CN109031186A - 2q rank nesting battle array DOA estimation method based on multifrequency Higher Order Cumulants - Google Patents
2q rank nesting battle array DOA estimation method based on multifrequency Higher Order Cumulants Download PDFInfo
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- CN109031186A CN109031186A CN201810927427.4A CN201810927427A CN109031186A CN 109031186 A CN109031186 A CN 109031186A CN 201810927427 A CN201810927427 A CN 201810927427A CN 109031186 A CN109031186 A CN 109031186A
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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
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
- G01S3/14—Systems for determining direction or deviation from predetermined direction
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
Abstract
The invention discloses the 2q rank nesting battle array DOA estimation methods based on multifrequency Higher Order Cumulants, it is related to radar signal and technical field of information processing, aiming at the problem that appearance empty in the prior art causes Virtual array that cannot adequately utilize, the present invention fills up the cavity in original high-order virtual array by the Virtual array that multiple-frequency signal generates, the continuous uniform linear array with more high-freedom degree is formed, to improve DOA estimation performance.
Description
Technical field
The present invention relates to radar signals and technical field of information processing, more particularly to the 2q based on multifrequency Higher Order Cumulants
Rank nesting battle array DOA estimation method.
Background technique
Direction of arrival (direction of arrival, DOA) estimation aims at high-precision target angle measurement, with
Classical uniform array is compared, and Sparse Array has higher freedom degree and lower redundancy, thus obtains in DOA estimation
Extensive concern and research.Typical Sparse Array include minimal redundancy battle array, minimum empty battle array and relatively prime battle array proposed in recent years,
Nested battle array etc., wherein the formation solution procedure of minimal redundancy battle array and minimum empty battle array is complicated and without closed solutions, thus is difficult to practical.
And relatively prime battle array has the element position expression formula of enclosed with nested battle array, can be realized higher freedom degree under same array number, it is real
It is strong with property.One of relatively prime battle array and critical issue of nested battle array research realize the optimization for forming virtual array, from initial and mutual
Battle array structure and the mutual battle array structure of difference, then mutually battle array structure, virtual aperture continuous improvement bring survey to based on Higher Order Cumulants and difference
Raising to precision.However, the nested battle array based on Higher Order Cumulants, which is formed by high-order virtual array, has cavity, lead to portion
Divide Virtual array that can not be utilized.For this problem, there are two types of current solutions, first is that continuously and virtually array element portion is used only
Point, give up discrete Virtual array, it is apparent that wasting part effective freedom degree；Second is that passing through matrix fill-in for the cavity of missing
It fills, to discrete array element be connected, but matrix fill-in needs complicated operation.Multifrequency array DOA is proposed in recent years
Estimation method, but be applied only in the DOA estimation method based on second moment at present, not yet it is applied to the neck of Higher Order Cumulants
Domain.
Summary of the invention
The embodiment of the invention provides the 2q rank nesting battle array DOA estimation methods based on multifrequency Higher Order Cumulants, can solve
Problems of the prior art.
The present invention provides the 2q rank nesting battle array DOA estimation methods based on multifrequency Higher Order Cumulants, comprising the following steps:
The higher order cumulants moment matrix for constructing radar return signal carries out vector quantization to higher order cumulants moment matrix and obtains accordingly
The high mutual battle array of scale；
For the mutual battle array of high scale to work in initial operating frequency, determines wherein empty position and fill up the cavity
Working frequency ωh；The 2q rank nesting battle array of building is set to work in ωh, work is obtained in ωhRadar return signal expression formula, extract
The position collection of repeat element is rejected in the expression formulaWork is filled up in the position collection of initial operating frequencyIn
Cavity obtains work in the continuously and virtually linear array position collection without cavity of initial operating frequencyIt is corresponded to this
Relationship: f:It is determined and is worked in ω according to corresponding relationship fhAnd the high scale for rejecting repeat element is mutual
Battle array position collectionCorresponding vector quantization receives signal
Utilizing spatial smoothing in algorithm willIt is divided into sub-vector, indicates optimal Higher Order Cumulants using sub-vector
Matrix Coptimal, pass through CoptimalCarry out DOA estimation.
The 2q rank nesting battle array DOA estimation method based on multifrequency Higher Order Cumulants in the embodiment of the present invention, its advantages
It is:
1, the mutual battle array freedom degree of high scale that Higher Order Cumulants are formed in conjunction with high-order nesting battle array significantly extends；
2, the utilization of Higher Order Cumulants is able to suppress Gaussian noise, improves signal-to-noise ratio；
3, multiple-frequency signal can fill up the cavity in the mutual battle array of high scale, and all Virtual arrays is made to be fully used, from
It is further increased by degree；
4, strong operability lower compared to operand for technology before of the invention.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is the stream of the 2q rank nesting battle array DOA estimation method provided in an embodiment of the present invention based on multifrequency Higher Order Cumulants
Cheng Tu；
Fig. 2 is the schematic diagram of 7 array element quadravalence nesting battle arrays (q=2)；
Fig. 3 is algorithms of different angle estimation spatial spectrum (D=7)；
Fig. 4 is situation of change (D=7) of the RMSE with signal-to-noise ratio；
Fig. 5 is situation of change (D=7) of the RMSE with number of snapshots；
Fig. 6 is the angle estimation spatial spectrum (D=2) of algorithms of different；
Fig. 7 is situation of change (D=2) of the RMSE with signal-to-noise ratio；
Fig. 8 is situation of change (D=2) of the RMSE with number of snapshots.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Referring to Fig.1, the embodiment of the invention provides the 2q rank nesting battle array DOA estimation method based on multifrequency Higher Order Cumulants,
Method includes the following steps:
Step 1, higher order cumulants moment matrix and the mutual battle array of high scale are constructed
For the linear array with N number of array element, receiving signal be may be expressed as:
Wherein sd(t) (d=1,2 ..., D) is source signal, and u (t) is that N × 1 ties up zero-mean Gaussian noise vector.Steering vector is tieed up for the N × 1 of d-th of signal source, wherein xn(n=0,1 ...,
N-1 distance of n-th of the array element relative to reference array element) is represented.Y (t)=[y1(t),y2(t),…,yN(t)]T, obtained by y (t)
Higher order cumulants moment matrix are as follows:
Whereindj=d, 1≤j≤2q.When l difference, higher order cumulants moment matrix is also different
Form.The energy for representing noise, as q >=2, the above cumulant of the quadravalence of Gaussian noise is 0, thus is expressed asForm, wherein δ (q-1) be impulse function.Formula (2) vector quantization is obtained:
Wherein
B2qThe equivalent steering vector matrix formed after (θ) representative vector, h ∈ CD×1It is the 2q rank cumulant by signal sourceThe vector of composition.ForFor, wherein element may be expressed as:
Wherein
Represent the position coordinates of physics array element, 1≤i≤q.It can be with by formula (4) and formula (5)
It was found that it is unrelated with the value of l to the mutual battle array of 2q scale formed after Higher Order Cumulants matrix vector, and the freedom of the mutual battle array of four scales
Degree further increases.
Step 2, the 2q rank nesting battle array based on multifrequency Higher Order Cumulants is constructed
If 2q rank nesting battle array is sharedA array element, wherein when 1≤i≤2q-1, the array number of every rank
For Ni- 1, corresponding element position are as follows:
The array number of 2q rank is N2q, element position are as follows:
When mono- timing of N, so that being formed by the maximum method of structuring the formation of the mutual battle array freedom degree of 2q scale are as follows:
Wherein m and n is the quotient and the remainder that N+2q-1 is obtained divided by 2q.Array element quadravalence nesting battle array schematic diagram is as shown in Figure 2.Its
(a) show physics element position in middle Fig. 2, and (b) show the virtual poor mutual battle array of quadravalence in Fig. 2, it is seen that exists in virtual array
Cavity causes the Virtual array of discrete portions that can not utilize.For this purpose, the present invention proposes multifrequency point working method filling cavity.
If initial operating frequency is ω0, then formula (3) may be expressed as: again
cvec(ω0)=B2q(ω0)h (9)
Extract B2q(ω0) in location information, be defined as support vector p (ω0), it may be assumed that
WhereinRepresent p (ω0) in Nq(j-1)+i row element.Represent B2q
(ω0) in the i-th row j column element [B2q(ω0)]i,jCorresponding Virtual array position.Reject cvec(ω0) in repeat element can
It obtainsCorrespondingly, p (ω is rejected0) in repeat element obtain(b) is empty in actually Fig. 2
The location sets of matroid member.AnalysisThe position for determining cavity, by taking negative semiaxis as an example, if the position in cavity is γhole,
The non-empty Virtual array position in adjacent first of its left side is γleft, then the working frequency of cavity needs is filled up are as follows:
Wherein h=1,2 ... H, H are negative the total empty number of semiaxis.The 2q rank nesting battle array is enabled to work in frequencies omegah, then have:
y(ωh)=A (ωh)s(ωh)+u(ωh) (12)
Whereinkh=ωh/ c=αhω0/ c=αhk0, obtain after respective vectors
WithDue to In γleftRow is preciselyIn γholeRow, thus it is logical
Cross extractionThe array element of middle corresponding position is filled upMiddle cavity can obtain one without cavity
Continuously and virtually linear array position collectionDefine corresponding relationship f:f
It represents simultaneouslyWith finally receive signal without the corresponding vector quantization of empty continuously and virtually linear arrayPair
It should be related to, therefore can be utilized according to corresponding relationship in fTo constructTo have:
Aoptimal(θ) is free from the corresponding steering vector matrix of continuous 2q rank virtual array in cavity, is based onIt can be real
Existing DOA estimation.
Step 3, DOA estimates
Since h is equivalent to a single snapshot data, so cannot be directly used to DOA estimation.It, will by space smoothing algorithmIt is divided into (No+1) × 1 and ties up sub-vectorNo is positive axis Virtual array number, to have:
For CoptimalDOA estimation can be realized by MUSIC, ESPRIT scheduling algorithm.
Experimental verification
By simulation results show effectiveness of the invention, if quadravalence nesting battle array (q=2) shares 7 array elements.
Experiment 1: inspection inventive algorithm chooses 2q MUSIC algorithm, is based on single-frequency to the Measure direction performance of multiple target first
2q rank nesting battle array (SFHOC 2q NA) the DOA algorithm for estimating of Higher Order Cumulants is based on multifrequency higher order cumulants with proposed by the present invention
2q rank nesting battle array (the Multiple Frequency High Order Cumulant based 2q-level Nested of amount
Array, MFHOC 2q NA) DOA algorithm for estimating compares.Equipped with 7 targets, i.e. D=7, angle is respectively 10 °, 12 °,
14°,……,28°.When signal-to-noise ratio is 10dB, and number of snapshots are 300, direction finding result is as shown in Figure 3.From the figure 3, it may be seen that only originally
Invention algorithm can accurately estimate the angle of 7 targets, 2q MUSIC (q=1,2) angle measurement failure, and SFHOC2q NA is also deposited
In large error.Then, target component setting is constant, further studies under different signal-to-noise ratio and different number of snapshots, each algorithm
Root-mean-square error (Root mean square error, RMSE).When Fig. 4 is number of snapshots 500, the RMSE of algorithms of different is with letter
Make an uproar the situation of change of ratio, the RMSE of algorithms of different that Fig. 5 is signal-to-noise ratio when being 10dB with number of snapshots situation of change.It can from Figure 4 and 5
See, the angle error of mentioned algorithm is minimum, this is because inventive algorithm realizes virtual freedom degree compared to other algorithms
It maximally utilizes.
Experiment 2: resolving power of this experimental verification inventive algorithm to adjacent objects.If the angle of two targets is respectively
10 ° and 10.5 °, equally as a comparison with 2q MUSIC algorithm, SFHOC 2q NA method, when signal-to-noise ratio is 10dB, number of snapshots are
When 300, as shown in fig. 6, only inventive algorithm can accurately estimate the angle of two adjacent objects, other are calculated direction finding result
Method cannot accurate direction finding.Then, it further studies under different signal-to-noise ratio and different number of snapshots, the variation feelings of each algorithm RMSE
Condition.When Fig. 7 is number of snapshots 500, with the situation of change of signal-to-noise ratio, it is different when being 10dB that Fig. 8 is signal-to-noise ratio by the RMSE of algorithms of different
The RMSE of algorithm with number of snapshots situation of change.From Fig. 7 and 8 as it can be seen that the angle error of mentioned algorithm is minimum.It can be seen that freedom degree
Improve the promotion for bringing angular resolution.
Although preferred embodiments of the present invention have been described, it is created once a person skilled in the art knows basic
Property concept, then additional changes and modifications may be made to these embodiments.So it includes excellent that the following claims are intended to be interpreted as
It selects embodiment and falls into all change and modification of the scope of the invention.
Obviously, various changes and modifications can be made to the invention without departing from essence of the invention by those skilled in the art
Mind and range.In this way, if these modifications and changes of the present invention belongs to the range of the claims in the present invention and its equivalent technologies
Within, then the present invention is also intended to include these modifications and variations.
Claims (4)
1. the 2q rank nesting battle array DOA estimation method based on multifrequency Higher Order Cumulants, which comprises the following steps:
The higher order cumulants moment matrix for constructing radar return signal carries out vector quantization to higher order cumulants moment matrix and obtains corresponding high-order
The mutual battle array of difference；
For the mutual battle array of high scale to work in initial operating frequency, determines the wherein position in cavity and fill up the work in the cavity
Frequencies omegah；The 2q rank nesting battle array of building is set to work in ωh, work is obtained in ωhRadar return signal expression formula, extract the table
Up to the position collection for rejecting repeat element in formulaWork is filled up in the position collection of initial operating frequencyIn cavity,
Work is obtained in the continuously and virtually linear array position collection without cavity of initial operating frequencyCorresponding relationship is obtained with this:
f:It is determined and is worked in ω according to corresponding relationship fhAnd reject the mutual battle array position of high scale of repeat element
Set collectionCorresponding vector quantization receives signal
Utilizing spatial smoothing in algorithm willIt is divided into sub-vector, indicates optimal higher order cumulants moment matrix using sub-vector
Coptimal, pass through CoptimalCarry out DOA estimation.
2. the 2q rank nesting battle array DOA estimation method based on multifrequency Higher Order Cumulants as described in claim 1, which is characterized in that
For the linear array with N number of array element, receiving signal is indicated are as follows:
Wherein sd(t), d=1,2 ..., D are source signal, and D is signal source number, and u (t) is that N × 1 ties up zero-mean Gaussian noise arrow
Amount,Steering vector is tieed up for the N × 1 of d-th of signal source, wherein xn, n=0,
1 ..., N-1 represents distance of n-th of the array element relative to reference array element；Y (t)=[y1(t),y2(t),…,yN(t)]T, by y (t)
Obtained higher order cumulants moment matrix are as follows:
Whereindj=d, 1≤j≤2q,0≤l≤q-1,The energy of noise is represented, δ (q-1) is impulse function,
Formula (2) vector quantization is obtained into the corresponding high mutual battle array of scale:
Whereinθ=[θ1,θ2…θD]T,B2q(θ) is represented
The equivalent steering vector matrix formed after vector quantization, h ∈ CD×1It is the 2q rank cumulant by signal source1≤d≤D composition
Vector.
3. the 2q rank nesting battle array DOA estimation method based on multifrequency Higher Order Cumulants as claimed in claim 2, which is characterized in that
It is ω for initial operating frequency0, formula (3) expression are as follows:
cvec(ω0)=B2q(ω0)h (4)
Extract B2q(ω0) in location information, be defined as support vector p (ω0), it may be assumed that
WhereinRepresent p (ω0) in Nq(j-1)+i row element,Represent B2q(ω0) in
I-th row j column element [B2q(ω0)]i,jC is rejected in corresponding Virtual array positionvec(ω0) in repeat element obtainReject p (ω0) in repeat element obtainAnalysisThe position in cavity is determined, if the position in cavity
For γhole, the non-empty Virtual array position in adjacent first of left side is γleft, then the working frequency of cavity needs is filled up
Are as follows:
Wherein h=1,2 ... H, H are negative the total empty number of semiaxis, and 2q rank nesting battle array is enabled to work in frequencies omegah, then have:
y(ωh)=A (ωh)s(ωh)+u(ωh) (7)
Whereinkh=ωh/ c=αhω0/ c=αhk0, obtain after vector quantizationWithIt extractsThe array element of middle corresponding position is filled upMiddle cavity obtains the continuously and virtually linear array position without cavity
CollectionDefine corresponding relationship f:F is represented simultaneouslyWith finally without sky
Continuously and virtually linear array corresponding vector quantization in hole receives signalCorresponding relationship utilized according to corresponding relationship in fConstructionTo have:
Aoptimal(θ) is free from the corresponding steering vector matrix of continuous 2q rank virtual array in cavity.
4. the 2q rank nesting battle array DOA estimation method based on multifrequency Higher Order Cumulants as claimed in claim 3, which is characterized in that
It, will by space smoothing algorithmIt is divided into (No+ 1) sub-vector × 1 is tieed upNoIt is virtual for positive axis
Array number, to have:
For CoptimalDOA estimation is realized by MUSIC or ESPRIT algorithm.
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Cited By (4)
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| CN110133574A (en) * | 2019-07-02 | 2019-08-16 | 华南理工大学 | Utilize the one-dimensional DOA estimation method of the secondary virtual extended of multiple-frequency signal |
| CN111965591A (en) * | 2020-07-21 | 2020-11-20 | 南京航空航天大学 | Direction-finding estimation method based on fourth-order cumulant vectorization DFT |
| CN112485755A (en) * | 2020-11-20 | 2021-03-12 | 中国人民解放军空军工程大学 | Angle estimation method based on 2 q-order nested MIMO array structure |
| CN112986900B (en) * | 2021-02-07 | 2023-09-19 | 中国人民解放军国防科技大学 | Flexible mutual mass array for DOA estimation |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110133574A (en) * | 2019-07-02 | 2019-08-16 | 华南理工大学 | Utilize the one-dimensional DOA estimation method of the secondary virtual extended of multiple-frequency signal |
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| CN111965591A (en) * | 2020-07-21 | 2020-11-20 | 南京航空航天大学 | Direction-finding estimation method based on fourth-order cumulant vectorization DFT |
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| CN112485755A (en) * | 2020-11-20 | 2021-03-12 | 中国人民解放军空军工程大学 | Angle estimation method based on 2 q-order nested MIMO array structure |
| CN112485755B (en) * | 2020-11-20 | 2023-05-12 | 中国人民解放军空军工程大学 | Angle estimation method based on 2 q-order nested MIMO array structure |
| CN112986900B (en) * | 2021-02-07 | 2023-09-19 | 中国人民解放军国防科技大学 | Flexible mutual mass array for DOA estimation |
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