CN108828506A - A kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition - Google Patents
A kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition Download PDFInfo
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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
Abstract
The electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition that the invention discloses a kind of solves the problem of that prior art array manifold Power estimation method can not be adapted to relevant multiple target, fewer snapshots condition under high spatial Power estimation accuracy constraint.The present invention includes the following steps：Step 1 establishes array manifold model；Step 2, array error correction；Redundant dictionary model D after step 3, building sparse decomposition model and building sparse decomposition；Array received snap model after step 4, construction sparse decomposition；Step 5, artificial setting evaluated error thresholding ε；Step 6, solution room spectrum, searching meet constraint conditionAnd 0 Norm minimum airspace rarefaction representation coefficient β, after iterating, the position of nonzero term is the space spectral position of electromagnetic target in stable β.The high-precision spatial Power estimation to relevant multiple target, fewer snapshots electromagnetic target can be achieved in the present invention, and can promote array manifold Power estimation performance.
Description
Technical field
The present invention relates to Estimation of Spatial Spectrum technical fields, and in particular to a kind of electromagnetic target spatial spectrum based on sparse decomposition
Estimation method.
Background technique
Traditional array manifold Power estimation technology is to weight to form spectral peak progress space search, spectral peak position using array data
It sets and is corresponded with incidence angle, and then incident angle is obtained by maximum spectrum peak position.In the prior art, based on conventional wave beam shape
At Estimation of Spatial Spectrum method be that each array element data are carried out with phase or time delay weighting, simple and easy but estimated accuracy is high；
MVDR method obtains spatial spectrum expression formula by solving optimization function, and precision is higher but vulnerable to array error, sampling number of snapshots shadow
It rings；MUSIC method constructs Power estimation function by feature decomposition, using the orthogonality of signal subspace and noise subspace, point
Resolution surmounts Rayleigh limit, belongs to super resolution algorithm, but need to predict target number, fail and be engineered more multiple to relevant multiple target
It is miscellaneous.The practical application condition of Estimation of Spatial Spectrum is often more complicated, it is desirable to be able under the premise of guaranteeing high estimated accuracy, to phase
Dry multiple target, small sampling snap said conditions stand good.
In order to solve this problem, the present invention proposes to carry out sparse decomposition using array data, and then constructs array airspace
Estimation of Spatial Spectrum problem is converted to convex optimization problem and solved by redundant dictionary.This method utilizes target sparse characteristic, and spatial spectrum is estimated
It is higher and insensitive to multiple target coherence to count precision, stands good in fewer snapshots.
Summary of the invention
The technical problem to be solved by the present invention is to：A kind of electromagnetic target Estimation of Spatial Spectrum side based on sparse decomposition is provided
Method solves prior art array manifold Power estimation method under high spatial Power estimation accuracy constraint, can not be to relevant multiple target, small
The problem of snap said conditions are adapted to.
To achieve the above object, the technical solution adopted by the present invention is as follows：
A kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition, includes the following steps：
Step 1 establishes array manifold model, establishes array manifold model using the essential information of array and signal；
Step 2, array error correction, using input signal known to parameter to array manifold model established in step 1
Error be corrected；
Step 3, building sparse decomposition model, construct sparse point using the array manifold model information after correcting in step 2
Redundant dictionary model D after solution；
Array received snap model after step 4, construction sparse decomposition, utilizes the redundant dictionary model D constructed in step 3
Array received snap model x after constructing sparse decomposition；
Step 5, artificial setting evaluated error thresholding ε；
Step 6, solution room spectrum, searching meet constraint conditionAnd 0 Norm minimum airspace sparse table
Show factor beta, after iterating, the position of nonzero term is the space spectral position of electromagnetic target in stable β.
Specifically, using the essential information of array, determining array manifold model, the essential information packet in the step 1
Include the mode of structuring the formation, array number M, each information source centre frequency flAnd incident angle θl, wherein l=1,2 ..., N, therefore, the array stream
Pattern type A (θ) is expressed as：A (θ)=[a (θ1),a(θ2),…,a(θN)], whereinrq
=uqcosθ+vqSin θ, q=1,2 ..., M, c are the transmission speed of medium medium wave, []TExpression makees transposition operation, θ to matrix
For the angle of information source and array normal direction, uqAnd vqRespectively indicate abscissa and ordinate of q-th of the array element in rectangular coordinate system.
Further, in the step 2, when to array error correction, respectively to the array manifold model established
Sensor position uncertainties, channel amplitude phase error and array element mutual coupling error are corrected.
Further, it in the step 2, by inputting signal known to parameter to array, and then measures and believes in array
The method of number Parameters variation, to the sensor position uncertainties, the channel amplitude phase error and the array element mutual coupling error
Calibration is carried out, record calibration matrix is C (θ), then the array manifold model A after correctingc(θ) is expressed as：Ac(θ)=C (θ) A (θ).
Further, in the step 4, the snapshot data x (n) of array received is expressed as：X (n)=Acs(n)+n
(n), wherein s (n) is N × α dimension, and α indicates that Space domain sampling number of snapshots, physical meaning are the N number of original of the every information source α point sampling in space
Information source set；By total space orientation discretization, then s (n) is represented by total space orientation round (2 π η) a discrete angular information source
Linear combination, η (η > 0) be resolution ratio, round () indicate to variable be rounded；It is in corresponding target θiIt is indicated in angle
Coefficient is 1, other orientation are 0；Argument n is omitted, original signal s can be expressed as s=ψ β, and β is that round (2 π η) × α ties up airspace
Rarefaction representation coefficient, ψ are that N × round (2 π η) ties up airspace sparse transformation base；Array received snap model x table after sparse decomposition
It is shown as x=As+n=A ψ β+n, by airspace sparse transformation base ψ and array manifold model Ac(θ) is combined into spatial redundancy dictionary model
D, then spatial redundancy dictionary model D is expressed as D=Acψ, therefore, the array received snap model x after sparse decomposition are expressed as：x
=D β+n.
Further, in the step 6, the nonzero term position in the rarefaction representation coefficient β of airspace has corresponded to electromagnetism mesh
Target dimensional orientation, according to sparse decomposition characteristic, constitution optimization problem is argmin | | β | |0, constraint condition isWherein argmin | | β | |0Indicate that 0 Norm minimum of vector β, ε are the evaluated error being manually arranged in step 5
Thresholding,Indicate the square value of 2 norm of vector；Above-mentioned mathematical problem is solved by the method for convex optimization, airspace sparse table is set
Show coefficient vector β initial value all 0, algorithm automatic Iterative searches for the optimal solution for meeting constraint condition, nonzero term in stable β
Position be electromagnetic target space spectral position.
Compared with prior art, the invention has the advantages that：
Design is scientific and reasonable for the method for the present invention, using the electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition, passes through
Sparse decomposition is carried out to array received data, thresholding is estimated by step-up error, and then solve electromagnetism mesh using convex optimization method
Airspace rarefaction representation coefficient is marked, to realize the high-precision spatial Power estimation to relevant multiple target, fewer snapshots electromagnetic target, and energy
Promote array manifold Power estimation performance.
The present invention establishes array manifold model using the essential information of array and signal, utilizes input signal known to parameter
The correction of sensor position uncertainties, channel amplitude phase error, array element mutual coupling equal error is carried out to array；Utilize the array after correction
Redundant dictionary model D after flow pattern information architecture sparse decomposition；It is connect using the array after redundant dictionary Construction of A Model sparse decomposition
Receive snap model x=D β+n；Artificial setting evaluated error thresholding ε, searching meet constraint conditionAnd 0 norm most
Small airspace rarefaction representation coefficient β.After iterating, the position of nonzero term is the spatial spectrum position of electromagnetic target in stable β
It sets.
Detailed description of the invention
Fig. 1 is flow chart of the present invention.
Fig. 2 is coherent Estimation of Spatial Spectrum figure in numerical simulation tests example of the present invention.
Fig. 3 is the estimated accuracy in numerical simulation tests example of the present invention under the conditions of different signal-to-noise ratio.
Fig. 4 is Estimation of Spatial Spectrum figure under the conditions of 10 snaps in numerical simulation tests example of the present invention.
Fig. 5 is Estimation of Spatial Spectrum figure under the conditions of 50 snaps in numerical simulation tests example of the present invention.
Fig. 6 is Estimation of Spatial Spectrum figure under the conditions of 100 snaps in numerical simulation tests example of the present invention.
Fig. 7 is Estimation of Spatial Spectrum figure under the conditions of 500 snaps in numerical simulation tests example of the present invention.
Specific embodiment
The invention will be further described with embodiment for explanation with reference to the accompanying drawing, and mode of the invention includes but not only limits
In following embodiment.
A kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition, includes the following steps：
Step 1 establishes array manifold model, establishes array manifold model using the essential information of array and signal.
The essential information for specially utilizing array, determines array manifold model, and the essential information includes the mode, battle array of structuring the formation
First number M, each information source centre frequency flAnd incident angle θl, wherein l=1,2 ..., N, therefore, the array manifold model A
(θ) is expressed as：A (θ)=[a (θ1),a(θ2),…,a(θN)], whereinrq=
uqcosθ+vqSin θ, q=1,2 ..., M, c are the transmission speed of medium medium wave, []TExpression makees transposition operation to matrix, and θ is
The angle of information source and array normal direction, uqAnd vqRespectively indicate abscissa and ordinate of q-th of the array element in rectangular coordinate system.
Step 2, array error correction, using input signal known to parameter to array manifold model established in step 1
Error be corrected.
When to array error correction, the sensor position uncertainties to the array manifold model established, channel amplitude respectively
Phase error and array element mutual coupling error are corrected.By inputting signal known to parameter to array, and then measure in array
The method of signal parameter variation, misses the sensor position uncertainties, the channel amplitude phase error and the array element mutual coupling
Difference carries out calibration, and record calibration matrix is C (θ), then the array manifold model A after correctingc(θ) is expressed as：Ac(θ)=C (θ) A
(θ)。
Step 3, building sparse decomposition model, construct sparse point using the array manifold model information after correcting in step 2
Redundant dictionary model D after solution.
Array received snap model after step 4, construction sparse decomposition, utilizes the redundant dictionary model D constructed in step 3
Array received snap model x after constructing sparse decomposition.
The snapshot data x (n) of array received is expressed as：X (n)=AcS (n)+n (n), wherein s (n) is N × α dimension, and α is indicated
Space domain sampling number of snapshots, physical meaning are N number of original source set of the every information source α point sampling in space；Total space orientation is discrete
Change, then s (n) is represented by the linear combination of total space orientation round (2 π η) a discrete angular information source, and η (η > 0) is to differentiate
Rate, round () indicate to be rounded variable；It is in corresponding target θiIndicate that coefficient is 1 in angle, other orientation are 0；It omits
Argument n, original signal s can be expressed as s=ψ β, and β is that round (2 π η) × α ties up airspace rarefaction representation coefficient, and ψ is N × round
(2 π η) ties up airspace sparse transformation base；Array received snap model x after sparse decomposition is expressed as x=As+n=A ψ β+n, will be empty
Domain sparse transformation base ψ and array manifold model Ac(θ) is combined into spatial redundancy dictionary model D, then spatial redundancy dictionary model D table
It is shown as D=Acψ, therefore, the array received snap model x after sparse decomposition are expressed as：X=D β+n.
Step 5, artificial setting evaluated error thresholding ε.
Step 6, solution room spectrum, searching meet constraint conditionAnd 0 Norm minimum airspace sparse table
Show factor beta, after iterating, the position of nonzero term is the space spectral position of electromagnetic target in stable β.
Nonzero term position in the rarefaction representation coefficient β of airspace is the dimensional orientation for having corresponded to electromagnetic target, according to sparse point
Characteristic is solved, constitution optimization problem is argmin | | β | |0, constraint condition isWherein argmin | | β | |0Indicate to
0 Norm minimum of β is measured, ε is the evaluated error thresholding being manually arranged in step 5,Indicate the square value of 2 norm of vector；Pass through
The method of convex optimization solves above-mentioned mathematical problem, airspace rarefaction representation coefficient vector β initial value all 0 is arranged, algorithm is automatic
Iterative search meets the optimal solution of constraint condition, and the position of nonzero term is the space spectral position of electromagnetic target in stable β.By
In sparse decomposition and subsequent optimization to target coherence, sampling number of snapshots and insensitive, therefore relevant multiple target, small can be solved
The Estimation of Spatial Spectrum problem of number of snapshots target.
Design is scientific and reasonable for the method for the present invention, using the electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition, passes through
Sparse decomposition is carried out to array received data, thresholding is estimated by step-up error, and then solve electromagnetism mesh using convex optimization method
Airspace rarefaction representation coefficient is marked, realizes the high-precision spatial Power estimation to relevant multiple target, fewer snapshots electromagnetic target, promotes battle array
The purpose of column space Power estimation performance.
The present invention establishes array manifold model using the essential information of array and signal, utilizes input signal known to parameter
The correction of sensor position uncertainties, channel amplitude phase error, array element mutual coupling equal error is carried out to array；Utilize the array after correction
Redundant dictionary model D after flow pattern information architecture sparse decomposition；It is connect using the array after redundant dictionary Construction of A Model sparse decomposition
Receive snap model x=D β+n；Artificial setting evaluated error thresholding ε, searching meet constraint conditionAnd 0 norm most
Small airspace rarefaction representation coefficient β.After iterating, the position of nonzero term is the spatial spectrum position of electromagnetic target in stable β
It sets.
In order to make those skilled in the art can better understand that the technology of the present invention content, now provides following values emulation
Test examples are illustrated the present invention.
It is handled according to process flow shown in FIG. 1.Emulation uses 10 yuan of uniform straight line arrays, carries out error to array
Correction.Two electromagnetic target incidence angle of space is respectively 50 °, 60 °.It is two Coherent Targets in Fig. 2, incident signal-to-noise ratio 10dB is adopted
Sample number of snapshots are 1000；Fig. 3 is the estimated accuracy of this method under the conditions of different signal-to-noise ratio；Incident signal-to-noise ratio is in Fig. 4-Fig. 7
10dB, wherein Fig. 4 sample number of snapshots be 10, Fig. 5 50, Fig. 6 100, Fig. 7 500.Abscissa show excellent in Fig. 2,4-7
Change the incidence angle obtained after the airspace rarefaction representation coefficient conversion acquired, ordinate is normalization spatial spectrum；Abscissa is in Fig. 3
Signal-to-noise ratio, ordinate are the root-mean-square error of orientation estimation.
Exact space Power estimation can be carried out to two Coherent Targets by being illustrated in figure 2 method proposed by the invention, and estimation misses
Difference is better than 0.5 °；Shown in Fig. 3, with the continuous improvement of signal-to-noise ratio, the root-mean-square error of this method Estimation of Spatial Spectrum is constantly reduced；
Shown in Fig. 4-Fig. 7, under the conditions of fewer snapshots, the Estimation of Spatial Spectrum precision of this method is superior to 1 °, under the conditions of different number of snapshots
Estimate that performance difference is about 0.5 °, i.e., stands good to fewer snapshots condition.
In summary, method proposed by the invention can be realized higher under the conditions of Coherent Targets, small sampling number of snapshots
The Estimation of Spatial Spectrum of precision, it was demonstrated that the validity of invention.
Above-described embodiment is only one of the preferred embodiment of the present invention, should not be taken to limit protection model of the invention
It encloses, as long as that in body design thought of the invention and mentally makes has no the change of essential meaning or polishing, is solved
The technical issues of it is still consistent with the present invention, should all be included within protection scope of the present invention.
Claims (6)
1. a kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition, which is characterized in that include the following steps：
Step 1 establishes array manifold model, establishes array manifold model using the essential information of array and signal；
Step 2, array error correction, using input signal known to parameter to the mistake of array manifold model established in step 1
Difference is corrected；
Step 3, building sparse decomposition model, after the array manifold model information building sparse decomposition after being corrected in step 2
Redundant dictionary model D；
Array received snap model after step 4, construction sparse decomposition, is constructed using the redundant dictionary model D constructed in step 3
Array received snap model x after sparse decomposition；
Step 5, artificial setting evaluated error thresholding ε；
Step 6, solution room spectrum, searching meet constraint conditionAnd 0 Norm minimum airspace rarefaction representation system
Number β, after iterating, the position of nonzero term is the space spectral position of electromagnetic target in stable β.
2. a kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition according to claim 1, which is characterized in that
In the step 1, using the essential information of array, array manifold model is determined, the essential information includes the mode, battle array of structuring the formation
First number M, each information source centre frequency flAnd incident angle θl, wherein l=1,2 ..., N, therefore, the array manifold model A
(θ) is expressed as：A (θ)=[a (θ1),a(θ2),…,a(θN)], whereinrq
=uq cosθ+vqSin θ, q=1,2 ..., M, c are the transmission speed of medium medium wave, []TExpression makees transposition operation to matrix,
θ is the angle of information source and array normal direction, uqAnd vqRespectively indicate abscissa and ordinate of q-th of the array element in rectangular coordinate system.
3. a kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition according to claim 2, which is characterized in that
In the step 2, when to array error correction, the sensor position uncertainties to the array manifold model established, channel respectively
Amplitude-phase error and array element mutual coupling error are corrected.
4. a kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition according to claim 3, which is characterized in that
In the step 2, by inputting signal known to parameter to array, and then the method that signal parameter changes in array is measured,
Calibration is carried out to the sensor position uncertainties, the channel amplitude phase error and the array element mutual coupling error, records calibration
Matrix is C (θ), then the array manifold model A after correctingc(θ) is expressed as：Ac(θ)=C (θ) A (θ).
5. a kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition according to claim 4, which is characterized in that
In the step 4, the snapshot data x (n) of array received is expressed as：X (n)=AcS (n)+n (n), wherein s (n) is N × α
Dimension, α indicate that Space domain sampling number of snapshots, physical meaning are N number of original source set of the every information source α point sampling in space；By the total space
Orientation discretization, then s (n) is represented by the linear combination of total space orientation round (2 π/η) a discrete angular information source, η (η >
It 0) is resolution ratio, round () indicates to be rounded variable；It is in corresponding target θiIndicate that coefficient is 1 in angle, other orientation
It is 0；Argument n is omitted, original signal s can be expressed as s=ψ β, and β is that round (2 π/η) × α ties up airspace rarefaction representation coefficient, ψ
Airspace sparse transformation base is tieed up for N × round (2 π/η)；Array received snap model x after sparse decomposition is expressed as x=As+n=
A ψ β+n, by airspace sparse transformation base ψ and array manifold model Ac(θ) is combined into spatial redundancy dictionary model D, then spatial redundancy
Dictionary model D is expressed as D=Acψ, therefore, the array received snap model x after sparse decomposition are expressed as：X=D β+n.
6. a kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition according to claim 5, which is characterized in that
In the step 6, the nonzero term position in the rarefaction representation coefficient β of airspace is the dimensional orientation for having corresponded to electromagnetic target, according to
Sparse decomposition characteristic, constitution optimization problem are argmin | | β | |0, constraint condition isWherein argmin | | β | |0
Indicate that 0 Norm minimum of vector β, ε are the evaluated error thresholding being manually arranged in step 5,Indicate square of 2 norm of vector
Value；Above-mentioned mathematical problem is solved by the method for convex optimization, airspace rarefaction representation coefficient vector β initial value all 0 is set, is calculated
Method automatic Iterative searches for the optimal solution for meeting constraint condition, and the position of nonzero term is the spatial spectrum of electromagnetic target in stable β
Position.
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