CN106950553A - The MIMO radar super-resolution Direction Finding Algorithm of coherent under Colored Noise - Google Patents
The MIMO radar super-resolution Direction Finding Algorithm of coherent under Colored Noise Download PDFInfo
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- 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 present invention relates to MIMO radar (MIMO radar) super-resolution Direction Finding Algorithm field, the MIMO radar super-resolution Direction Finding Algorithm of coherent under open Colored Noise, specifically propose a kind of smooth (ISDS) algorithm of improved space difference, and on the basis of ISDS algorithms, have also been proposed a kind of fast algorithm based on propagation operator, i.e. PM ISDS algorithms.Theory analysis and emulation show that carried algorithm has very strong coloured noise rejection ability, and estimation performance is saved, information source overload capacity better than conventional space smoothing algorithm with preferable array element, and need not carry out Eigenvalues Decomposition, and operand is smaller.
Description
Technical field
The present invention relates to MIMO radar super-resolution Direction Finding Algorithm field, coherent under Colored Noise is particularly related to
MIMO radar super-resolution Direction Finding Algorithm.
Background technology
The current research on MIMO radar super-resolution direction finding commonly assumes that noise for white Gaussian noise, but practical application
In, such as when the flicker caused by there is big reflecting surface in echo or the spike interference caused as wave, noise is coloured noise.
Further, since the presence of low latitude multipath effect so that the target echo that MIMO radar is received is often relevant.In these situations
Under, the most frequently used subspace class algorithm, such as ESPRIT, MUSIC performance will drastically decline.Therefore, Colored Noise or relevant
The super-resolution direction finding of information source has been received significant attention.Pertinent literature [Wen C and Wang T.Reduced- are had at present
dimensional unitary ESPRIT algorithm for monostatic MIMO radar[J].Systems
Engineering and Electronics,2014,36(6): 1062–1067；Zheng G M,Chen B X,and Yang
M L.Unitary ESPRIT algorithm for bistatic MIMO radar[J].Electronics Letters,
2012,48(3):179-181] coloured noise is handled using the method for carrying out calculus of differences, but coherent can not be differentiated.Document
[Spatial Smoothing Differencing Techniques [J] communication journals, 1997,18 (9) are paid in leaf:1-7] use front-rear space smooth difference
(FBSSD) algorithm, can differentiate coherent but resolving power is relatively low, and not account for the influence of coloured noise.Document [neat Chong Ying
High-resolution Mutual coupling sane Journal of Sex Research [D] Xi'an：Air force engineering university, 2005:74-79] also propose a kind of color
Smooth (SDS) algorithm of the space difference of coherent under noise background, but algorithm difference covariance matrix under specific circumstances
Occur that rank defect is damaged.
The content of the invention
It is an object of the invention to provide the MIMO radar super-resolution Direction Finding Algorithm of coherent under Colored Noise, the algorithm
Realize to information source decorrelation LMS and to difference matrix amendment, calculated with more preferable Measure direction performance, and compared to matrix decomposition class simultaneously
Method operand is smaller.
To achieve these goals, present invention employs following technical scheme：Coherent under Colored Noise
MIMO radar super-resolution Direction Finding Algorithm, using a kind of smooth (ISDS) algorithm of space difference, and on the basis of ISDS algorithms
On, it is proposed that a kind of fast algorithm PM-ISDS algorithms based on propagation operator, specifically include following steps：
Step 1：Set up compound information MIMO radar data model
Array antenna transmit-receive sharing in MIMO radar, is the equidistant linear array of M array elements, and it is load to take array element spacing d=λ/2, λ
Ripple wavelength；
Assuming that there is P target in radar far field, DOA and DOD are θp.Then target be ideal point target in the case of, reception
Echo-signal can be obtained after matched filtering：
y(tl)=A α (tl)+n(tl) (1)
In formula
n(tl) represent noise column vector, a (θp) p-th target direction vector, ξpFor the reflectance factor of p-th of target, fdpFor pth
The normalization Doppler frequency of individual target, tlRepresent umber of pulse,Represent Kronecker products；
If existing independent source also has coherent in P information source, preceding G might as well be set as coherent, then independent letter
Source number U=P-G, therefore MIMO radar covariance matrix is represented by：
Wherein, Rnc、RcThe respectively covariance matrix of independent source and coherent,Coloured noise covariance matrix, then Rnc
WithFor Hermite matrixes and Toeplitz matrixes, RcFor Hermite matrixes and non-Toeplitz matrixes, array manifold can occur
Degenerate, be changed into the vector of P × 1, information source covariance can also degenerate, be changed into constant η, noise subspace is extended for P-U-1 dimensions,
And signal subspace deteriorates to U+1 dimensions；
Step 2：First use ISDS algorithms
Further to make full use of the cross-correlation information between the elements in a main diagonal and each submatrix, by the autocorrelation matrix of submatrix
Cross correlation process is carried out, and the cross-correlation matrix of submatrix in symmetric position is subjected to cross correlation process, then result is asked
Equivalent space smoothing matrix is averagely obtained, so as to improve Measure direction performance.
Array difference matrix can be expressed as：
Formula (2) substitution formula (5) can be obtained into array difference matrix is：
From (6), gained matrix does not have Toeplitz, contains only the information of coherent source, not comprising independent letter
Source and the information of spatial noise；
Had according to formula (3), (4) to Δ R progress calculating：
Wherein
It can prove, matrixOrder be G, be unsatisfactory for antisymmetric matrix form, realize array difference
The amendment of matrix；
Step 3：PM-ISDS algorithms are used on the basis of ISDS algorithms
Noise subspace is obtained by Eigenvalues Decomposition, amount of calculation is larger when element number of array is more, here, can profit
Further reduce the amount of calculation of ISDS algorithms with propagation operator method (PM, PropagatorMethod)；
Because being free of noise information in the covariance matrix of ISDS algorithms, then matrixIt can be written as：
Wherein, AmAfter smoothArray manifold matrix corresponding to matrix,For information source covariance matrix of equal value；
By matrix AmPiecemeal is：
Wherein, A1、A2Respectively G × G, (P-G) × G rank matrixes.Assuming that array manifold is without fuzzy, then A1For nonsingular square
Battle array, therefore there is F, meet FHA1=A2, order：
QH=[FH -I] (11)
Then the space of Q belongs to noise subspace, i.e.,：
Span (Q)=span (EN) (12)
By matrixPiecemeal is：
Then V=WF, i.e. F=(WHW)-1WHV, is obtained by formula (11)：
QH=[((WHW)-1WHV)H-I] (14)
But Q and ENDifference be：It is not orthogonal basis that obtained base is respectively arranged by Q, and orthogonalization Q can be obtained：
Q0=Q (QHQ)-1/2 (15)
Therefore, PM-ISDS space spectral function is represented by：
The beneficial effects of the present invention are：Propose a kind of smooth (ISDS) algorithm of improved space difference, and
On the basis of ISDS algorithms, a kind of fast algorithm based on propagation operator, i.e. PM-ISDS algorithms are had also been proposed.Theory analysis and
Emulation experiment shows that the PM-ISDS algorithms based on propagation operator carried have very strong coloured noise rejection ability, estimation property
Can be better than conventional space smoothing algorithm, the method handled in two steps can reuse the reception data of radar, with preferable
Array element save and information source overload capacity, and Eigenvalues Decomposition need not be carried out in solution procedure, operand is smaller.
Brief description of the drawings
Technical scheme in order to illustrate more clearly the embodiments of the present invention, embodiment will be described below needed for be used
Accompanying drawing is briefly described, it should be apparent that, drawings in the following description are only the present invention in order to illustrate more clearly of this hair
Bright embodiment or technical scheme of the prior art, it is attached by what is used needed for p- embodiment or description of the prior art below
Figure is briefly described, for those of ordinary skill in the art, on the premise of not paying creative work, can be with root
Other accompanying drawings are obtained according to these accompanying drawings.
Fig. 1 is MIMO radar super-resolution direction-finding chart；
Fig. 2 is that coherent resolution capability relatively descends FSS (forward direction space smoothing), FBSS (front and rear under Colored Noise
To space smoothing) spatial spectrum of algorithm simulating；
Fig. 3 is that coherent resolution capability relatively descends SDS, ISDS and PM-ISDS algorithm simulating under Colored Noise
Spatial spectrum；
Fig. 4 is relatively to descend FSS (forward direction space smoothing), FBSS (front-rear space smooth) in the rejection ability to coloured noise
The spatial spectrum of algorithm simulating；
Fig. 5 be the rejection ability to coloured noise relatively descend SDS (space difference is smooth), IFBSDS (it is improved it is front and rear to
Space difference is smooth), the spatial spectrum of PM-IFBSDS algorithm simulatings；
Fig. 6 is the spatial spectrum that MUSIC algorithm simulatings are relatively descended in the rejection ability to coloured noise；
Fig. 7 is the spatial spectrum that SDS, IFBSDS, PM-IFBSDS algorithm simulating are relatively descended in information source overload capacity；
Fig. 8 is the spatial spectrum that MUSIC (multiple signal classification algorithm) algorithm simulating is relatively descended in information source overload capacity.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
1st, compound information MIMO radar data model
Consideration MIMO radar as shown in Figure 1, wherein array antenna transmit-receive sharing, are the equidistant linear array of M array elements, take battle array
First spacing d=λ/2, λ are carrier wavelength.
Assuming that there is P target in radar far field, DOA and DOD are θp.Then target be ideal point target in the case of, reception
Echo-signal can be obtained after matched filtering：
y(tl)=A α (tl)+n(tl) (1)
In formula
n(tl) represent noise column vector, a (θp) p-th target direction vector, ξpFor the reflectance factor of p-th of target, fdpFor pth
The normalization Doppler frequency of individual target, tlRepresent umber of pulse,Represent Kronecker products.
If existing independent source also has coherent in P information source, preceding G might as well be set as coherent, then independent letter
Source number U=P-G, therefore MIMO radar covariance matrix is represented by：
Wherein, Rnc、RcThe respectively covariance matrix of independent source and coherent,It is coloured noise covariance matrix.Then Rnc
WithFor Hermite matrixes and Toeplitz matrixes, RcFor Hermite matrixes and non-Toeplitz matrixes.Array manifold can occur
Degenerate, be changed into the vector of P × 1, information source covariance can also degenerate, be changed into constant η, noise subspace is extended for P-U-1 dimensions,
And signal subspace deteriorates to U+1 dimensions.
2nd, the quick ISDS algorithms based on propagation operator
2.1 ISDS algorithm principles
Further to make full use of the cross-correlation information between the elements in a main diagonal and each submatrix, by the autocorrelation matrix of submatrix
Cross correlation process is carried out, and the cross-correlation matrix of submatrix in symmetric position is subjected to cross correlation process, then result is asked
Equivalent space smoothing matrix is averagely obtained, so as to improve Measure direction performance.
Array difference matrix can be expressed as：
Formula (2) substitution formula (5) can be obtained into array difference matrix is：
From (6), gained matrix does not have Toeplitz, contains only the information of coherent source, not comprising independent letter
Source and the information of spatial noise.
The ISDS algorithms used herein, are not only able to be modified array difference matrix, and can realize coherent source
Decorrelation LMS processing, its principle is as follows：
Had according to formula (3), (4) to Δ R progress calculating：
Wherein
It can prove, matrixOrder be G, be unsatisfactory for antisymmetric matrix form, realize array difference square
The amendment of battle array.
2.2PM-ISDS algorithm principles
Noise subspace is obtained by Eigenvalues Decomposition, amount of calculation is larger when element number of array is more.Here, can profit
Further reduce the amount of calculation of ISDS algorithms with propagation operator method (PM, PropagatorMethod).
Because being free of noise information in the covariance matrix of ISDS algorithms, then matrixIt can be written as：
Wherein, AmAfter smoothArray manifold matrix corresponding to matrix,For information source covariance square of equal value
Battle array.
By matrix AmPiecemeal is：
Wherein, A1、A2Respectively G × G, (P-G) × G rank matrixes.Assuming that array manifold is without fuzzy, then A1For nonsingular square
Battle array, therefore there is F, meet FHA1=A2, order：
QH=[FH -I] (11)
Then the space of Q belongs to noise subspace, i.e.,：
Span (Q)=span (EN) (12)
By matrixPiecemeal is：
Then V=WF, i.e. F=(WHW)-1WHV, is obtained by formula (11)：
QH=[((WHW)-1WHV)H-I] (14)
But Q and ENDifference be：It is not orthogonal basis that obtained base is respectively arranged by Q, and orthogonalization Q can be obtained：
Q0=Q (QHQ)-1/2 (15)
Therefore, PM-ISDS space spectral function is represented by：
2.3 PM-ISDS algorithm steps
Derivation more than, is summarized as follows the step of by PM-ISDS algorithms：
Step 1：Super-resolution direction finding is carried out to the information source for meeting independence using PM algorithms；
Step 2：The array difference matrix Δ R of MIMO radar is calculated according to formula (6)；
Step 3：Calculated according to formula (7) or (8)Or
Step 4：It is rightOrUsing PM algorithms, Q is obtained by formula (14)H；
Step 5：According to formula (15) to QHIt is normalized；
Step 6：Super-resolution direction finding is carried out according to formula (16).
3rd, PM-ISDS algorithm performances are analyzed
3.1 computational complexity gains
Multiplying number of times needed for the MUSIC algorithms that feature based is decomposed is approximately o (m3), multiplication needed for propagation operator method
Operation times are approximately o (Gm2), therefore, gain of the PM-ISDS fast algorithms relative to ISDS algorithms on operand is o
(G/m)。
3.2 information source overload capacity
All sometimes, according to conventional algorithm to independent source direction finding, maximum can estimate L- for independent source and coherent
2 incoherent information sources, L/2 or 2L/3 relevant information sources can be estimated according to ISDS algorithms maximum.Therefore, ISDS algorithms
Maximum can estimate 3L/2-2 or 5L/3-2 information source.This means ISDS algorithms information source number can be more than element number of array,
The overload capacity of information source is stronger.
3.3 array elements save ability
Independent source and coherent all sometimes, 2G+U array element are needed according to FSS algorithms；3/ is needed according to FBSS algorithms
2G+U array element；And incoherent information source is differentiated by conventional treatment according to the ISDS algorithms first step, U+2 array element is needed, second step
Handled by ISDS and differentiate relevant information source, need 2G or 3G/2 array element.Therefore, max [U+2,3G/2] or max [U+2,2G] are
The required element number of array of ISDS algorithms.It can be seen that element number of array needed for FSS algorithms, FBSS algorithms is more than information source number, and ISDS is calculated
Method can but accomplish to save array element.
4th, computer artificial result
4.1 algorithms are under Colored Noise to coherent direction finding ability
Under Colored Noise, there is the equal coherent of 4 power in -30 °, -25 °, 10 ° and 40 ° orientation, using 10
The MIMO radar of array element, is divided into 4 submatrixs by MIMO radar, takes fast umber of beats 200, SNR takes 10dB.Fig. 2 gives FSS, FBSS
The spatial spectrum of algorithm simulating, Fig. 3 gives the spatial spectrum of SDS, ISDS and PM-ISDS algorithm simulating.
By emulating under visible Colored Noise, FSS and FBSS algorithms are to the direction finding of coherent complete mistake；SDS is calculated
Method is using conventional forward direction space smoothing, and the resolving power of algorithm is poor, IFBSDS and PM-IFBSDS algorithms change because make use of
The front-rear space smooth algorithm entered, resolving power is preferable, and both space spectral curves are substantially coincidence.
Comparison of the 4.2 several algorithms of different to coloured noise rejection ability
Under the conditions of coloured noise, it is assumed that MIMO radar has in 10 array elements, 20 °, 40 °, 10 °, -5 °, -20 °, -45 ° of orientation
Have the equal signal source of 6 power, before 2 be incoherent signal source, behind 4 be relevant signal source, by MIMO thunders
Up to 2 submatrixs are divided into, 200 fast umber of beats emulation are taken, SNR takes 10dB.Fig. 4 gives the spatial spectrum of FBSS, FSS algorithm simulating, figure
5 give the spatial spectrum of SDS, IFBSDS, PM-IFBSDS algorithm simulating, and Fig. 6 gives the spatial spectrum of MUSIC algorithm simulatings.
From emulation, FSS algorithms, FBSS algorithms can not correctly direction findings under the conditions of coloured noise；SDS, IFBSDS and
PM-IFBSDS algorithms can be correctly to coherent direction finding, and the resolving power of IFBSDS and PM-IFBSDS algorithms is higher than SDS
Algorithm；Simultaneously it is also seen that MUSIC algorithms by coloured noise due to being influenceed, larger pseudo- peak occurs in its space spectral curve.
The information source overload capacity of 4.3PM-ISDS algorithms
Under the conditions of coloured noise, it is assumed that MIMO radar has 9 array elements, -30 ° of orientation, -10 °, 15 °, 35 °, 50 °, -45 °, -
Have the equal information source source of 9 power on 20 °, 5 °, 25 °, before 5 be incoherent signal source, behind 4 be relevant letter
Number source, is divided into 4 submatrixs by MIMO radar, takes 200 fast umber of beats emulation, and SNR takes 10dB.Fig. 7 emulation be SDS, IFBSDS,
The spatial spectrum of PM-IFBSDS algorithms, Fig. 8 emulation is the spatial spectrum of MUSIC algorithms.
From Fig. 7 and Fig. 8, the signal source being concerned with according to ISDS and PM-ISDS algorithm process, and with MUSIC algorithms
The irrelevant signal source of reason, two kinds of algorithm joint direction findings remain to oversubscription in the case where information source number is more than radar element number of array
Direction finding is distinguished, with information source overload capacity；And though SDS algorithms also have information source overload capacity, the resolution capability of its spectral line is not so good as
ISDS and PM-ISDS algorithms.When information source number is more than element number of array, FSS and FBSS algorithms do not possess overload capacity, lose
Effect.
The upper only presently preferred embodiments of the present invention, is not intended to limit the invention, all spirit in the present invention
Within principle, any modifications, equivalent substitutions and improvements made etc. should be included within the scope of the present invention.
Claims (1)
1. the MIMO radar super-resolution Direction Finding Algorithm of coherent under Colored Noise, it is characterised in that：Using a kind of space parallax
Divide smooth (ISDS) algorithm, and on the basis of ISDS algorithms, it is proposed that a kind of fast algorithm PM- based on propagation operator
ISDS algorithms, specifically include following steps：
Step 1：Set up compound information MIMO radar data model
Array antenna transmit-receive sharing in MIMO radar, is the equidistant linear array of M array elements, and it is carrier wave ripple to take array element spacing d=λ/2, λ
It is long；
Assuming that there is P target in radar far field, DOA (direction of arrival) and DOD (ripple is from direction) are θp.Then target is ideal point mesh
In the case of mark, the echo-signal of reception can be obtained after matched filtering：
y(tl)=A α (tl)+n(tl) (1)
In formula
n(tl) represent noise column vector, a (θp) p-th target direction vector, ξpFor the reflectance factor of p-th of target, fdpFor p-th
The normalization Doppler frequency of target, tlRepresent umber of pulse,Represent Kronecker products；
If existing independent source also has coherent in P information source, preceding G might as well be set as coherent, then independent source
Number U=P-G, therefore MIMO radar covariance matrix is represented by：
Wherein, Rnc、RcThe respectively covariance matrix of independent source and coherent,Coloured noise covariance matrix, then RncWithFor
Hermite matrixes and Toeplitz matrixes, RcFor Hermite matrixes and non-Toeplitz matrixes, array manifold can degenerate,
It is changed into the vector of P × 1, information source covariance can also degenerate, is changed into constant η, noise subspace is extended for P-U-1 dimensions, and believes
Work song space deteriorates to U+1 dimensions；
Step 2：First use ISDS algorithms
Further to make full use of the cross-correlation information between the elements in a main diagonal and each submatrix, the autocorrelation matrix of submatrix is carried out
Cross correlation process, and the cross-correlation matrix of submatrix in symmetric position is subjected to cross correlation process, then result progress summation is flat
Equivalent space smoothing matrix is obtained, so as to improve Measure direction performance；
Array difference matrix can be expressed as：
Formula (2) substitution formula (5) can be obtained into array difference matrix is：
From (6), gained matrix does not have Toeplitz, contains only the information of coherent source, not comprising independent source and
The information of spatial noise；
Had according to formula (3), (4) to Δ R progress calculating：
Wherein
It can prove, matrixOrder be G, be unsatisfactory for antisymmetric matrix form, realize array difference matrix
Amendment；
Step 3：PM-ISDS algorithms are used on the basis of ISDS algorithms
Noise subspace is obtained by Eigenvalues Decomposition, amount of calculation is larger when element number of array is more, herein, it is possible to use pass
Operator Method (PM, PropagatorMethod) is broadcast further to reduce the amount of calculation of ISDS algorithms；
Because being free of noise information in the covariance matrix of ISDS algorithms, then matrixIt can be written as：
Wherein, AmAfter smoothArray manifold matrix corresponding to matrix,For information source covariance matrix of equal value；
By matrix AmPiecemeal is：
Wherein, A1、A2Respectively G × G, (P-G) × G rank matrixes.Assuming that array manifold is without fuzzy, then A1For nonsingular matrix, therefore
There is F, meet FHA1=A2, order：
QH=[FH -I] (11)
Then the space of Q belongs to noise subspace, i.e.,：
Span (Q)=span (EN) (12)
By matrixPiecemeal is：
Then V=WF, i.e. F=(WHW)-1WHV, is obtained by formula (11)：
QH=[((WHW)-1WHV)H-I] (14)
But Q and ENDifference be：It is not orthogonal basis that obtained base is respectively arranged by Q, and orthogonalization Q can be obtained：
Q0=Q (QHQ)-1/2 (15)
Therefore, PM-ISDS space spectral function is represented by：
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| CN110531311A (en) * | 2019-08-27 | 2019-12-03 | 武汉大学深圳研究院 | A kind of LTE external illuminators-based radar DOA estimation method based on matrix recombination |
| CN110940933A (en) * | 2019-12-02 | 2020-03-31 | 国网河北省电力有限公司电力科学研究院 | Comprehensive calculation method for measuring rising edge starting time of steep pulse |
| CN113341372A (en) * | 2021-05-31 | 2021-09-03 | 电子科技大学 | DOA estimation method based on decoherence unitary Root-MUSIC algorithm |
| CN114325565A (en) * | 2021-12-27 | 2022-04-12 | 中国科学技术大学 | Subspace relationship-based array super-resolution direction finding method |
| CN114325565B (en) * | 2021-12-27 | 2024-05-14 | 中国科学技术大学 | Array super-resolution direction finding method based on subspace relation |
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