CN109709510A - A kind of estimation method and system of coherent 2-d direction finding - Google Patents
A kind of estimation method and system of coherent 2-d direction finding Download PDFInfo
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Abstract
This disclosure relates to a kind of estimation method and system of coherent 2-d direction finding, the described method includes: deployment receiving array receives coherent signal value, covariance matrix is constructed by the signal value received, Eigenvalues Decomposition is carried out to covariance matrix, the feature vector comprising all signal messages is extracted, reconstructs Toeplitz matrix using the feature vector extracted.The invention has the advantages that realizing simply, the complexity of calculating is reduced, the accuracy estimated under low signal-to-noise ratio is improved.
Description
Technical field
The present invention relates to the estimation methods and system of a kind of coherent 2-d direction finding.
Background technique
Spatial outlier technology is the emerging airspace signal processing technology to grow up in the past 30 years, it may also be said to it
It is a kind of new technology to grow up on the basis of beam-forming technology, zero point technology and Time Domain Spectrum estimation technique, it is main
Target be research improve in processing bandwidth spacing wave (including independent, part it is related with mutually print angle) estimated accuracy, angle
It spends resolving power and improves the various algorithms of arithmetic speed.The earliest method of estimation to spacing wave angle of arrival is using mechanical wave
The method of beam scanning, this method all can not meet actual needs in speed and in precision, the research of beam-forming technology,
There is breakthrough progress in these areas.
It is likely that there are multi-source (in processing bandwidth) signal in current spacing wave, angle given by Wave beam forming is missed
Difference will will increase, or even non-required interference signal is mistakenly considered to the angle of arrival of desired signal.Accordingly, there exist when source signal,
Urgent project is just become to the estimation of desired signal angle of arrival.
One basic problem of array signal processing be spacing wave arrival direction (direction of arrival,
The major issue in many fields such as the problem of DOA) estimating and radar, sonar.But due to the complexity in broadcasting system,
There can be coherent, this will will cause false-alarm or target positions the problems such as wrong.Such as MUSIC caused by being concerned with due to believing
Work song space and noise subspace interpenetrate, and can not carry out good estimation to coherent signal.
Summary of the invention
Technical problem to be solved by the present invention lies in providing a kind of estimation method of coherent 2-d direction finding,
Solve the estimation problem to coherent 2-d direction finding.
In order to solve the above technical problems, the technical solution adopted by the present invention is that: a kind of coherent 2-d direction finding
Estimation method characterized by comprising
It disposes receiving array and receives coherent signal value；
Covariance matrix is constructed by the signal value received；
Eigenvalues Decomposition is carried out to covariance matrix, extracts the feature vector comprising all signal messages；
Toeplitz matrix is reconstructed using the feature vector extracted.
Another object of the present invention is to provide a kind of estimating system of coherent 2-d direction finding, feature exists
In, comprising:
Deployment module receives coherent signal value for disposing receiving array；
Module is constructed, constructs covariance matrix for the signal value by receiving；
Extraction module extracts the feature comprising all signal messages for carrying out Eigenvalues Decomposition to covariance matrix
Vector；
Processing module, for reconstructing Toeplitz matrix using the feature vector extracted.
Compared with prior art, the invention has the following beneficial technical effects:
It realizes simple, comprising: deployment receiving array receives coherent signal value；Pass through the signal value building association received
Variance matrix；Eigenvalues Decomposition is carried out to covariance matrix, extracts the feature vector comprising all signal messages；Utilize extraction
Feature vector out reconstructs Toeplitz matrix, reduces the complexity of calculating, improves the accuracy estimated under low signal-to-noise ratio.
Detailed description of the invention
Fig. 1 is the flow chart of the estimation method of coherent 2-d direction finding of the invention；
Fig. 2 is the embodiment of the present invention schematic diagram.
Specific embodiment
Below by specific embodiment, present invention is further described in detail, but these embodiments are only that citing
Illustrate, the scope of the present invention is not defined.
Please refer to Fig. 1, a kind of estimation method of coherent 2-d direction finding of the invention characterized by comprising
Step S101, deployment receiving array receive coherent signal value；Step S102 constructs covariance by the signal value received
Matrix；Step S103 carries out Eigenvalues Decomposition to covariance matrix, extracts the feature vector comprising all signal messages；Step
Rapid S104 reconstructs Toeplitz matrix using the feature vector extracted.
In one embodiment, the deployment receiving array receives the reception that coherent signal value includes: adjustment deployment
The position of array element is in M array element on the straight line of same level.
In one embodiment, the deployment receiving array reception coherent signal value further comprises: deployment P remote
Field coherent signal source, is allowed in same plane, and coherent signal source makes reception array element be located at coherent signal far from receiving array
The far field in source.
In one embodiment, described that Eigenvalues Decomposition is carried out to covariance matrix, it extracts comprising all signal messages
Feature vector include: variance matrix R row Eigenvalues Decomposition, resolve into R=Us∑sUs H+σ2UnUn HForm, wherein UsIndicate big
The vector block of feature vector composition is the subspace of signal, UnThe vector block for indicating small feature vector composition is that noise is empty
Between.
In one embodiment, described that Eigenvalues Decomposition is carried out to covariance matrix, it extracts comprising all signal messages
Feature vector further comprise: in the big feature vector block UsIn extract maximum feature value vector.
In one embodiment, described that Eigenvalues Decomposition is carried out to covariance matrix, it extracts comprising all signal messages
Feature vector further comprise: described eigenvector is indicated with the linear combination of array steering vector, then is done at decoherence
Reason, the vector after obtaining decoherence.
In one embodiment, the feature vector reconstruct Toeplitz matrix that the utilization extracts further comprises: imitative
It is true to go out to use the spatial spectrum of MUSIC algorithm.
In one embodiment, further comprise: finding out the peak value of the spatial spectrum.
In one embodiment, the peak value for finding out the spatial spectrum includes: to establish using abscissa as angle, θ, indulges and sits
It is designated as the two-dimensional Cartesian coordinate system of signal-to-noise ratio, draws the space spectral function of MUSIC algorithm in this coordinate system；Find out the space
The corresponding wave crest of spectral function, the angle, θ of the corresponding abscissa of crest value are the corresponding direction of arrival of coherent.
As specific embodiment, the method comprise the steps that receiving P relevant letters comprising deployment signal receiving array
It number is incident on the signal value of receiving array, reconstruct includes the Toeplitz matrix of all signal messages, based on receiving array
It establishes coordinate system, estimates the angle of incident information source and Y-axis to determine the 2-d direction finding of coherent.
As specific embodiment, referring to figure 2., the estimation method the following steps are included:
Step 1: deployment receives the array of signal.
Step 2: receiving the signal that information source issues, receiving the signal value that information source issues may be expressed as: x1(t),x2(t),x3
(t),...xM(t)。
Step 3: taking N number of coherent signal source, it is assumed that incident direction is respectively [θ1, θ2..., θN], write as vector form are as follows:
X (t)=AS (t)+N (t).A is space array prevalence matrix (steering vector battle array).
Step 4: according to the array signal model, constructing covariance matrix.
Step 5: Eigenvalues Decomposition being carried out to covariance matrix, finds out feature vector corresponding to maximum eigenvalue.
Step 6: described eigenvector being indicated with the linear combination of array steering vector, then to decoherence processing is done, is obtained
Vector after to decoherence.
Step 7: utilizing the Toeplitz matrix of reconstruct M × M.
Step 8: Eigenvalues Decomposition being carried out to matrix Y, then simulates the spatial spectrum using MUSIC algorithm.
Step 9: finding out the peak value of the spatial spectrum, corresponding angle is the DOA estimate value of coherent, corresponding
Direction be coherent direction.
The present invention also provides a kind of estimating systems of coherent 2-d direction finding, comprising: deployment module, for disposing
Receiving array receives coherent signal value；Module is constructed, constructs covariance matrix for the signal value by receiving；It extracts
Module extracts the feature vector comprising all signal messages for carrying out Eigenvalues Decomposition to covariance matrix；Handle mould
Block, for reconstructing Toeplitz matrix using the feature vector extracted.
As specific embodiment, deployment described in step 1 receives the array of signal, further comprising the steps of:
Step 1.1: deployment receives the array of signal, comprising M sensor is array element, phase in the reception signal array
The spacing d of adjacent two sensors is equal to the half of signal wavelength lambda；
Step 1.2: the height dimension for receiving sensor in signal array is much smaller than wavelength X, can be approximately considered and connect
Receiving array element is origin；
Step 1.3: adjusting the position of the reception array element of deployment, be in M array element on the straight line of same level, with array element
Place straight line is X-axis, and vertical X axis is set to Y-axis, and array element and information source are in XOY plane.
Step 1.4: deployment P far field coherent signal source is allowed in same plane, and coherent signal source is far from reception battle array
Column make to receive the far field that array element is located at coherent signal source.
As specific embodiment, by the array described in step 2, the signal that information source issues is received, receives information source
The signal value of sending may be expressed as: x1(t),x2(t),x3(t),...xM(t), further comprising the steps of:
Step 2.1: passing through first array element received signal x of the array received1(t)=s (t)+n1(t)
Then second signal value of same timeI.e.Same time third array element, the 4th array element, until the signal x of m-th array element can similarly be obtained2
(t),x3(t),...xM(t)；
Step 2.2: M signal value of expression is subjected to column storehouse, forms higher dimensional matrix column vector:
As specific embodiment, step 3: taking N number of coherent signal source, it is assumed that incident direction is respectively [θ1, θ2...,
θN], write as vector form are as follows: X (t)=AS (t)+N (t), further comprising the steps of:
Step 3.1: setting information source and Y-axis is formed by angle as θ, for N number of signal source, incident direction is respectively [θ1,
θ2..., θN]；
Step 3.2 [θ1, θ2..., θN] replace θ described in step 2.2i, there is shown signal matrix is as follows:
Write above formula as vector form are as follows: X (t)=AS (t)+N (t) extracts space array prevalence matrix (steering vector
Battle array) A.
As specific embodiment, according to the array signal model described in step 4, covariance matrix is constructed, is also wrapped
Include step in detail below:
Step 4.1: to its covariance of asking described in step 3.2, covariance formula are as follows:
In formula ()HExpression takes conjugate transposition, RSS=SSHFor the covariance matrix of signal.
As specific embodiment, Eigenvalues Decomposition is carried out to covariance matrix described in step 5, finds out maximum eigenvalue
Corresponding feature vector, also includes the following specific steps:
Step 5.1: by the method for mathematics to the variance matrix R row Eigenvalues Decomposition, specifically resolving into R=Us∑sUs H+σ2UnUn HForm, wherein UsThe vector block for indicating big feature vector composition, is the subspace of signal, UnIndicate small feature to
The vector block of composition is measured, is noise subspace.
Step 5.2: in the big feature vector block UsIn extract maximum feature value vector.
As specific embodiment, feature vector is indicated with the linear combination of array steering vector described in step 6, then
To doing decoherence processing, the vector after obtaining decoherence.The following steps are included:
Step 6.1: being indicated with the linear combination of array steering vector are as follows:
tkIt (n) is linear combination factor；
Step 6.2: taking coherent signal, may be expressed as:
Step 6.3: to decoherence processing is carried out, specific processing mode is rm=uk1×ukm, m=1,2 ... M.
As specific embodiment, the Toeplitz matrix for reconstructing M × M is utilized described in step 7.The following steps are included:
Step 7.1: using the reconstruct M rank matrix Y, the specific method is as follows:
As specific embodiment, Eigenvalues Decomposition is carried out to matrix Y described in step 8, is then simulated using MUSIC
The spatial spectrum of algorithm, also includes the following specific steps:
Step 8.1: Eigenvalues Decomposition being carried out to matrix Y, specifically decomposes expression formula are as follows: Y=Us∑sUs H+σ2UnUn H, UsTable
Show the vector block of big feature vector composition, UnIndicate the vector block of small feature vector composition；
Step 8.2: the ∑sIt is the diagonal matrix being made of P big characteristic value, it may be assumed that
It is the duplicate small characteristic value of R, the spatial spectrum expression formula of MUSIC algorithm can be obtained are as follows:
As specific embodiment, the peak value of spatial spectrum is found out described in step 9, corresponding angle is coherent
DOA estimate value, corresponding direction are the direction of coherent, are also included the following specific steps:
Step 9.1: establishing using abscissa as angle, θ, ordinate is the two-dimensional Cartesian coordinate system of signal-to-noise ratio, in the coordinate system
Under draw the space spectral function of MUSIC algorithm；
Step 9.2: finding out the corresponding wave crest of the space spectral function, the angle, θ of the corresponding abscissa of crest value is phase
The dry corresponding direction of arrival of information source.
In one embodiment, the evaluation method includes:
Step 1: deployment receives the array of signal, comprising M sensor is array element, two-phase in the reception signal array
The spacing d of adjacent two sensors is equal to the half of signal wavelength；The height gauge for receiving sensor in signal array
Very little to be much smaller than wavelength X, can be approximately considered and receive array element is origin.
In an implementation, the receiving array include M omnidirectional's electromagnetic sensor, and array can be it is randomly topologically structured,
Here the value of M is natural number, and the quantity of array element M is greater than the quantity P of coherent；The array element that M sensor of deployment is constituted
Must keep constituting even linear array on same plane straight line, using straight line where array element as X-axis, vertical X axis is set to Y-axis, array element and
Information source is in XOY plane.
Step 2: receiving the signal that information source issues, receiving the signal value that information source issues may be expressed as: x1(t),x2(t),x3
(t),...xM(t)。
In an implementation, if receiving the far field that array element is located at coherent signal source, can be approximately considered the signal received is plane
Wave signal, the array element spacing of receiving array are much larger than array element size, and influencing each other between each array element can be ignored.For battle array
Each array element of column receives and is transmitted to processor through respective transmission channel after signal, that is to say, that processing receives logical from M
The data in road, the data in M channel of record are signal value x1(t),x2(t),...xM(t).Then by M signal value of expression into
Ranks storehouse forms higher dimensional matrix column vector:
Step 3: N number of coherent signal source is taken by the array, it is assumed that incident direction is respectively [θ1, θ2..., θN],
Write as vector form are as follows: X (t)=AS (t)+N (t).
In one embodiment, if the angle that the incident direction in coherent signal source and Y direction are formed is θ, then N number of relevant
Incidence angle [the θ of signal source1, θ2..., θN], it brings into higher dimensional matrix column vector, there is shown space array flow pattern matrix A (guiding
Vector array).
Step 4: according to the array signal model, constructing covariance matrix；
In an implementation, using the method for mathematics to above-mentioned vector X (t) and its transposition XT(t) covariance is sought, association side is obtained
Poor matrix R.
Step 5: Eigenvalues Decomposition being carried out to covariance matrix, finds out feature vector corresponding to maximum eigenvalue；
In an implementation, the corresponding big feature vector decomposited is signal subspace, and corresponding small feature vector is noise
Subspace.If wherein noise is space white noise, σ2It is the M-P duplicate small characteristic values of R.
Step 6: feature vector being indicated with the linear combination of array steering vector, then to decoherence processing is done, is gone
Vector after relevant.
In an implementation, k indicates the number of value, should control between 300 to 600, value is too small to be easy to produce distortion, takes
The data volume for being worth too big generation is more, influences computational efficiency.
Step 7: utilizing the Toeplitz matrix of reconstruct M × M；
In an implementation, using mathematical method, according to the array element M restructuring matrix Y.
Step 8: Eigenvalues Decomposition being carried out to matrix Y, specifically decomposes expression formula are as follows: Y=Us∑sUs H+σ2UnUn H, UsIt indicates
The vector block of big feature vector composition, UnIndicate the vector block of small feature vector composition；
In an implementation, Eigenvalues Decomposition is carried out to matrix Y, decomposites the subspace U of small feature vector compositionn, He great Te
The vector block U of value indicative vector compositions, since the value of K is limited, it cannot be guaranteed that the strict orthogonal of the characteristic vector decomposited
Property, it is used when with MUSIC spatial spectrum:
Step 9: finding out the peak value of spatial spectrum, corresponding angle is the DOA estimate value of coherent, corresponding side
To the direction of as coherent.
In one embodiment, P can be drawn according to above-mentioned relevant parameter by the processing method of emulationMUSICFunction, letter
Several abscissas indicate that ordinate is indicated with signal-to-noise ratio with angle, find out angle corresponding to peak value in image, corresponding side
To the direction for being the coherent signal source for using this method estimated.During simulation process, the signal-to-noise ratio parameter that is taken
Value is unsuitable too small.
The present invention realizes following beneficial technical effect:
It realizes simple, comprising: deployment receiving array receives coherent signal value；Pass through the signal value building association received
Variance matrix；Eigenvalues Decomposition is carried out to covariance matrix, extracts the feature vector comprising all signal messages；Utilize extraction
Feature vector out reconstructs Toeplitz matrix, reduces the complexity of calculating, improves the accuracy estimated under low signal-to-noise ratio.
Although the present invention has chosen preferable embodiment and discloses as above, it is not intended to limit the present invention.Obviously, it is not necessarily to here
Also all embodiments can not be exhaustive.Any this field researcher without departing from the spirit and scope of the present invention,
The design method and content that all can be used in embodiment disclosed above are changed and are modified to research approach of the invention, because
This, all contents without departing from the present invention program, research essence according to the present invention is to any simple made by above-described embodiment
Modification, Parameters variation and modification, belong to the protection scope of the present invention program.
Claims (10)
1. a kind of estimation method of coherent 2-d direction finding characterized by comprising
It disposes receiving array and receives coherent signal value；
Covariance matrix is constructed by the signal value received；
Eigenvalues Decomposition is carried out to covariance matrix, extracts the feature vector comprising all signal messages；
Toeplitz matrix is reconstructed using the feature vector extracted.
2. the estimation method of coherent 2-d direction finding according to claim 1, which is characterized in that the deployment connects
The position that array received coherent signal value includes: the reception array element of adjustment deployment is received, M array element is made to be in same level
On straight line.
3. the estimation method of coherent 2-d direction finding according to claim 2, which is characterized in that the deployment connects
Receiving array received coherent signal value further comprises: deployment P far field coherent signal source is allowed in same plane,
Coherent signal source makes to receive the far field that array element is located at coherent signal source far from receiving array.
4. the estimation method of coherent 2-d direction finding according to claim 1, which is characterized in that described pair of association side
Poor matrix carries out Eigenvalues Decomposition, and extracting the feature vector comprising all signal messages includes: variance matrix R row characteristic value point
Solution, resolves into R=Us∑sUs H+σ2UnUn HForm, wherein UsThe vector block for indicating big feature vector composition is that the son of signal is empty
Between, UnThe vector block for indicating small feature vector composition, is noise subspace.
5. the estimation method of coherent 2-d direction finding according to claim 4, which is characterized in that described pair of association side
Poor matrix carries out Eigenvalues Decomposition, and extracting the feature vector comprising all signal messages further comprises: in the big spy
Levy vector block UsIn extract maximum feature value vector.
6. the estimation method of coherent 2-d direction finding according to claim 5, which is characterized in that described pair of association side
Poor matrix carries out Eigenvalues Decomposition, and extracting the feature vector comprising all signal messages further comprises: to the feature to
Amount is indicated with the linear combination of array steering vector, then does decoherence processing, the vector after obtaining decoherence.
7. the estimation method of coherent 2-d direction finding according to claim 4, which is characterized in that the utilization mentions
The feature vector reconstruct Toeplitz matrix of taking-up further comprises: simulating the spatial spectrum using MUSIC algorithm.
8. the estimation method of coherent 2-d direction finding according to claim 7, which is characterized in that further packet
It includes: finding out the peak value of the spatial spectrum.
9. the estimation method of coherent 2-d direction finding according to claim 8, which is characterized in that described to find out institute
The peak value for stating spatial spectrum includes:
It establishes using abscissa as angle, θ, ordinate is the two-dimensional Cartesian coordinate system of signal-to-noise ratio, draws MUSIC in this coordinate system
The space spectral function of algorithm；
The corresponding wave crest of the space spectral function is found out, the angle, θ of the corresponding abscissa of crest value is that coherent is corresponding
Direction of arrival.
10. a kind of estimating system of coherent 2-d direction finding characterized by comprising
Deployment module receives coherent signal value for disposing receiving array；
Module is constructed, constructs covariance matrix for the signal value by receiving；
Extraction module extracts the feature vector comprising all signal messages for carrying out Eigenvalues Decomposition to covariance matrix；
Processing module, for reconstructing Toeplitz matrix using the feature vector extracted.
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