CN107092007A - A kind of Wave arrival direction estimating method of virtual second order array extension - Google Patents
A kind of Wave arrival direction estimating method of virtual second order array extension Download PDFInfo
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- CN107092007A CN107092007A CN201710379098.XA CN201710379098A CN107092007A CN 107092007 A CN107092007 A CN 107092007A CN 201710379098 A CN201710379098 A CN 201710379098A CN 107092007 A CN107092007 A CN 107092007A
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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
- G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae
Abstract
A kind of Wave arrival direction estimating method of virtual second order array extension of the disclosure of the invention, belong to the antenna array signals processing category for receiving wireless transmission signal, specifically, it is that one kind is directed to the method that vector is built into virtual Volterra filter constructions and carries out direction of arrival (DOA) estimation with reference to beam-forming technology and method of Lagrange multipliers technology.Vector is directed to be built into virtual Volterra filter constructions and combine beam-forming technology and method of Lagrange multipliers technology to carry out direction of arrival (DOA) estimation.This algorithm can not only realize that DOA estimates under information source number unknown condition, but also independent of Subspace Decomposition.Avoiding problems the influence that performance is produced is estimated DOA because of mistake estimation information source number, improve DOA estimation resolution capabilities, while also reducing computation complexity.
Description
Technical field
Category is handled the invention belongs to the antenna array signals for receiving wireless transmission signal, is that one kind will be led specifically
Virtual Volterra filter constructions are built into vector and combine beam-forming technology and method of Lagrange multipliers technology to enter
The method of row direction of arrival (DOA) estimation.
Background technology
In recent decades, array signal processing is as an important branch in modern signal processing field, and development is extremely
Rapidly, in radar, sonar, communication, electronics, seismic prospecting, astronomical observation, biomedicine, numerous military and national economy etc.
Numerous areas is widely used.And topmost two research directions of array signal processing be adaptive spatial filtering and
DOA estimates.The generation of adaptive array processing technique will be estimated earlier than DOA, and be widely applied.Although on the contrary,
DOA estimations are also obtaining rapid development in recent decades, during current DOA estimation theories and technology are still in developing rapidly,
Turn into the main aspect of array signal processing discipline development.
Substantial amounts of DOA algorithm for estimating is suggested during this, as everyone knows by American scientist Schmidt R.O.
Et al. multiple signal classification (Multiple Signal Classification, MUSIC) algorithm and Roy et al. for working out carry
A kind of invariable rotary Subspace algorithm gone out.They are the once leaps in array signal processing field, realize normal resolution
DOA estimation method is strided forward to subspace class super-resolution DOA estimation method.The principle of MUSIC algorithms is that autocorrelation matrix is entered
Row Subspace Decomposition, obtains the noise subspace and signal subspace of matrix, then utilizes noise subspace and direction vector
Orthogonality relation, estimates the incident direction of signal, and it breaches " Rayleigh limit ", with very high resolution ratio.But there is also one for it
A little problems, are scanned, computationally intensive, the requirement to hardware is high if desired for all azimuths in space.In order to improve these
Deficiency, it is a series of that researcher has also been proposed rooting MUSIC, space smoothing MUSIC algorithms, minimum norm, characteristic vector method etc.
Noise subspace decompose space-like Power estimation algorithm.But in any case, this kind of algorithm based on signal characteristic space all must
Must known information source number.Akaike information criterion and Minimum description length criterion are often used in Sources number estimation.However, experiment card
It is bright under conditions of hits is less or signal to noise ratio is relatively low, these algorithms can not correctly estimate information source number.If to information source
There is mistake in number estimations, and the performance of above-mentioned DOA algorithm for estimating is by degradation.In order to avoid the estimation of information source number, Wave beam forming
Technology, such as minimum variance are undistorted, and response technology is also applied in DOA estimation problems.However, this beam-forming technology
DOA estimations resolution ratio is not high.Afterwards, the DOA algorithm for estimating under some other unknown information source numbers is suggested, and such as uses linear prediction
Or Pisarenko harmonic waves algorithm for estimating joint carries out the self-adapting signal parameter Estimation and sorting technique of DOA estimations.But this
It is only to be set up in the case of information source number is less than half number of arrays to plant algorithm, and pre-estimation information source number is not also solved.For
These problems are solved, a kind of new class MUSIC DOA estimation method is suggested, this algorithm avoids Subspace Decomposition, and
And information source number need not be determined, so as to reduce the influence produced by Sources number estimation error to performance.
The content of the invention
The present invention seeks to be improved for existing algorithm, it is proposed that a kind of new DOA estimation method, pass through
Volterra filter constructions build steering vector to carry out DOA estimations.This algorithm can not only realize information source number unknown condition
Under DOA estimations, but also independent of Subspace Decomposition.Avoiding problems estimate property to DOA because of mistake estimation information source number
The influence that can be produced, improves DOA estimation resolution capabilities.
The present invention solution be：It is first with Second-Order Volterra Filter, observation data configuration is new into one
Array received data, and obtain a new steering vector.Then the covariance matrix of array received signal vector is estimated,
The weight vector of optimal spatial filter is obtained by beam-forming technology and method of Lagrange multipliers technology again afterwards.Finally
The space spectral function estimated to DOA.
The present invention is a kind of Wave arrival direction estimating method of virtual second order array extension, and this method is concretely comprised the following steps：
Step 1：New array received data y (t) is constructed by the data x (t) of array received；
Step 1-1：Without loss of generality, it is assumed that the array number of even linear array is M, information source number is P, signal incident angle difference
For θ1,θ2,…,θP, then array received signal be represented by：
X (t)=As (t)+n (t)
Wherein, x (t)=[x1(t),x2(t),...,xM(t)]T,xm(t), m=1 ... M represents what m-th of array element was received
Signal；A=[a (θ1),a(θ2),…,a(θP)] it is array manifold matrix,I=
1 ..., P, are the steering vector of i-th of signal source, φi=2 π dsin θi/ λ represents the phase shift of i-th of signal；Wherein d is array element
Between be spaced, λ is signal wavelength, θiRepresent the arrival bearing angle of i-th of incoming signal；S (t)=[s1(t),s2..., s (t)P
(t)]T, si(t) it is i-th of target source signal；N (t)=[n1(t),n2(t) ..., nM(t)]T, wherein nm(t) m-th gust is represented
The additive Gaussian noise that member is received；
Step 1-2：The data of observation can obtain by Second-Order Volterra Filter：
Y (t)=Bz (t)+v (t)
In formula：
,
[·]TRepresent the transposition of matrix；xm(t), m=1,2 ..., M represent the signal that m-th of array element is received, and * represents conjugation；
,
si(t), i=1,2 ..., P are i-th of target source signal, and * represents conjugation；
,
nm(t), m=1,2 ..., M represent the additive Gaussian noise that m-th of array element is produced, and * represents conjugation；Matrix B is neotectonics
Array manifold matrix；
Step 2：The new array received data y (t) obtained by step 1, constructs the steering vector of signalθi, i=
1 ..., P represent the arrival bearing angle of i-th of incoming signal, and P is information source number；
Step 3：Calculate y (t) covariance matrixyH(t) be y (t) conjugate transposition, D is
Fast umber of beats；
Step 4：The y (t) obtained according to step 3 covariance matrix Ryy, calculate space spectral function P (θ)；
Step 5：According to space spectral function, power spectrum chart is calculated with MATLAB, and obtains by spectrum peak search the ripple of signal
Up to direction.
Further, the step 4 is concretely comprised the following steps：
Step 4-1：Can obtain a nonlinear optimization problem by beam-forming technology is：
Constraints is
Wherein,The steering vector of signal source, θ take [0 °, 180 ° be signal relative to the incident direction of normal direction, w
Represent the weight vector of spatial filter, RyyThe covariance matrix of array received data newly built is represented, c, β is represented more than zero
Constant；
Step 4-2：Object function is obtained using method of Lagrange multipliers：
Step 4-3：Local derviation is sought object function f (w), and makes it be equal to 0, can be obtained
I is unit matrix, due toβ I are invertible matrix, thenOrderHere β=kM/ (ξ are takenM-1/ξM- 1), k≤1, ξ1≥...≥ξP＞ ξP+1≥...ξM-1≥
ξMIt is RyyCharacteristic value, M is array number, can obtain Cw=η w；
Step 4-4：The characteristic value and corresponding characteristic vector for understanding to be respectively Matrix C for η and w by Cw=η w, to square
Battle array C carries out Eigenvalues Decomposition, obtains M characteristic value η1≥…≥ηP＞ ηP+1≥…≥ηMAnd corresponding characteristic vector u1,…
uP,uP+1,…uM, optimal weight vector w=u hereM；
Step 4-5：Space spectral function, which can finally be obtained, is
The present invention seeks to be improved for existing algorithm, it is proposed that a kind of new DOA estimation method, be directed to arrow
Amount is built into virtual Volterra filter constructions and combines beam-forming technology and method of Lagrange multipliers technology to enter traveling wave
Up to direction (DOA) estimation.This algorithm can not only realize that DOA estimates under information source number unknown condition, but also independent of sub empty
Between decompose.Avoiding problems the influence that performance is produced is estimated DOA because of mistake estimation information source number, improve DOA estimation resolutions
Rate ability, while also reducing computation complexity.
Brief description of the drawings
Fig. 1, inventive algorithm flow chart；
The power spectrum chart of Fig. 2, the algorithm proposed compared with MUSIC algorithms and MVDR beamforming algorithms；
The curve map that Fig. 3, estimation angle root-mean-square error change with fast umber of beats.
Embodiment
Present embodiment is using array number as M=2, the uniform linear antenna array of array element spacing d=λ/2 (λ is signal wavelength)
Example is classified as, and only considers two incoherent narrow band signal far field scenes, then centre frequency f is setc=70MHz, independent experiment
Number of times is NMC=50.
Step 1：According to the situation of signal and antenna this body structure received, corresponding parameter is set, and utilize two
Rank Volterra filter constructions construction y (t)；
Step 1-1：Without loss of generality, it is assumed that the array number of even linear array is M=2, and information source number is P=2, signal incidence angle
Degree is respectively θ1=30 °, θ2=33 °, then array received signal be represented by：
X (t)=As (t)+n (t)
Wherein x (t)=[x1(t),x2(t),...,xM(t)]T,xm(t), m=1 ... M represents what m-th of array element was received
Signal.A=[a (θ1),a(θ2),…,a(θP)] it is array manifold matrix,I=
1 ..., P, are the steering vector of i-th of signal source, φi=2 π dsin θi/ λ represents the phase shift of i-th of signal, and wherein d is array element
Between be spaced, d=λ/2, λ are signal wavelength, θiIt is the arrival bearing angle of i-th of incoming signal.S (t)=[s1(t),s2(t) ...,
sP(t)]T, wherein si(t), i=1 ..., P is i-th of far field narrow band signal.The power or amplitude of signal all for 1 i.e. E | si(t)
|2}=1, n (t)=[n1(t),n2(t),…,nM(t)]T, wherein nm(t), m=1 ..., M represents zero that m-th of array element is received
Average white noise, if noise power is σ2, can by SNR=10log10 (E | s (t) |2}/σ2)=20dB, can obtain σ2=0.01.
Step 1-2：The data of observation are available by Second-Order Volterra Filter：
Y (t)=Bz (t)+v (t)
In formula,[·]TRepresent
The transposition of matrix.x1And x (t)2(t) signal that the 1st and the 2nd array element are received is represented,Represent x2(t) conjugation.s1And s (t)2(t) it is the 1st and the 2nd target source signal.n1And n (t)2(t) the 1st is represented
The additive Gaussian noise received with the 2nd array element,Represent n2(t) conjugation.Its
In,I=1,2, aT(θi) it is a
(θi) transposition,φi=2 π dsin θi/ λ, m=1 ..., M, i=1 ..., P.
It is a respectively1(θ2), a2(θ1), a2(θ2) conjugation, Re { } represents the reality of number
Portion.
Step 2：WillI=1 ..., P as signal steering vector,；
Step 3：Calculate y (t) covariance matrixyH(t) be y (t) conjugate transposition, D=
100 be fast umber of beats；
Step 4：Space spectral function is tried to achieve for P (θ)；
Step 4-1：It can be obtained by Wave beam forming principle：
Constraints is
Wherein it isThe steering vector of signal source, θ takes [0 °, 180 °] the incidence side for signal relative to normal direction
To the sampling interval is 0.1 °, and w represents the weight vector of spatial filter, RyyRepresent the covariance square of array received data built
Battle array, c represents any constant more than zero, β=kM/ (ξM-1/ξM- 1), k≤1, ξ1≥...≥ξP＞ ξP+1≥...≥ξMIt is Ryy's
Characteristic value, M is array number；
Step 4-2：Obtaining object function using method of Lagrange multipliers technology is：
Step 4-3：Local derviation is sought object function f (w), and makes it be equal to 0, can be obtained
I is unit matrix, due toβ I are invertible matrix, thenOrderHere β=kM/ (ξ are takenM-1/ξM- 1), k≤1, ξ1≥...≥ξP＞ ξP+1≥...ξM-1≥
ξMIt is RyyCharacteristic value, M is array number, can obtain Cw=η w；
Step 4-4：The characteristic value and corresponding characteristic vector for understanding to be respectively Matrix C for η and w by Cw=η w, to square
Battle array C carries out Eigenvalues Decomposition, obtains M characteristic value η1≥…≥ηP＞ ηP+1≥…≥ηMAnd corresponding characteristic vector u1,…
uP,uP+1,…uM.Here optimal weight vector w takes the characteristic vector corresponding to Matrix C minimal eigenvalue, i.e. w=uM；
Step 4-5：Space spectral function, which can finally be obtained, is
Step 5：Calculated with MATLABValue, θ takes [0 °, 180 °], and with MUSIC algorithms and
MVDR beamforming algorithms are compared.
Test result indicates that, as shown in Fig. 2 the figure by MUSIC algorithms, MVDR beamforming algorithms and we propose
The spectrogram of algorithm, can not to tell two spaces very close for MUSIC algorithms and MVDR beamforming algorithms as seen from the figure
Information source, but the algorithm that we are proposed can estimate the two information sources well, this shows that the algorithm that we are proposed is improved
DOA estimates the ability of resolution ratio.Fig. 3 is the root-mean-square error (RMSE, Root-Mean-Square Error) for estimating angle
The curve map changed with fast umber of beats, whereinNMC=50 be independent experiment number of times,For
The deflection that ith independent experiment is estimated, θ is the incident deflection of actual signal.As seen from the figure, with the increasing of fast umber of beats
Plus, estimate that the root-mean-square error of angle is less and less.
Claims (2)
1. a kind of Wave arrival direction estimating method of virtual second order array extension, this method is concretely comprised the following steps：
Step 1：New array received data y (t) is constructed by the data x (t) of array received；
Step 1-1：Without loss of generality, it is assumed that the array number of even linear array is M, and information source number is P, and signal incident angle is respectively θ1,
θ2,…,θP, then array received signal be represented by：
X (t)=As (t)+n (t)
Wherein, x (t)=[x1(t),x2(t),...,xM(t)]T,xm(t), m=1 ... M represents the letter that m-th of array element is received
Number；A=[a (θ1),a(θ2),…,a(θP)] it is array manifold matrix,I=
1 ..., P, are the steering vector of i-th of signal source, φi=2 π dsin θi/ λ represents the phase shift of i-th of signal；Wherein d is array element
Between be spaced, λ is signal wavelength, θiRepresent the arrival bearing angle of i-th of incoming signal；S (t)=[s1(t),s2(t) ..., sP
(t)]T, si(t) it is i-th of target source signal；N (t)=[n1(t),n2(t) ..., nM(t)]T, wherein nm(t) m-th gust is represented
The additive Gaussian noise that member is received；
Step 1-2：The data of observation can obtain by Second-Order Volterra Filter：
Y (t)=Bz (t)+v (t)
In formula：
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[·]TRepresent the transposition of matrix；xm(t), m=1,2 ..., M represent the signal that m-th of array element is received, and * represents conjugation；
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nm(t), m=1,2 ..., M represent the additive Gaussian noise that m-th of array element is produced, and * represents conjugation；Matrix B is neotectonics
Array manifold matrix；
Step 2：The new array received data y (t) obtained by step 1, constructs the steering vector of signalθi, i=
1 ..., P represent the arrival bearing angle of i-th of incoming signal, and P is information source number；
Step 3：Calculate y (t) covariance matrixyH(t) be y (t) conjugate transposition, D is snap
Number；
Step 4：The y (t) obtained according to step 3 covariance matrix Ryy, calculate space spectral function P (θ)；
Step 5：According to space spectral function, power spectrum chart is calculated with MATLAB, and the ripple for obtaining signal by spectrum peak search reaches side
To.
2. a kind of Wave arrival direction estimating method of virtual second order array extension as claimed in claim 1, it is characterised in that described
Step 4 is concretely comprised the following steps：
Step 4-1：Can obtain a nonlinear optimization problem by beam-forming technology is：
Constraints is
Wherein,The steering vector of signal source, θ take [0 °, 180 °] for signal relative to the incident direction of normal direction, w tables
Show the weight vector of spatial filter, RyyThe covariance matrix of array received data newly built is represented, c, β represents normal more than zero
Amount；
Step 4-2：Object function is obtained using method of Lagrange multipliers：
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Step 4-3：Local derviation is sought object function f (w), and makes it be equal to 0, can be obtainedI is single
Bit matrix, due toFor invertible matrix, thenOrder
Here β=kM/ (ξ are takenM-1/ξM- 1), k≤1, ξ1≥...≥ξP＞ ξP+1≥...ξM-1≥ξMIt is RyyCharacteristic value, M is array element
Number, can obtain Cw=η w；
Step 4-4：The characteristic value and corresponding characteristic vector for understanding to be respectively Matrix C for η and w by Cw=η w, enter to Matrix C
Row Eigenvalues Decomposition, obtains M characteristic value η1≥…≥ηP＞ ηP+1≥…≥ηMAnd corresponding characteristic vector u1,…uP,
uP+1,…uM, optimal weight vector w=u hereM；
Step 4-5：Space spectral function, which can finally be obtained, is
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| CN109188345A (en) * | 2018-08-27 | 2019-01-11 | 电子科技大学 | Coherent signal source DOA estimation method based on structure when removing predelay sky |
| CN109471065A (en) * | 2018-09-28 | 2019-03-15 | 中国电子科技集团公司第三十六研究所 | A kind of direction-finding method of coherent signal |
| CN109683519A (en) * | 2018-12-21 | 2019-04-26 | 南京航空航天大学 | A kind of FPGA implementation method of adaptive algorithm |
| CN109814134A (en) * | 2018-12-26 | 2019-05-28 | 哈尔滨工程大学 | It is a kind of based on the virtual antenna array extended method for prolonging pushing manipulation |
| CN110018452A (en) * | 2018-01-08 | 2019-07-16 | 现代摩比斯株式会社 | The method and apparatus of arrival direction is estimated using the virtual generation for receiving signal |
| CN110031794A (en) * | 2019-04-16 | 2019-07-19 | 中国人民解放军国防科技大学 | Coherent information source DOA estimation method based on difference common matrix reconstruction |
| CN111884689A (en) * | 2020-07-10 | 2020-11-03 | 中国科学技术大学 | Direction-of-arrival-distance adaptive beam forming method based on ladder array |
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| CN113420411A (en) * | 2021-05-25 | 2021-09-21 | 北京科技大学 | High-resolution narrowband DOA estimation algorithm for wireless signals and implementation method |
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| CN107870315A (en) * | 2017-11-06 | 2018-04-03 | 重庆邮电大学 | One kind utilizes iterative phase compensation technique estimation General Cell direction of arrival method |
| CN110018452A (en) * | 2018-01-08 | 2019-07-16 | 现代摩比斯株式会社 | The method and apparatus of arrival direction is estimated using the virtual generation for receiving signal |
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| CN109188345B (en) * | 2018-08-27 | 2023-03-10 | 电子科技大学 | Coherent signal source DOA estimation method based on pre-delay space-time structure removal |
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| CN109471065B (en) * | 2018-09-28 | 2021-05-25 | 中国电子科技集团公司第三十六研究所 | Direction finding method for coherent signals |
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| CN109814134A (en) * | 2018-12-26 | 2019-05-28 | 哈尔滨工程大学 | It is a kind of based on the virtual antenna array extended method for prolonging pushing manipulation |
| CN110031794B (en) * | 2019-04-16 | 2021-11-09 | 中国人民解放军国防科技大学 | Coherent information source DOA estimation method based on difference common matrix reconstruction |
| CN110031794A (en) * | 2019-04-16 | 2019-07-19 | 中国人民解放军国防科技大学 | Coherent information source DOA estimation method based on difference common matrix reconstruction |
| CN111884689B (en) * | 2020-07-10 | 2021-10-22 | 中国科学技术大学 | Direction-of-arrival-distance adaptive beam forming method based on ladder array |
| CN111884689A (en) * | 2020-07-10 | 2020-11-03 | 中国科学技术大学 | Direction-of-arrival-distance adaptive beam forming method based on ladder array |
| CN112924926A (en) * | 2021-01-27 | 2021-06-08 | 东南大学 | DOA estimation method under multi-path channel |
| CN113420411A (en) * | 2021-05-25 | 2021-09-21 | 北京科技大学 | High-resolution narrowband DOA estimation algorithm for wireless signals and implementation method |
| CN113420411B (en) * | 2021-05-25 | 2024-02-20 | 北京科技大学 | High-resolution narrowband DOA estimation algorithm for wireless signals and implementation method |
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Application publication date: 20170825 |