CN110286352A - A kind of non-iterative mixed source localization method based on order damage - Google Patents
A kind of non-iterative mixed source localization method based on order damage Download PDFInfo
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Abstract
The invention discloses a kind of non-iterative mixed source localization methods based on order damage, comprising the following steps: the reception data of mixed source to be positioned are obtained by array received；The estimated value of covariance matrix R is calculated by reception dataCalculate near field and far-field signal source in mixed sourceDirection of arrival angleCalculate near field and far-field signal source in mixed sourceDistanceMixed source is classified as far-field signal source and near-field signals source；Wherein, work as estimated valueWhen, it is believed that signal source is near-field signals source, thus estimates K2A near-field signals source；According to the signal direction of arrival angle and distance in the near-field signals source of estimation, far-field signal source candidate is obtained, obtains K using direction of arrival selection strategy1The direction of arrival angle in a far-field signal source.The present invention overcomes the saturation behavior in signal source positioning using the second-order statistics positioning far field of array data and near field mixing narrow band signal, while by non-iterative method.
Description
Technical field
The invention belongs to array signal processing technologies, and in particular to a kind of non-iterative mixed source based on order damage
Localization method.
Background technique
The positioning of narrow band signal signal source is a underlying issue in array signal processing application.In many application scenarios,
Near-field signals and far-field signal exist simultaneously, and the orientation problem in near-field signals source and far-field signal source in mixed signal is very heavy
It wants.
Currently, having had some Higher order Statistics and circulation for solving to mix far and near field signal source orientation problem
Stationarity method, but these methods have higher calculation amount, and can be only applied to non-Gaussian signal source or cyclo-stationary signal source
Positioning；Other second-order statistic and matrix difference method need the property of the oblique variance matrix by signal source to go to estimate
The energy for counting signal source can be only applied to the signal source positioning of a large amount of number of snapshots；The method of still other oblique projection is suggested, this
In kind method when number of snapshots are not sufficiently large, off-diagonal influences and the erroneous estimation of oblique projection operator usually will cause saturation row
For phenomenon, although the phenomenon that LOFNS method can eliminate this saturation behavior by a kind of strategy for exchanging iteration, this
Iterative process is not that total energy guarantees convergence, and reliability is poor.
To sum up, a kind of non-iterative mixed source localization method based on order damage is needed.
Summary of the invention
It is above-mentioned to solve the purpose of the present invention is to provide a kind of non-iterative mixed source localization method based on order damage
Existing one or more technical problem.
In order to achieve the above objectives, the invention adopts the following technical scheme:
A kind of non-iterative mixed source localization method based on order damage of the invention, comprising the following steps:
Step 1, the reception data of mixed source to be positioned are obtained by array received；Construct the oblique variance matrix of array
R is calculated the estimated value of covariance matrix R by reception dataArray includes 2M+1 omnidirectional's sensor array element；Mixed source
K incoherent signal is obtained on incident array
Step 2, the estimated value obtained by step 1Calculate near field and far-field signal source in mixed sourceDirection of arrival angleIncluding (K1-1)K1/ 2 spurious signal direction of arrival；θkIndicate kth
A incoherent signal sk(n) direction of arrival angle；Direction of arrival angle is k-th of incoherent signal sk(n) relative to symmetrically and evenly line
The tactical deployment of troops to angle counterclockwise；As k ≠ l, θk≠θl；
Step 3, the estimated value obtained by step 1Calculate near field and far-field signal source in mixed sourceDistanceIncluding (K1-1)K1The distance of/2 spurious signals；rkIt is non-k-th
Coherent signal sk(n) distance relative to the center of symmetrically and evenly linear array；As k ≠ l, rk≠rl；
Step 4, mixed source is classified as by far-field signal source and near-field signals source according to the distance that step 3 obtains；Its
In, work as estimated valueWhen, it is believed that signal source is near-field signals source, thus estimates K2It is a close
Field signal source；Wherein, D=2Md；λ represents the wavelength of mixed source, and d is equal to the 1/4 of wavelength X；
Step 5, the signal direction of arrival angle and distance in the near-field signals source estimated according to step 4, obtain (K1-1)K1/2+
K-K2=K1+(K1-1)K1/ 2 far-field signal source candidates obtain K using direction of arrival selection strategy1A far-field signal source
Direction of arrival angle.
A further improvement of the present invention is that the array used is symmetrically and evenly linear array in step 1；
Construct the oblique variance matrix of array are as follows:
Its feature decomposition is:
Estimated value
In formula, N indicates that hits, n=1,2 ..., N indicate time series, and x (n) indicates array received data, E { } table
Show and asks expectation, ()HIndicate conjugate transposition, Us、UnRespectively indicate signal subspace and noise subspace, Λs、ΛnIt respectively indicates
Signal subspace and noise subspace are to deserved characteristic value.
A further improvement of the present invention is that the signal that the uniform linear array receives indicates in step 1 are as follows:
It is array response matrix；
Indicate the corresponding array response matrix of far-field signal；
Indicate the corresponding array response square of near-field signals
Battle array
Indicate the corresponding array response vector of far-field signal；
Indicate that near-field signals are corresponding
Array response vector；
In formula, K indicates the signal number for including in mixed source, and k=1,2 ..., K indicate signal original label, K1And K2
The far field for including in mixed source and near-field signals number are respectively indicated, ω (n) and s (n) are respectively additional noise vector sum
Signal source vector, sf(n) and sn(n) the signal source vector in far field and near field is respectively indicated,Indicate all mixed sources
Direction of arrival angle,Indicate the distance in the near-field signals source in mixed source, j indicates imaginary unit, and e is indicated certainly
Right constant, ψkAnd φkRespectively indicate high-order and low order Electron Angular component, ()TIndicate transposition.
A further improvement of the present invention is that in step 2, the wave of the mixed signal near-field signals and far-field signal that need to estimate
Up to deflectionAnd distancePass through af(θk) and an(θk,rk) obtain；
It specifically includes: according to
af(θk)=D (θk)bf,
an(θk,rk)=D (θk)bn,
It obtains:
In formula, bfAnd bnIt is (M+1) × 1 vector, and
D(θk) it is one (2M+1) × (M+1) matrix,
It is (M+1) × (M+1) matrix, C (θk) matrix only includes signal direction of arrival
Angle information；As θ=θkWhen, C (θk) it can tend to be minimum；
The direction of arrival angle of mixed signal is obtained by finding K wave crest of cost function, the expression formula of cost function are as follows:
(K is estimated according to cost function1-1)K1/ 2+K signal source direction of arrival angle；Wherein, (K1-1)K1/ 2 falsenesses
Signal.
A further improvement of the present invention is that the direction of arrival angle of mixed source is by finding p in step 2θ(z)
(K1-1)K1/ 2+K 0 phase solutions and acquire；
A further improvement of the present invention is that the array response vector a in near-field signals sourcen(θk,rk) it include Electron Angular ψkWith
φk, indicate are as follows:
an(θk,rk)=D (θk)bn(θk,rk)；
(K1-1)K1/ 2+K distanceIt is obtained by minimizing following cost function, cost function expression formula
Are as follows:
In (K1-1)K1/ 2+K range estimation works as estimated valueIn, whenWhen, it is believed that signal source is near-field signals source, thus estimates K2The wave in a near-field signals source
Up to deflection and distance (θk,rk)。
A further improvement of the present invention is that the distance in near-field signals source is by finding p in step 3r(z) (K1-1)
K1/ 2+K 0 phase solutions and acquire；
A further improvement of the present invention is that the direction of arrival selection strategy of use specifically includes in step 5:
Work as K1When=1, generated without spurious signal；
Work as K1When=2, K is had1+0.5(K1-1)K1=3 candidate far field direction of arrival angle, i.e. θ1<θ2<θ3, θ2For falseness
Signal；
Work as K1When=3, K is had1+0.5(K1-1)K1=6 candidate far field direction of arrival angle, i.e. θ1<θ2<θ3<θ4<θ5<θ6,
θ1, θ6For two true direction of arrival angle, the false direction of arrival angle of its generation is rejected；Remaining 3 direction of arrival angle, wherein
Second largest is true direction of arrival angle；
And so on.
Compared with prior art, the invention has the following advantages:
It is fixed using the second-order statistics of array data in non-iterative mixed source localization method based on order damage of the invention
Position far field and near field mixing narrow band signal, while overcoming by non-iterative method " being saturated behavior " in signal source positioning.Specifically
, method of the invention obtains the direction of arrival of all signal sources in mixed signal first；It is obtained secondly by subspace estimation device
Signal source distance and signal source classification are obtained, wherein subspace estimation device is obtained by array correlation matrix；Finally by direction of arrival
Selection strategy obtains the multiple signal sources in far field.Compared to current existing far field and near field mixing narrow band signal source location algorithm, originally
The method of invention overcomes " saturation behavior " phenomenon in the calculating process for not needing iterative operation, so that the present invention calculates complexity
Spend lower, method is simple and effective, and performance is significantly improved.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below to embodiment or existing
Attached drawing needed in technical description does simple introduction；It should be evident that the accompanying drawings in the following description is of the invention
Some embodiments to those skilled in the art without creative efforts, can also be according to this
A little attached drawings obtain other attached drawings.
Fig. 1 be in the embodiment of the present invention performance of far field and near field narrow band signal source parameter Estimation with signal-to-noise ratio (SNR)
Change curve schematic diagram；Fig. 1 (a) is change curve schematic diagram of the far-field signal direction of arrival angle with signal-to-noise ratio；Fig. 1 (b) is close
Field signal direction of arrival angle with signal-to-noise ratio change curve schematic diagram；Wherein, chain-dotted line: GESPR；Scribing line: OPMUSIC；" o ":
The not LOFNS of iteration；Chain-dotted line adds " x ": LOFNS；Solid line: the method for the present invention；Dotted line: CRB lower bound；
Fig. 2 be in the embodiment of the present invention performance of far field and near field narrow band signal source parameter Estimation with the change of hits (NS)
Change curve synoptic diagram；Fig. 2 (a) is change curve schematic diagram of the far-field signal direction of arrival angle with hits；Fig. 2 (b) is near field
Signal direction of arrival angle with hits change curve schematic diagram；Wherein, chain-dotted line: GESPR；Scribing line: OPMUSIC；" o ": no
The LOFNS of iteration；Chain-dotted line adds " x ": LOFNS；Solid line: the method for the present invention；Dotted line: CRB lower bound.
Specific embodiment
To keep the purpose, technical effect and technical solution of the embodiment of the present invention clearer, implement below with reference to the present invention
Attached drawing in example, technical scheme in the embodiment of the invention is clearly and completely described；Obviously, described embodiment
It is a part of the embodiment of the present invention.Based on embodiment disclosed by the invention, those of ordinary skill in the art are not making creation
Property labour under the premise of other embodiments obtained, all should belong to the scope of protection of the invention.
A kind of non-iterative mixed source localization method based on order damage of the embodiment of the present invention, comprising the following steps:
Symmetrically and evenly linear array includes 2M+1 omnidirectional's sensor array element；
Narrowband mixing far field and near-field signals are K incoherent signal being incident in symmetrically and evenly linear array
By obtaining K1To parameterPosition K1A incoherent far-field signal
By obtaining K2To parameterPosition K2A incoherent near-field signals
Wherein, θkIndicate k-th of incoherent signal sk(n) direction of arrival angle；Direction of arrival angle is k-th of incoherent letter
Number sk(n) angle counterclockwise relative to symmetrically and evenly linear array normal direction；rkIt is k-th of incoherent signal sk(n) relative to symmetrical equal
The distance at the center of even linear array, and as k ≠ l, θk≠θl, rk≠rl。
Assuming that symmetrically and evenly the central sensor array element (array element 0) of linear array is phase reference point, the signal which receives
It indicates are as follows:
Wherein, wmIt (n) is additional noise, τmkIt is phase delay of k-th of signal for m-th of array element.
Assuming that narrowband near-field signals source sk(n) with linear array element in Fresnel apart from interior rk∈(0.62(D3/λ)1/2,2D2/
λ), narrowband far-field signal source and linear array element are in not bright Hough apart from interior rk∈(2D2/ λ, ∞), D=2Md here.
τ in formula (1)mkIt is about θkAnd rkNonlinear approximation second order Taylor form:
τmk≈mψk+m2φk (2)
Wherein ψkAnd φkIt may be expressed as:
The wavelength in λ representation signal source.
When signal source is far-field signal source, τmkIt can be with approximate expression are as follows:
τmk≈mψk (5)
In fact, the τ of (5) formulamkOnly and signal source direction of arrival θkIt is related.Therefore the signal that uniform linear array receives
It can indicate are as follows:
Wherein, x (n), ω (n) and s (n) are the signal vector that array received arrives, additional noise vector sum signal source vector.
Also,It is array response matrix,
HaveWith
af(θk) and an(θk,rk) can indicate are as follows:
In formula, K indicates the signal number for including in mixed source, and k=1,2 ..., K indicate signal original label, K1And K2
The far field for including in mixed source and near-field signals number are respectively indicated, ω (n) and s (n) are respectively additional noise vector sum
Signal source vector, sf(n) and sn(n) the signal source vector in far field and near field is respectively indicated,Indicate all mixed sources
Direction of arrival angle,Indicate the distance in the near-field signals source in mixed source, j indicates imaginary unit, and e is indicated certainly
Right constant, ψkAnd φkRespectively indicate high-order and low order Electron Angular component, ()TIndicate transposition.
The present invention solve fromArray element receives to estimate that the wave of mixed signal near-field signals and far-field signal reaches in signal
DeflectionAnd distanceThe problem of.
Narrowband mixes the direction of arrival angle θ of far and near field signalkNon-iterative estimation method the following steps are included:
(1) data are received by symmetrically and evenly linear array and calculates covariance matrix R estimated value
Construct the oblique variance matrix of array are as follows:
(2) estimated value is usedCalculate near field and far-field signal source in mixed sourceDirection of arrival
AngleIncluding (K1-1)K1/ 2 spurious signal direction of arrival.
Wherein, near-field signals source in narrowband, which is located through, finds pθ(z) (K1-1)K1/ 2+K 0 phase solutions, and
(3) near field and far-field signal source in mixed signal are calculatedDistanceWherein
Including (K1-1)K1The distance of/2 spurious signals.
Wherein, near-field signals source in narrowband, which is located through, finds pr(z) (K1-1)K1/ 2+K 0 phase solutions, andWherein,
(4) signal source is classified as by far-field signal source and near-field signals source according to the distance that step (3) obtain, wherein when estimating
EvaluationWhen, it is believed that signal source is near-field signals source, thus estimates K2A near-field signals
Source.
(5) according to the signal direction of arrival angle and distance in the near-field signals source of step (4) estimation, (K is obtained1-1)K1/2+K-
K2=K1+(K1-1)K1/ 2 far-field signal source candidates.K is obtained using direction of arrival selection strategy1The wave in a far-field signal source
Up to deflection.
To sum up, the invention discloses a kind of far fields based on symmetrically and evenly linear array and near field mixing narrow band signal source non-iterative
Localization method, RARE (Rank reduction) estimator in this method using array data second-order statistics positioning far field and
Near field mixing narrow band signal, while this method overcomes " the saturation behavior " in signal source positioning by non-iterative method.This hair
Bright method passes through the direction of arrival that RARE estimator obtains all signal sources in mixed signal first；Secondly by subspace estimation
Device obtains signal source distance and signal source classification, and wherein subspace estimation device is obtained by array correlation matrix；It is reached finally by wave
Direction selection strategy obtains the multiple signal sources in far field.Compared to existing far field and near field mixing narrow band signal source location algorithm, originally
Invention overcomes " saturation behavior " phenomenon in the calculating process for not needing iterative operation, so that computation complexity is lower, method
It is simple and effective, and performance is significantly improved.
Embodiment
A kind of non-iterative mixed source localization method based on order damage of the embodiment of the present invention, comprising:
The direction of arrival angular estimation of mixed signal:
Firstly, fromArray element receives the direction of arrival that mixed signal near-field signals and far-field signal are estimated in signal
AngleAnd distanceBy formula (6) to (8) it is found that the wave of the mixed signal near-field signals and far-field signal that need to estimate
Up to deflectionAnd distanceA can be passed throughf(θk) and an(θk,rk) obtain.For symmetrically linear array, the present invention
Using center battle array source as R-matrix, a of arrayf(θk) and an(θk,rk) may be expressed as:
af(θk)=D (θk)bf(9)
an(θk,rk)=D (θk)bn(10)
Wherein, bfAnd bnIt is (M+1) × 1 vector, and bf=1,
D(θk) it is one (2M+1) × (M+1) matrix,
Secondly, the construction oblique variance matrix of array are as follows:
And its feature decomposition is:
Wherein, UsAnd UnIt is orthogonal matrix, they are the signal subspace of matrix R and the feature vector of noise subspace,
ΛsIt is the orthogonal matrix of K × K, includes K maximum eigenvalue, ΛnIt is the diagonal matrix of one (2M+1-K) × (2M+1-K),
Including 2M+1-K minimal eigenvalue.
When the array data of N number of number of snapshots of array data is valid data, the spy of the oblique variance matrix of array and it
Value indicative decomposition can be calculated as:
In formula, N indicates that hits, n=1,2 ..., N indicate time series, and x (n) indicates array received data, E { } table
Show and asks expectation, ()HIndicate conjugate transposition, Us、UnRespectively indicate signal subspace and noise subspace, Λs、ΛnIt respectively indicates
Signal subspace and noise subspace are to deserved characteristic value.
It is knownThe column matrix and U of vectorsColumn vector by a vector space at, such as: R (A)=
span{US, therefore our available following expression formulas:
(9) and (10) formula is inserted into (12) and (13) formula, can be obtained:
Wherein,It is (M+1) × (M+1) matrix.It is worth noting that, C (θk) matrix
Only include signal direction of arrival angle information, also, works as θ=θkWhen, C (θk) it can tend to be minimum.Therefore, the wave of mixed signal reaches side
It can be obtained to angle by finding K wave crest of following cost function,
(K will be estimated from (16) formula1-1)K1/ 2+K signal source direction of arrival angle, wherein (K1-1)K1/ 2 falsenesses
Signal.
Array response vector a corresponding to near-field signals sourcen(θk,rk) it include Electron Angular ψkAnd φk, and an(θk,rk) can
To indicate are as follows:
an(θk,rk)=D (θk)bn(θk,rk) (17)
It is observed that ψkAnd φkOccur in pairs, so θk(θk,rk) also occur in pairs.Therefore, (the K of acquisition is utilized1-
1)K1/ 2+K direction of arrival angleCorresponding (K can be obtained1-1)K1/ 2+K distance
(K1-1)K1/ 2+K distanceIt can be obtained by minimizing cost function below:
In (K1-1)K1/ 2+K range estimation works as estimated valueIn, whenWhen, it is believed that signal source is near-field signals source, thus automatically estimates K2A near-field signals
The direction of arrival angle and distance (θ in sourcek,rk)。
Direction of arrival angle selection:
Lemma: assuming that there are two far-field signal sources, their direction of arrival angle is (α, β) respectively, and assumes α < β.Therefore,
D (θ) in formula (9) and (10) meets following equalities:
D (α)+D (β)=D (γ) P (19)
Wherein, γ is obtained by following formula:
Sin (α)+sin (β)=2sin (γ) (20)
Wherein, P=diag { p } is the diagonal matrix of (M+1) × (M+1),
It is aobvious
Right, α < γ < β.
It proves:
In the presence of more than one far-field signal source, it is assumed that their direction of arrival angle is (α, β) respectively, therefore by
(9) formula is available:
af(α)=D (α) bf (21)
af(β)=D (β) bf (22)
Therefore available from lemma:
Due toSo that
(af(β)+af(α))HUn=0M+1 (24)
Have simultaneously:
It will be apparent that p ≠ 0M+1, soNot full rank:
Therefore, can there are your false far-field signal, K in every two far-field signal1A far-field signal source has (K1-1)
K1/ 2 false far-field signals.
It, can be from (K according to the above lemma1-1)K1/2+K1K is selected in a candidate's far-field signal1A real far field letter
Number.Specific choice strategy is as follows:
Situation 1: if K1=2, it has 3 far-field signal sources and is detected, one of them is false far-field signal source,
Assuming that three far-field signal direction of arrival angle are θ respectively1,θ2,θ3, and meet θ1<θ2<θ3.Obviously from the available θ of lemma2It is
False far-field signal source.
Situation 2: if K1=3, it has 6 far-field signal sources and is detected, one of them is false far-field signal source,
Assuming that three far-field signal direction of arrival angle are θ respectively1,θ2,θ3,θ4,θ5,θ6, and meet θ1<θ2<θ3<θ4<θ5<θ6.Obviously from
The available θ of lemma1And θ6It is two true far-field signal sources, while we can calculate another false far-field signal source
θ1,6=arcsin0.5 (sin θ1+sinθ6), delete θ2,θ3,θ4,θ5Neutralize θ1,6Equal signal source, remaining 3 signal sources, can
To be solved with situation 1.
Situation 3: similar situation 2, and so on.
It, can be from (K according to above-mentioned selection strategy1-1)K1/2+K1K is selected in a candidate's far-field signal1A real far field
The direction of arrival angle and distance (θ of signalk,rk)。
Fig. 1 and Fig. 2 are please referred to, is illustrated by effect of the following different situations to the above method:
There are four the unknown incoming signal of direction of arrival angle, azimuth information is respectively (- 43 °, ∞) in space, (- 21 °,
∞), (12 °, 4.6 λ), (52 °, 4.8 λ) symmetrically and evenly linear array contains 2M+1=15 array element, and λ/4 d=are divided between array element.Emulation
In compared the present invention and GESPR, OPMUSIC, non-iterative LOFNS and iteration LOFNS algorithm, while giving CRB circle, referring to
Fig. 1 and Fig. 2.In addition, the root-mean-square error calculation formula of direction of arrival angle is respectively as follows: in figure
In formula,WithIt is illustrated respectively in θ in pth time emulation experimentkEstimated value, each simulation result be through
It is obtained by P=1000 independent repetition experiment.
By Fig. 1, it can be seen that, the present invention and GESPR, OPMUSIC, non-iterative LOFNS are compared with iteration LOFNS algorithm, letter
It makes an uproar than changing to 40Db, hits 500 by -10D.Change with signal-to-noise ratio, the estimation performance of direction of arrival angle is better than
GESPR, OPMUSIC, non-iterative LOFNS and iteration LOFNS algorithm.
By Fig. 2, it can be seen that, the present invention changes with hits, and the estimation performance of direction of arrival angle is better than GESPR,
OPMUSIC, non-iterative LOFNS and iteration LOFNS algorithm.
The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, although referring to above-described embodiment pair
The present invention is described in detail, those of ordinary skill in the art still can to a specific embodiment of the invention into
Row modification perhaps equivalent replacement these without departing from any modification of spirit and scope of the invention or equivalent replacement, applying
Within pending claims of the invention.
Claims (8)
1. a kind of non-iterative mixed source localization method based on order damage, which comprises the following steps:
Step 1, the reception data of mixed source to be positioned are obtained by array received；The oblique variance matrix R for constructing array, by
Receive the estimated value that data calculate covariance matrix RArray includes 2M+1 omnidirectional's sensor array element；Mixed source is incident
K incoherent signal is obtained on array
Step 2, the estimated value obtained by step 1Calculate near field and far-field signal source in mixed sourceDirection of arrival angleIncluding (K1-1)K1/ 2 spurious signal direction of arrival；θkIndicate kth
A incoherent signal sk(n) direction of arrival angle；Direction of arrival angle is k-th of incoherent signal sk(n) relative to symmetrically and evenly line
The tactical deployment of troops to angle counterclockwise；As k ≠ l, θk≠θl；
Step 3, the estimated value obtained by step 1Calculate near field and far-field signal source in mixed sourceDistanceIncluding (K1-1)K1The distance of/2 spurious signals；rkIt is non-k-th
Coherent signal sk(n) distance relative to the center of symmetrically and evenly linear array；As k ≠ l, rk≠rl；
Step 4, mixed source is classified as by far-field signal source and near-field signals source according to the distance that step 3 obtains；Wherein, when
Estimated valueWhen, it is believed that signal source is near-field signals source, thus estimates K2A near-field signals
Source；Wherein, D=2Md；λ represents the wavelength of mixed source, and d is equal to the 1/4 of wavelength X；
Step 5, the signal direction of arrival angle and distance in the near-field signals source estimated according to step 4, obtain (K1-1)K1/2+K-K2
=K1+(K1-1)K1/ 2 far-field signal source candidates obtain K using direction of arrival selection strategy1The wave in a far-field signal source reaches
Deflection.
2. a kind of non-iterative mixed source localization method based on order damage according to claim 1, which is characterized in that step
In rapid 1, the array used is symmetrically and evenly linear array；
Construct the oblique variance matrix of array are as follows:
Its feature decomposition is:
Estimated value
In formula, N indicates that hits, n=1,2 ..., N indicate time series, and x (n) indicates array received data, and E { } expression is asked
It is expected that ()HIndicate conjugate transposition, Us、UnRespectively indicate signal subspace and noise subspace, Λs、ΛnRespectively indicate signal
Subspace and noise subspace are to deserved characteristic value.
3. a kind of non-iterative mixed source localization method based on order damage according to claim 2, which is characterized in that step
In rapid 1, the signal that the uniform linear array receives is indicated are as follows:
It is array response matrix；
Indicate the corresponding array response matrix of far-field signal；
Indicate the corresponding array response matrix of near-field signals
Indicate the corresponding array response vector of far-field signal；
Indicate that the corresponding array of near-field signals is rung
Answer vector；
In formula, K indicates the signal number for including in mixed source, and k=1,2 ..., K indicate signal original label, K1And K2Respectively
Indicate the far field for including in mixed source and near-field signals number, ω (n) and s (n) are respectively additional noise vector sum signal
Source vector, sf(n) and sn(n) the signal source vector in far field and near field is respectively indicated,Indicate the wave of all mixed sources
Up to deflection,Indicate the distance in the near-field signals source in mixed source, j indicates imaginary unit, and e indicates that nature is normal
Number, ψkAnd φkRespectively indicate high-order and low order Electron Angular component, ()TIndicate transposition.
4. a kind of non-iterative mixed source localization method based on order damage according to claim 3, which is characterized in that step
In rapid 2, the direction of arrival angle of the mixed signal near-field signals and far-field signal that need to estimateAnd distancePass through af
(θk) and an(θk,rk) obtain；
It specifically includes: according to
af(θk)=D (θk)bf,
an(θk,rk)=D (θk)bn,
It obtains:
In formula, bfAnd bnIt is (M+1) × 1 vector, and
D(θk) it is one (2M+1) × (M+1) matrix,
It is (M+1) × (M+1) matrix, C (θk) matrix only include signal direction of arrival angle letter
Breath；As θ=θkWhen, C (θk) it can tend to be minimum；
The direction of arrival angle of mixed signal is obtained by finding K wave crest of cost function, the expression formula of cost function are as follows:
(K is estimated according to cost function1-1)K1/ 2+K signal source direction of arrival angle；Wherein, (K1-1)K1/ 2 spurious signals.
5. a kind of non-iterative mixed source localization method based on order damage according to claim 3, which is characterized in that step
In rapid 2, the direction of arrival angle of mixed source is by finding pθ(z) (K1-1)K1/ 2+K 0 phase solutions and acquire；
6. a kind of non-iterative mixed source localization method based on order damage according to claim 4, which is characterized in that close
The array response vector a in field signal sourcen(θk,rk) it include Electron Angular ψkAnd φk, indicate are as follows:
an(θk,rk)=D (θk)bn(θk,rk)；
(K1-1)K1/ 2+K distanceIt is obtained by minimizing following cost function, cost function expression formula are as follows:
In (K1-1)K1/ 2+K range estimation works as estimated valueIn, whenWhen,
Think that signal source is near-field signals source, thus estimates K2The direction of arrival angle and distance (θ in a near-field signals sourcek,rk)。
7. a kind of non-iterative mixed source localization method based on order damage according to claim 3, which is characterized in that step
In rapid 3, the distance in near-field signals source is by finding pr(z) (K1-1)K1/ 2+K 0 phase solutions and acquire；
8. a kind of non-iterative mixed source localization method based on order damage according to claim 6, which is characterized in that step
In rapid 5, the direction of arrival selection strategy of use is specifically included:
Work as K1When=1, generated without spurious signal；
Work as K1When=2, K is had1+0.5(K1-1)K1=3 candidate far field direction of arrival angle, i.e. θ1<θ2<θ3, θ2For spurious signal；
Work as K1When=3, K is had1+0.5(K1-1)K1=6 candidate far field direction of arrival angle, i.e. θ1<θ2<θ3<θ4<θ5<θ6, θ1, θ6
For two true direction of arrival angle, the false direction of arrival angle of its generation is rejected；Remaining 3 direction of arrival angle, wherein second
Big is true direction of arrival angle；
And so on.
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