial array " set of SA-FISThen SA-FIS has following feature：
(a) relatively prime spreading factor meets：1≤α≤2N-1,1≤β≤2M-1；
(b) gatherContinuously and virtually array element range be [- c, c], wherein c=α M+ β N- α β -1；
(c)In total Virtual array number be 2g+1, g=α (M-1)+β (N-1)-(α -1) (β -1)/2；
Search Space Smoothing is only capable of utilizing continuously and virtually array element, freedom degree c+1；CS algorithm can utilize all virtual arrays
Member, freedom degree 2g+1；To select suitable spreading factor to obtain more Virtual array numbers, now respectively to total virtual array
First number and the optimization of continuously and virtually array number are as follows：
(1) total Virtual array number g
By Optimal Parameters g determine spreading factor α, β and total physics array number in the optimal distribution structure of transmitting terminal and receiving end,
Optimization object function is as follows：
(2) continuously and virtually array number c
Similarly, it establishes and is about the objective function of optimization array number c：
4. the method as described in claim 1, which is characterized in that the step 3 the specific steps are：According to formula (9), array
The covariance matrix of echo-signal can be expressed as again：
Wherein,
It is obtained to after matrix R vectorization：
Wherein, For the signal energy of k-th of target；
By formula (17) it is found that first itemBy target covariance matrix RsDiagonal element composition, Section 2By Rs
Off-diagonal element composition, for the compound target of relevant and incoherent target composition, non-zero off-diagonal element is by Coherent Targets
Coherence factor is constituted；From formula (17) as can be seen that using first item can direct estimation target covariance matrix diagonal element into
And determine target angle, and Section 2 can be handled directly as redundant term；
In conjunction with above-mentioned model analysis, drop two step CS algorithm model of complexity, particular content are established by estimating and correcting redundant term
It is as follows：
(1), for echo-signal vector model in formula (2), the estimated value of echo signal s (t) can be obtained using lowest mean square technology
For：
Where it is assumed that matrix A row full rank, A+=AH(AAH)-1, then target covariance matrix is represented by：
According to formula (19), Section 2 is expressed as in formula (17)：
Using the estimated value of formula (19), formula (17) is expressed as again：
Wherein, parameter lambda1∈[0,1]；
The signal model that removes the row of the repetition in data vector r and can obtain newly that puts in order in conjunction with total Virtual array is：
Wherein, vector e is 2g+1 ranks vector, and g+1 row element is 1, remaining behavior 0；For with Virtual array position phase
Corresponding (2g+1) × K ties up matrix, B0For corresponding (2g+1) × K2Tie up matrix；
Setting search vector is θ={ θj, j=1,2 ..., P }, then can establish optimization object function according to formula (22) is：
Wherein：
And noise statistics amount is it is known that η is regularization parameter；
Optimized model in formula (23) is solved using LASSO algorithm, and to illustrate convenient for step 2, solution is defined as：
(2), the Section 2 in formula (23) is calculated according to search vector θ, and since θ is there are biggish angular error, which is missed
Difference is relatively large；For this purpose, using estimated result θ in formula (26)(1)Again Section 2 is corrected, to further increase estimation performance；
According to estimated result θ(1)The target covariance matrix that can be obtained newly is：
Wherein：
It can be obtained according to formula (27)：
New objective optimization function, which can be constructed, according to formula (30) is：
Wherein, parameter lambda2∈[0,1]；
Comparison expression (23) and (31) are it is found that revised Section 2It is more accurate, therefore λ1≤λ2, so the algorithm has
There are lower operand and higher estimation performance；Meanwhile angle can must be reevaluated by formula (31) and be：
It is pointed out that parameter lambda1,λ2It is constant, value is influenced by echo signal model, therefore, for given signal
Model can determine optimal value by the method for exhaustion.
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