CN109375154A - Coherent signal method for parameter estimation based on uniform circular array under a kind of impulsive noise environment - Google Patents
Coherent signal method for parameter estimation based on uniform circular array under a kind of impulsive noise environment Download PDFInfo
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- CN109375154A CN109375154A CN201811236543.8A CN201811236543A CN109375154A CN 109375154 A CN109375154 A CN 109375154A CN 201811236543 A CN201811236543 A CN 201811236543A CN 109375154 A CN109375154 A CN 109375154A
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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 invention belongs to array signal processing parameter Estimation fields, and in particular to the coherent signal method for parameter estimation based on uniform circular array under a kind of impulsive noise environment, comprising the following steps: carry out snap sampling to D source signal in space；Impact is gone to pre-process snap sampled data；Mode excitation transformation is carried out to array output data；Construct sparse reconstruct wordbook；Sparse reconstruct obtains coherent azimuth；Judge whether to reach maximum number of iterations, if so, executing step 7；Otherwise t=t+1, return step five are enabled；Sparse reconstruction result is obtained, information source azimuth information is obtained using indexed set U, exports coherent Mutual coupling result.The present invention solves the coherent signal Parameter Estimation Problem under impulsive noise environment based on uniform circular array, the basis of use pattern excitation transformation and the sparse reconstruct thought of compressed sensing as parameter Estimation, designed method have the advantages that computation complexity is low, the calculating time is short and robustness is high.
Description
Technical field
The invention belongs to array signal processing parameter Estimation fields, and in particular to based on uniform under a kind of impulsive noise environment
The coherent signal method for parameter estimation of circle battle array.
Background technique
Estimation of Spatial Spectrum is the key that the fields such as shortwave radio monitor, radio intelligence, radar target locating and tracking, smart antenna
Technology, accurate direction of arrival (DOA) estimation is for improving communication system performance important in inhibiting.Since structure is simple, divides
Analysis is convenient, and the spatial spectral estimation algorithm of early stage and application are all based on linear array proposition, but linear array can only provide deviation array
The orientation angular estimation of axis.Compared with linear array, circle battle array is capable of providing 360 ° omni-directional, without fuzzy orientation angular estimation, each
There is approximately uniform resolution ratio in orientation, azimuth and the estimation of pitch angle two dimension angular can be provided simultaneously, with more practical
Value.The particularity of uniform circular array array structure makes vandermonde structure of its array manifold without linear array, therefore many suitable
Excellent estimation scheme for linear array not can be used directly in circle battle array.Beam space transformation based on phase mode excitation is to be directed to
The array manifold of uniform circular array can be transformed to similar by a kind of effective scheme that uniform circular array proposes by beam space transformation
The form of generalized circular matrix.
Spatial diversity between smart antenna mobile subscriber realizes that message capacity doubles, in practical mobile environment
In, same mobile subscriber's signal passes through the multipath signal that various reflectors are formed, and is typically considered relevant.Common high score
It distinguishes signal estimation method, there is preferable resolution performance in independent source, but estimate that performance is bright under coherent environment
It is aobvious to be deteriorated or even entirely ineffective be unable to estimate.Due to the presence of coherent signal, traditional multiple signal classification (MUSIC) algorithm
The direction of arrival of signal all can not be correctly estimated with invariable rotary subspace (ESPRIT) algorithm.For even linear array, although having
Space smoothing class algorithm can handle coherent signal source, but these decorrelation LMS algorithms are but not directly applicable uniform circular array
In.Uniform circular array is converted to virtual uniform linear array, thus obtained virtual uniform linear array has translation as common linear array
Invariance so as to use space smoothing decoherence, but increases calculation amount while space smoothing.
What traditional high-resolution direction finding estimation scheme considered is white Gaussian noise signal model, and under actual conditions, back
There is the impact noise situation indicated with symmetric alpha-stable distribution process (S α S) in scape environment and nonideal white Gaussian noise.By
Second order and the above High Order Moment of second order is not present in impact noise, the Mutual coupling problem under impact noise can not directly transplanting
Target component estimation scheme under Gaussian noise, the sharply decline that otherwise will cause algorithm performance are even failed.It is existing to be based on
The MUSIC method of co-variation and Fractional Lower Order Moments, although the DOA estimation problem under the conditions of being able to solve impact noise, multidimensional
Search brings higher calculation amount, and performance decline is significant in the case where few number of snapshots.Based on uniform under impact noise
The coherent signal source DOA estimation problem of circle battle array, should establish the uniform circular array data receiver model under impulsive noise environment first,
Impact pretreating scheme is removed in design, is solved under the physical conditions such as few number of snapshots, low signal-to-noise ratio using new method for parameter estimation
Quick, accurate DOA estimation problem.
By the retrieval discovery to existing technical literature, high book man of virtue and ability it is equal " electronics and information journal " (2007, Vol.29,
No.12, pp.2832-2835) on mode sky is utilized in " the pattern space matrix reconstruction algorithm based on uniform circular array " delivered
Between matrix reconstruction algorithm, reconstruct Toeplitz matrix, successfully estimate the arrival bearing of coherent source, but carried on the back in impact noise
Under scape, method penalty seriously causes to fail.Han Xiaodong etc. is at " applicating technology " (2012, Vol.39, No.1, pp.35-39)
On in the DOA of uniform circular array coherent " under the impact noise background estimation " delivered based on mode space transform algorithm and sky
Between the thought of smoothing algorithm realize uniform circular array under impact noise background in conjunction with ROC-MUSIC algorithm and FLOM-MUSIC algorithm
The DOA of coherent estimates, but the required calculating time is longer, the penalty in the case where low signal-to-noise ratio lacks snap sampling condition, no
It can solve the DOA estimating speed and precision problem of coherent under impulsive noise environment.
Compressed sensing is theoretical as a kind of new Signal acquiring and processing, can make full use of the sparsity of signal, extensively
Applied to various fields such as signal processings.Compressive sensing theory extracts interested target information from a small amount of observation data, if
Counting observing matrix reduces required data dimension, and can accurately restore the parameter letter of original signal from less observation data
Breath.Therefore when this patent solves coherent signal source DOA estimation problem under the conditions of impact noise, impact pretreatment side is gone in design
Case carries out mode excitation to the output signal of uniform circular array, becomes the virtual array in model space, on this basis base
The sparsity possessed by signal estimates required parameter by the sparse reconstruct of orthogonal matching, has using a small amount of measured value
Solves to effect the target component estimation problem under adverse noise environment.Simulation result shows the base under this impulsive noise environment
It can guarantee the accuracy of estimation in the coherent signal method for parameter estimation of uniform circular array, it is possible to provide 360 ° of azimuth informations, point
It distinguishes that power is strong, reduces due to space smoothing bring calculation amount, advantage is aobvious especially under few snap hits, Low SNR
It writes.
In conclusion the prior art exists estimates that performance is obviously deteriorated or even entirely ineffective nothing under coherent environment
Method estimation；The orientation angular estimation for deviateing array axis, the problems such as calculation amount is too big, can only be provided.
Summary of the invention
It is nicely rounded the purpose of the present invention is to provide being based under a kind of validity and the higher impulsive noise environment of robustness
The coherent DOA estimation method of battle array.
Coherent signal method for parameter estimation based on uniform circular array under a kind of impulsive noise environment, comprising the following steps:
(1) snap sampling is carried out to D source signal in space；
(2) impact is gone to pre-process snap sampled data；
(3) mode excitation transformation is carried out to array output data；
(4) sparse reconstruct wordbook is constructed；
(5) sparse reconstruct obtains coherent azimuth；
(6) judge whether to reach maximum number of iterations, if so, executing step 7；Otherwise t=t+1, return step five are enabled；
(7) sparse reconstruction result is obtained, obtains information source azimuth information using indexed set U, output coherent wave reaches side
To estimated result.
It is described that snap sampling is carried out to D, space source signal, comprising:
Antenna array is the circle battle array that the radius on x/y plane is r, is uniform-distribution with isotropic M array element on circumference,
The center of circle of circle array antenna is reference point, and D far field narrow band signal is with azimuth { θ1,θ2,…,θDBe incident on uniform circular array,
Middle azimuth angle thetad∈ [0,360 °] (d=1,2 ..., D) refers to origin to projection and x-axis of the line of information source on x/y plane inverse
Angle on hour hands, and information source is coplanar with array；
Array received kth time snap sampled data are as follows:
X (k)=A (θ) S (k)+N (k)
Wherein, X (k)=[x1(k),x2(k),…,xM(k)]TFor the reception data vector of array；
A (θ)=[a (θ1) a(θ2) … a(θD)] it is signal guide vector matrix, θ=(θ1,θ2,…,θD) it is angle arrow
Amount, θdIt is the arrival bearing of d-th of information source, d=1,2 ..., D；S (k)=[s1(k),s2(k),…,sD(k)]TFor receiving antenna
The reception signal phasor of reference point；N (k)=[n1(k),n2(k),…,nM(k)]TMeet what S α S was distributed to be independent identically distributed
Impact noise vector is determined the impact degree of noise by characteristic index α；
D-th of steering vector:
a(θd)=[exp (jk0rcos(θd-γ0)),exp(jk0rcos(θd-γ1)),…,exp(jk0rcos(θd-
γM-1))]T
Wherein, d=1,2 ..., D；k0Indicate wave number, k0=2 π/λ；λ is the wavelength of incoming signal；γm=2 π m/M, m=
0,1,2 ..., M-1 indicate m-th of array element of array and the angle of x-axis.
It is described to go impact to pre-process snap sampled data, comprising:
As unit of single snap sampled data, the amplitude upper limit max of construction kth time snap sampled data | x1(k)|,|
x2(k)|,…,|xM(k) | }, withFor standard to receive data into
Row normalized, wherein the value of q is determined according to the characteristic index α that impact noise S α S is distributed.
It is described that mode excitation transformation is carried out to array output data, comprising:
Wherein, T=J-1CvF/M, F=[w-l,w-l+1,…,wl]H, l=-h ..., 0 ..., h,
wl=[1, exp (j2 π l/M) ..., exp (j2 π l (M-1)/M)]H,
J=diag { J-h(β),…,J-1(β),J0(β),J1(β),…,Jh(β) },
Cv=diag { j-h,…,j-1,j0,j1,…,jh, 2 π r/ λ of h ≈ is the max model number of mode excitation, Jl(β), l
=-h ..., 0 ..., h are l rank Bessel function of the first kind.
The sparse reconstruct wordbook of construction, comprising:
Under K snap sampling condition, output signal data matrix isIt defines defeated
The covariance matrix of signal outTo covariance matrixEigenvalues Decomposition is carried out, it is wherein D big
The corresponding characteristic vector of characteristic value is respectively v1,v2,…,vD, utilize ES=span { v1,v2,…vDConstruction signal subspace ES；
By information source range that may be present (0,360 °) equally spaced division, Φ=(φ1,φ2,…,φP), wherein the value of P is by drawing
Precision is divided to determine, P is greater than far field narrow band signal number D, constructs signal guide vector sparse dictionary collection B (Φ)=[b (φ1) b
(φ2) … b(φP)], b (φp) it is sparse dictionary collection atom, p=1,2 ..., P, b (φp)=exp (jl φp), l=-
h,…,0,…,h；Signal subspace ESIt is defined as the initial residual error r of sparse reconstruct0, setting t is the number of iterations of sparse reconstruct, t
=1,2 ..., D, initial value set t=1, set indexed set U, and initial index integrates as empty set.
The sparse reconstruct obtains coherent azimuth, comprising:
Residual error r is calculated separately in the t times iterative processt-1In each signal guide vector sparse dictionary collection atom b (φp)
Projection value on (p=1,2 ..., P), the corresponding atom of record maximal projection coefficientBy its
Indexed set U is added；Original signal, the approximate solution s of original signal are reconstructed using indexed set Ut=U+rt-1=(UTU)-1UTrt-1, and
Updating residual error is
The beneficial effects of the present invention are:
(1) present invention solves the coherent signal Parameter Estimation Problem under impulsive noise environment based on uniform circular array, uses
The basis of mode excitation transformation and the sparse reconstruct thought of compressed sensing as parameter Estimation, designed method have calculating complicated
Spend low, the calculating advantage that the time is short and robustness is high.
(2) present invention can use and rush relative to the existing coherent signal method for parameter estimation based on uniform circular array
It hits pretreatment binding pattern excitation and converts the coherent signal source solved under impulsive noise environment with the sparse reconstruct thought of compressed sensing
Direction of arrival problem, and the coherent signal source direction of arrival that mentioned parameter Estimation scheme is equally applicable under Gaussian noise environment is estimated
Meter problem illustrates that designed method applicability is wider.
(3) proposed by the invention to utilize mode excitation transformation and compressed sensing sparse reconstruct thought progress coherent signal source
The method of Mutual coupling can obtain the estimated value of high accuracy in a relatively short period of time, illustrate mentioned robust parameter
Estimation method still be able under small snap hits, Low SNR it is quick, effectively carry out Mutual coupling.
Detailed description of the invention
Fig. 1 is the coherent signal method for parameter estimation schematic diagram under impulsive noise environment based on uniform circular array；
It is carried out using mode excitation transformation and the sparse reconstruct thought of compressed sensing based on equal when Fig. 2 is characteristic index α=1.5
The probability of success of the coherent signal Mutual coupling of nicely rounded battle array with signal-to-noise ratio figure of changing；
It is carried out using mode excitation transformation and the sparse reconstruct thought of compressed sensing based on equal when Fig. 3 is characteristic index α=0.8
The probability of success of the coherent signal Mutual coupling of nicely rounded battle array with signal-to-noise ratio figure of changing；
It is carried out using mode excitation transformation and the sparse reconstruct thought of compressed sensing based on equal when Fig. 4 is characteristic index α=1.5
The probability of success of the coherent signal Mutual coupling of nicely rounded battle array with snap hits figure of changing；
It is carried out using mode excitation transformation and the sparse reconstruct thought of compressed sensing based on equal when Fig. 5 is characteristic index α=0.8
The probability of success of the coherent signal Mutual coupling of nicely rounded battle array with snap hits figure of changing；
Specific embodiment
The present invention is described further with reference to the accompanying drawing.
Coherent signal method for parameter estimation based on uniform circular array under a kind of impulsive noise environment
The present invention relates to one kind by mode excitation and sparse Reconstruction Mechanism jointly come the considerations of realization in impact noise ring
The method for carrying out Robust Estimation to coherent signal direction of arrival based on uniform circular array under border, belongs to array signal processing parameter Estimation
Field.
Estimation of Spatial Spectrum is the key that the fields such as shortwave radio monitor, radio intelligence, radar target locating and tracking, smart antenna
Technology, accurate direction of arrival (DOA) estimation is for improving communication system performance important in inhibiting.Since structure is simple, divides
Analysis is convenient, and the spatial spectral estimation algorithm of early stage and application are all based on linear array proposition, but linear array can only provide deviation array
The orientation angular estimation of axis.Compared with linear array, circle battle array is capable of providing 360 ° omni-directional, without fuzzy orientation angular estimation, each
There is approximately uniform resolution ratio in orientation, azimuth and the estimation of pitch angle two dimension angular can be provided simultaneously, with more practical
Value.The particularity of uniform circular array array structure makes vandermonde structure of its array manifold without linear array, therefore many suitable
Excellent estimation scheme for linear array not can be used directly in circle battle array.Beam space transformation based on phase mode excitation is to be directed to
The array manifold of uniform circular array can be transformed to similar by a kind of effective scheme that uniform circular array proposes by beam space transformation
The form of generalized circular matrix.
Spatial diversity between smart antenna mobile subscriber realizes that message capacity doubles, in practical mobile environment
In, same mobile subscriber's signal passes through the multipath signal that various reflectors are formed, and is typically considered relevant.Common high score
It distinguishes signal estimation method, there is preferable resolution performance in independent source, but estimate that performance is bright under coherent environment
It is aobvious to be deteriorated or even entirely ineffective be unable to estimate.Due to the presence of coherent signal, traditional multiple signal classification (MUSIC) algorithm
The direction of arrival of signal all can not be correctly estimated with invariable rotary subspace (ESPRIT) algorithm.For even linear array, although having
Space smoothing class algorithm can handle coherent signal source, but these decorrelation LMS algorithms are but not directly applicable uniform circular array
In.Uniform circular array is converted to virtual uniform linear array, thus obtained virtual uniform linear array has translation as common linear array
Invariance so as to use space smoothing decoherence, but increases calculation amount while space smoothing.
What traditional high-resolution direction finding estimation scheme considered is white Gaussian noise signal model, and under actual conditions, back
There is the impact noise situation indicated with symmetric alpha-stable distribution process (S α S) in scape environment and nonideal white Gaussian noise.By
Second order and the above High Order Moment of second order is not present in impact noise, the Mutual coupling problem under impact noise can not directly transplanting
Target component estimation scheme under Gaussian noise, the sharply decline that otherwise will cause algorithm performance are even failed.It is existing to be based on
The MUSIC method of co-variation and Fractional Lower Order Moments, although the DOA estimation problem under the conditions of being able to solve impact noise, multidimensional
Search brings higher calculation amount, and performance decline is significant in the case where few number of snapshots.Based on uniform under impact noise
The coherent signal source DOA estimation problem of circle battle array, should establish the uniform circular array data receiver model under impulsive noise environment first,
Impact pretreating scheme is removed in design, is solved under the physical conditions such as few number of snapshots, low signal-to-noise ratio using new method for parameter estimation
Quick, accurate DOA estimation problem.
By the retrieval discovery to existing technical literature, high book man of virtue and ability it is equal " electronics and information journal " (2007, Vol.29,
No.12, pp.2832-2835) on mode sky is utilized in " the pattern space matrix reconstruction algorithm based on uniform circular array " delivered
Between matrix reconstruction algorithm, reconstruct Toeplitz matrix, successfully estimate the arrival bearing of coherent source, but carried on the back in impact noise
Under scape, method penalty seriously causes to fail.Han Xiaodong etc. is at " applicating technology " (2012, Vol.39, No.1, pp.35-39)
On in the DOA of uniform circular array coherent " under the impact noise background estimation " delivered based on mode space transform algorithm and sky
Between the thought of smoothing algorithm realize uniform circular array under impact noise background in conjunction with ROC-MUSIC algorithm and FLOM-MUSIC algorithm
The DOA of coherent estimates, but the required calculating time is longer, the penalty in the case where low signal-to-noise ratio lacks snap sampling condition, no
It can solve the DOA estimating speed and precision problem of coherent under impulsive noise environment.
Compressed sensing is theoretical as a kind of new Signal acquiring and processing, can make full use of the sparsity of signal, extensively
Applied to various fields such as signal processings.Compressive sensing theory extracts interested target information from a small amount of observation data, if
Counting observing matrix reduces required data dimension, and can accurately restore the parameter letter of original signal from less observation data
Breath.Therefore when this patent solves coherent signal source DOA estimation problem under the conditions of impact noise, impact pretreatment side is gone in design
Case carries out mode excitation to the output signal of uniform circular array, becomes the virtual array in model space, on this basis base
The sparsity possessed by signal estimates required parameter by the sparse reconstruct of orthogonal matching, has using a small amount of measured value
Solves to effect the target component estimation problem under adverse noise environment.Simulation result shows the base under this impulsive noise environment
It can guarantee the accuracy of estimation in the coherent signal method for parameter estimation of uniform circular array, it is possible to provide 360 ° of azimuth informations, point
It distinguishes that power is strong, reduces due to space smoothing bring calculation amount, advantage is aobvious especially under few snap hits, Low SNR
It writes.
It is nicely rounded the purpose of the present invention is to provide being based under a kind of validity and the higher impulsive noise environment of robustness
The coherent DOA estimation method of battle array.
The present invention is implemented as follows:
Step 1 carries out snap sampling to D, space source signal；
Antenna array is the circle battle array that the radius on x/y plane is r, is uniform-distribution with isotropic M array element on circumference,
The center of circle of circle array antenna is reference point；D far field narrow band signal is with azimuth { θ1,θ2,…,θDBe incident on uniform circular array, this
Azimuthal θd∈ [0,360 °] (d=1,2 ..., D) refers to origin to projection and x-axis of the line of information source on x/y plane inverse
Angle on hour hands, and information source is coplanar with array, i.e., the angle between the line and z-axis of regulation origin to information source is 90 °；Array
Receiving kth time snap sampled data is X (k)=A (θ) S (k)+N (k), X (k)=[x in formula1(k),x2(k),…,xM(k)]TFor
The reception data vector of array, A (θ)=[a (θ1) a(θ2) … a(θD)] it is signal guide vector matrix, wherein θ=(θ1,
θ2,…,θD) it is angle vector, θdIt is the arrival bearing of d-th of information source, d=1,2 ..., D, S (k)=[s1(k),s2(k),…,
sD(k)]TFor the reception signal phasor of receiving antenna reference point, N (k)=[n1(k),n2(k),…,nM(k)]TFor independent same distribution
Meet S α S distribution impact noise vector, the impact degree of noise is determined by characteristic index α；D-th of steering vector a (θd)
=[exp (jk0rcos(θd-γ0)),exp(jk0rcos(θd-γ1)),…,exp(jk0rcos(θd-γM-1))]T, d=1,
2 ..., D, in formula, k0Indicate wave number, k0=2 π/λ, λ are the wavelength of incoming signal, γm=2 π m/M, m=0,1,2 ..., M-1,
Indicate m-th of array element of array and the angle of x-axis；
Step 2 goes impact to pre-process snap sampled data；
As unit of single snap sampled data, the amplitude upper limit max of construction kth time snap sampled data | x1(k)|,|x2
(k)|,…,|xM(k) | }, max { } is to be maximized function in formula；With
It is normalized for standard to data are received, wherein the value of q is determined according to the characteristic index α that impact noise S α S is distributed；
Step 3 carries out mode excitation transformation to array output data；
In formula, T=J-1CvF/M, F=[w-l,w-l+1,…,wl]H, l=-h ..., 0 ..., h, in formula,
wl=[1, exp (j2 π l/M) ..., exp (j2 π l (M-1)/M)]H
J=diag { J-h(β),…,J-1(β),J0(β),J1(β),…,Jh(β) }, Cv=diag { j-h,…,j-1,j0,
j1,…,jh, in formula, 2 π r/ λ of h ≈ is the max model number of mode excitation, Jl(β), l=-h ..., 0 ..., h are l rank first
Class Bessel function；
Step 4 constructs sparse reconstruct wordbook；
Consider under K snap sampling condition, output signal data matrix isIt is fixed
The covariance matrix of adopted output signalTo covariance matrixEigenvalues Decomposition is carried out, wherein D
The corresponding characteristic vector of a big characteristic value is respectively v1,v2,…,vD, utilize ES=span { v1,v2,…vDConstruction signal subspace sky
Between ES；By information source range that may be present (0,360 °) equally spaced division, Φ=(φ1,φ2,…,φP), the wherein value of P
It is determined by dividing precision, P is far longer than far field narrow band signal number D, constructs signal guide vector sparse dictionary collection B (Φ)=[b
(φ1) b(φ2) … b(φP)], b (φp) it is sparse dictionary collection atom, p=1,2 ..., P, in formula, b (φp)=exp (jl
φp), l=-h ..., 0 ..., h；Signal subspace ESIt is defined as the initial residual error r of sparse reconstruct0, setting t is sparse reconstruct
The number of iterations, t=1,2 ..., D, initial value set t=1, set indexed set U, and initial index integrates as empty set；
Step 5, sparse reconstruct obtain coherent azimuth；
Residual error r is calculated separately in the t times iterative processt-1In each signal guide vector sparse dictionary collection atom b (φp)
Projection value on (p=1,2 ..., P), the corresponding atom of record maximal projection coefficientBy its
Indexed set U is added；Original signal, the approximate solution s of original signal are reconstructed using indexed set Ut=U+rt-1=(UTU)-1UTrt-1, and
Updating residual error is
Step 6 judges whether to reach maximum number of iterations, if so, executing step 7；Otherwise t=t+1, return step are enabled
Five；
Step 7 obtains sparse reconstruction result, obtains information source azimuth information using indexed set U, exports coherent wave
Up to direction estimation result.
(1) present invention solves the coherent signal Parameter Estimation Problem under impulsive noise environment based on uniform circular array, uses
The basis of mode excitation transformation and the sparse reconstruct thought of compressed sensing as parameter Estimation, designed method have calculating complicated
Spend low, the calculating advantage that the time is short and robustness is high.
(2) present invention can use and rush relative to the existing coherent signal method for parameter estimation based on uniform circular array
It hits pretreatment binding pattern excitation and converts the coherent signal source solved under impulsive noise environment with the sparse reconstruct thought of compressed sensing
Direction of arrival problem, and the coherent signal source direction of arrival that mentioned parameter Estimation scheme is equally applicable under Gaussian noise environment is estimated
Meter problem illustrates that designed method applicability is wider.
The experimental results showed that proposed by the invention is carried out using mode excitation transformation and the sparse reconstruct thought of compressed sensing
The method of coherent signal source Mutual coupling can obtain the estimated value of high accuracy in a relatively short period of time, illustrate institute
It proposes robust estimation method and still is able to quick, effective progress direction of arrival under small snap hits, Low SNR and estimate
Meter.
Fig. 1 is the coherent signal method for parameter estimation schematic diagram based on uniform circular array under impulsive noise environment.
It is carried out using mode excitation transformation and the sparse reconstruct thought of compressed sensing based on equal when Fig. 2 is characterized index α=1.5
The probability of success of the coherent signal Mutual coupling of nicely rounded battle array with signal-to-noise ratio situation of change.
It is carried out using mode excitation transformation and the sparse reconstruct thought of compressed sensing based on equal when Fig. 3 is characterized index α=0.8
The probability of success of the coherent signal Mutual coupling of nicely rounded battle array with signal-to-noise ratio situation of change.
It is carried out using mode excitation transformation and the sparse reconstruct thought of compressed sensing based on equal when Fig. 4 is characterized index α=1.5
The probability of success of the coherent signal Mutual coupling of nicely rounded battle array with snap hits situation of change.
It is carried out using mode excitation transformation and the sparse reconstruct thought of compressed sensing based on equal when Fig. 5 is characterized index α=0.8
The probability of success of the coherent signal Mutual coupling of nicely rounded battle array with snap hits situation of change.
The present invention is directed to the deficiency of coherent source method for estimating signal wave direction under existing impulsive noise environment, proposes one
Kind can realize Robust Estimation to signal direction of arrival based on uniform circular array under complicated noise and severe direction finding background
Method.This method initially sets up the data receiver model of uniform circular array under impulsive noise environment, and then design goes impact to pre-process
Method solves signal direction of arrival using mode excitation transformation and the sparse reconstruct thought of compressed sensing.In engineer application, work as punching
The characteristic index for hitting noise meets Gaussian noise distribution functional form when being 2, therefore method proposed by the invention is also able to solve
The signal Mutual coupling problem of Gaussian noise environment, and the method that is mentioned of the present invention can guarantee small snap hits,
The coherent source signal azimuth estimation of low computation complexity, the high probability of success under Low SNR.
The present invention is achieved by the following technical solution, and is mainly comprised the steps that
Step 1 carries out snap sampling to D, space source signal；
Antenna array is the circle battle array that the radius on x/y plane is r, is uniform-distribution with isotropic M array element on circumference,
The center of circle of circle array antenna is reference point；D far field narrow band signal is with azimuth { θ1,θ2,…,θDBe incident on uniform circular array, this
Azimuthal θd∈ [0,360 °] (d=1,2 ..., D) refers to origin to projection and x-axis of the line of information source on x/y plane inverse
Angle on hour hands, and information source is coplanar with array, i.e., the angle between the line and z-axis of regulation origin to information source is 90 °；Array
Receiving kth time snap sampled data is X (k)=A (θ) S (k)+N (k), X (k)=[x in formula1(k),x2(k),…,xM(k)]TFor
The reception data vector of array, A (θ)=[a (θ1) a(θ2) … a(θD)] it is signal guide vector matrix, wherein θ=(θ1,
θ2,…,θD) it is angle vector, θdIt is the arrival bearing of d-th of information source, d=1,2 ..., D, S (k)=[s1(k),s2(k),…,
sD(k)]TFor the reception signal phasor of receiving antenna reference point, N (k)=[n1(k),n2(k),…,nM(k)]TFor independent same distribution
Meet S α S distribution impact noise vector, the impact degree of noise is determined by characteristic index α；D-th of steering vector a (θd)
=[exp (jk0rcos(θd-γ0)),exp(jk0rcos(θd-γ1)),…,exp(jk0rcos(θd-γM-1))]T, d=1,
2 ..., D, in formula, k0Indicate wave number, k0=2 π/λ, λ are the wavelength of incoming signal, γm=2 π m/M, m=0,1,2 ..., M-1,
Indicate m-th of array element of array and the angle of x-axis；
Step 2 goes impact to pre-process snap sampled data；
As unit of single snap sampled data, the amplitude upper limit max of construction kth time snap sampled data | x1(k)|,|x2
(k)|,…,|xM(k) | }, max { } is to be maximized function in formula；With
It is normalized for standard to data are received, wherein the value of q is determined according to the characteristic index α that impact noise S α S is distributed；
Step 3 carries out mode excitation transformation to array output data；
In formula, T=J-1CvF/M, F=[w-l,w-l+1,…,wl]H, l=-h ..., 0 ..., h, in formula,
wl=[1, exp (j2 π l/M) ..., exp (j2 π l (M-1)/M)]H, J=diag { J-h(β),…,J-1(β),J0(β),J1
(β),…,Jh(β) }, Cv=diag { j-h,…,j-1,j0,j1,…,jh, in formula, 2 π r/ λ of h ≈ is the max model of mode excitation
Number, Jl(β), l=-h ..., 0 ..., h are l rank Bessel function of the first kind；
Step 4 constructs sparse reconstruct wordbook；
Consider under K snap sampling condition, output signal data matrix isIt is fixed
The covariance matrix of adopted output signalTo covariance matrixEigenvalues Decomposition is carried out, wherein D
The corresponding characteristic vector of a big characteristic value is respectively v1,v2,…,vD, utilize ES=span { v1,v2,…vDConstruction signal subspace sky
Between ES；By information source range that may be present (0,360 °) equally spaced division, Φ=(φ1,φ2,…,φP), the wherein value of P
It is determined by dividing precision, P is far longer than far field narrow band signal number D, constructs signal guide vector sparse dictionary collection B (Φ)=[b
(φ1) b(φ2) … b(φP)], b (φp) it is sparse dictionary collection atom, p=1,2 ..., P, in formula, b (φp)=exp (jl
φp), l=-h ..., 0 ..., h；Signal subspace ESIt is defined as the initial residual error r of sparse reconstruct0, setting t is sparse reconstruct
The number of iterations, t=1,2 ..., D, initial value set t=1, set indexed set U, and initial index integrates as empty set；
Step 5, sparse reconstruct obtain coherent azimuth；
Residual error r is calculated separately in the t times iterative processt-1In each signal guide vector sparse dictionary collection atom b (φp)
Projection value on (p=1,2 ..., P), the corresponding atom of record maximal projection coefficientBy its
Indexed set U is added；Original signal, the approximate solution s of original signal are reconstructed using indexed set Ut=U+rt-1=(UTU)-1UTrt-1, and
Updating residual error is
Step 6 judges whether to reach maximum number of iterations, if so, executing step 7；Otherwise t=t+1, return step are enabled
Five；
Step 7 obtains sparse reconstruction result, obtains information source azimuth information using indexed set U, exports coherent wave
Up to direction estimation result.
The present invention considers the estimation that the coherent source signal direction of arrival based on uniform circular array is completed under impulsive noise environment
Speed and estimated accuracy solve the shape after past impact pretreatment, mode excitation transformation using the sparse reconstruct thought of compressed sensing
At virtual line arrays included in aspect angle information.Designed method can also be in small snap hits, low noise
Parameter information is determined with lower computation complexity than under the conditions of, to make the coherent source signal wave based on uniform circular array of design
Arrival direction estimating method meets higher performance requirement.
The uniform circular array for the use of array number being 10 in experiment, array element radius are 1.5 λ/π, there is 2 relevant incoming signals,
Azimuth is 60 ° and 200 ° respectively, and ambient noise is the independent identically distributed impact noise vector for meeting S α S distribution, Monte Carlo
Experiment number is 100 times.During parameter Estimation scheme is implemented, broad sense signal-to-noise ratio expression formula is
γ indicates the coefficient of dispersion of impact noise in formula, and parameter q=1.7 in impact preprocessing process, max model number h warp are removed in γ=1
H=3 is calculated, 7 phase patterns can be excited, the region of search is [0 °, 360 °], P=361 in sparse restructuring procedure.
Under the conditions of snap hits is 1024, sense is converted and compressed using mode excitation under different impulsive noise environments
Know that sparse reconstruct thought solves the probability of success of coherent signal source signal direction of arrival with situation of change such as Fig. 2 and figure of signal-to-noise ratio
3.Under the conditions of broad sense signal-to-noise ratio GSNR=15dB, mode excitation transformation and compressed sensing are utilized under different impulsive noise environments
It is sparse reconstruct thought solve coherent signal source signal direction of arrival the probability of success with snap hits situation of change such as Fig. 4 and
Fig. 5.
As can be seen that institute Tilly is converted with mode excitation and the sparse reconstruct thought of compressed sensing solves phase from Fig. 2 and Fig. 3
The probability of success of dry signal source signal direction of arrival increases with the increase of signal-to-noise ratio.And in strong punching of the characteristic index less than 1
Hitting the method proposed under noise circumstance also can guarantee the coherent signal source signal wave based on uniform circular array up to side to a certain extent
To the probability of success of estimation scheme.Simulation results show utilizing mode excitation transformation and the sparse reconstruct think of of compressed sensing in patent
The scheme for wanting to carry out the coherent signal source signal Mutual coupling based on uniform circular array is suitable for complex environment noise, low noise
Than etc. direction findings environment.
As can be seen that institute Tilly is converted with mode excitation and the sparse reconstruct thought of compressed sensing solves phase from Fig. 4 and Fig. 5
The probability of success of dry signal source signal direction of arrival increases with the increase of hits.In the case where the sampling of small snap, mentioned
Scheme still is able to carry out the solution of the coherent signal source signal direction of arrival based on uniform circular array with the higher probability of success.Simulation result
It demonstrates in patent and carries out the coherent signal based on uniform circular array using mode excitation transformation and the sparse reconstruct thought of compressed sensing
The scheme of source signal Mutual coupling is suitable for the direction findings environment such as complex environment noise, the sampling of small snap.
Coherent signal method for parameter estimation under impulsive noise environment based on uniform circular array, comprehensive characteristics are: (1) handling
Array received data removes impact preprocess method under impulsive noise environment；(2) the array received data of uniform circular array are handled
Mode excitation transform method；(3) the weighting vector information in coherent signal source is solved using the sparse reconstruct thought of compressed sensing.It is rushing
Hit designed under noise circumstance go impact preprocess method, by set thresholding will influence have the fast of particular value because of impact noise
Sampled data normalization is clapped, the characteristic of impact noise has been fully considered, can be used to solve the signal parameter under impulsive noise environment
Estimation problem, the robustness also having had under thump noise circumstance and higher accuracy of estimation have practical application value.
For the mode excitation conversion process that the array received data of uniform circular array propose, the virtual array formed using mode space transform
The basis estimated as subsequent parameter is arranged, the design feature of array has been fully considered, can be used to provide 360 ° of azimuth informations, is protected
Demonstrate,prove the signal Mutual coupling scheme of high resolution, low computation complexity.Phase is solved using the sparse reconstruct thought of compressed sensing
The orientation angles information of dry signal source, successfully estimates coherent source arrival bearing at the characteristics of having fully considered sparse dictionary collection, can
To solve the Parameter Estimation Problem under complicated noise, low signal-to-noise ratio, small snap hits direction finding environment, has and calculate again
The advantage that miscellaneous degree is low, estimating speed is fast, estimation accuracy is high.
1. the coherent signal method for parameter estimation under a kind of impulsive noise environment based on uniform circular array, it is characterized in that, it presses
Implement according to following steps:
Step 1 carries out snap sampling to D, space source signal；
Antenna array is the circle battle array that the radius on x/y plane is r, is uniform-distribution with isotropic M array element on circumference,
The center of circle of circle array antenna is reference point；D far field narrow band signal is with azimuth { θ1,θ2,…,θDBe incident on uniform circular array, this
Azimuthal θd∈ [0,360 °] (d=1,2 ..., D) refers to origin to projection and x-axis of the line of information source on x/y plane inverse
Angle on hour hands, and information source is coplanar with array, i.e., the angle between the line and z-axis of regulation origin to information source is 90 °；Array
Receiving kth time snap sampled data is X (k)=A (θ) S (k)+N (k), X (k)=[x in formula1(k),x2(k),…,xM(k)]TFor
The reception data vector of array, A (θ)=[a (θ1) a(θ2) … a(θD)] it is signal guide vector matrix, wherein θ=(θ1,
θ2,…,θD) it is angle vector, θdIt is the arrival bearing of d-th of information source, d=1,2 ..., D, S (k)=[s1(k),s2(k),…,
sD(k)]TFor the reception signal phasor of receiving antenna reference point, N (k)=[n1(k),n2(k),…,nM(k)]TFor independent same distribution
Meet S α S distribution impact noise vector, the impact degree of noise is determined by characteristic index α；D-th of steering vector a (θd)
=[exp (jk0rcos(θd-γ0)),exp(jk0rcos(θd-γ1)),…,exp(jk0rcos(θd-γM-1))]T, d=1,
2 ..., D, in formula, k0Indicate wave number, k0=2 π/λ, λ are the wavelength of incoming signal, γm=2 π m/M, m=0,1,2 ..., M-1,
Indicate m-th of array element of array and the angle of x-axis；
Step 2 goes impact to pre-process snap sampled data；
As unit of single snap sampled data, the amplitude upper limit max of construction kth time snap sampled data | x1(k)|,|
x2(k)|,…,|xM(k) | }, max { } is to be maximized function in formula；With
It is normalized for standard to data are received, wherein the value of q is determined according to the characteristic index α that impact noise S α S is distributed；
Step 3 carries out mode excitation transformation to array output data；
In formula, T=J-1CvF/M, F=[w-l,w-l+1,…,wl]H, l=-h ..., 0 ..., h, in formula,
wl=[1, exp (j2 π l/M) ..., exp (j2 π l (M-1)/M)]H, J=diag { J-h(β),…,J-1(β),J0(β),J1
(β),…,Jh(β) }, Cv=diag { j-h,…,j-1,j0,j1,…,jh, in formula, 2 π r/ λ of h ≈ is the max model of mode excitation
Number, Jl(β), l=-h ..., 0 ..., h are l rank Bessel function of the first kind；
Step 4 constructs sparse reconstruct wordbook；
Consider under K snap sampling condition, output signal data matrix isIt is fixed
The covariance matrix of adopted output signalTo covariance matrixEigenvalues Decomposition is carried out, wherein D
The corresponding characteristic vector of a big characteristic value is respectively v1,v2,…,vD, utilize ES=span { v1,v2,…vDConstruction signal subspace sky
Between ES；By information source range that may be present (0,360 °) equally spaced division, Φ=(φ1,φ2,…,φP), the wherein value of P
It is determined by dividing precision, P is far longer than far field narrow band signal number D, constructs signal guide vector sparse dictionary collection B (Φ)=[b
(φ1) b(φ2) … b(φP)], b (φp) it is sparse dictionary collection atom, p=1,2 ..., P, in formula, b (φp)=exp (jl
φp), l=-h ..., 0 ..., h；Signal subspace ESIt is defined as the initial residual error r of sparse reconstruct0, setting t is sparse reconstruct
The number of iterations, t=1,2 ..., D, initial value set t=1, set indexed set U, and initial index integrates as empty set；
Step 5, sparse reconstruct obtain coherent azimuth；
Residual error r is calculated separately in the t times iterative processt-1In each signal guide vector sparse dictionary collection atom b (φp)
Projection value on (p=1,2 ..., P), the corresponding atom of record maximal projection coefficientBy its
Indexed set U is added；Original signal, the approximate solution s of original signal are reconstructed using indexed set Ut=U+rt-1=(UTU)-1UTrt-1, and
Updating residual error is
Step 6 judges whether to reach maximum number of iterations, if so, executing step 7；Otherwise t=t+1, return step are enabled
Five；
Step 7 obtains sparse reconstruction result, obtains information source azimuth information using indexed set U, exports coherent wave
Up to direction estimation result.
Claims (6)
1. the coherent signal method for parameter estimation under a kind of impulsive noise environment based on uniform circular array, which is characterized in that including with
Lower step:
(1) snap sampling is carried out to D source signal in space；
(2) impact is gone to pre-process snap sampled data；
(3) mode excitation transformation is carried out to array output data；
(4) sparse reconstruct wordbook is constructed；
(5) sparse reconstruct obtains coherent azimuth；
(6) judge whether to reach maximum number of iterations, if so, executing step 7；Otherwise t=t+1, return step five are enabled；
(7) sparse reconstruction result is obtained, obtains information source azimuth information using indexed set U, output coherent direction of arrival is estimated
Count result.
2. the coherent signal parameter Estimation side under a kind of impulsive noise environment according to claim 1 based on uniform circular array
Method, which is characterized in that described that snap sampling is carried out to D, space source signal, comprising:
Antenna array is the circle battle array that the radius on x/y plane is r, and isotropic M array element, circle battle array are uniform-distribution on circumference
The center of circle of antenna is reference point, and D far field narrow band signal is with azimuth { θ1,θ2,…,θDBe incident on uniform circular array, wherein side
Parallactic angle θd∈ [0,360 °] (d=1,2 ..., D) refers to origin to projection and x-axis of the line of information source on x/y plane counterclockwise
On angle, and information source is coplanar with array；
Array received kth time snap sampled data are as follows:
X (k)=A (θ) S (k)+N (k)
Wherein, X (k)=[x1(k),x2(k),…,xM(k)]TFor the reception data vector of array；
A (θ)=[a (θ1) a(θ2) … a(θD)] it is signal guide vector matrix, θ=(θ1,θ2,…,θD) it is angle vector, θd
It is the arrival bearing of d-th of information source, d=1,2 ..., D；S (k)=[s1(k),s2(k),…,sD(k)]TFor receiving antenna reference
The reception signal phasor of point；N (k)=[n1(k),n2(k),…,nM(k)]TFor the independent identically distributed impact for meeting S α S distribution
Noise vector is determined the impact degree of noise by characteristic index α；
D-th of steering vector:
a(θd)=[exp (jk0rcos(θd-γ0)),exp(jk0rcos(θd-γ1)),…,exp(jk0rcos(θd-γM-1))]T
Wherein, d=1,2 ..., D；k0Indicate wave number, k0=2 π/λ；λ is the wavelength of incoming signal；γm=2 π m/M, m=0,1,
2 ..., M-1 indicate m-th of array element of array and the angle of x-axis.
3. the coherent signal parameter Estimation side under a kind of impulsive noise environment according to claim 1 based on uniform circular array
Method, which is characterized in that described to go impact to pre-process snap sampled data, comprising:
As unit of single snap sampled data, the amplitude upper limit max of construction kth time snap sampled data | x1(k)|,|x2(k)
|,…,|xM(k) | }, withNormalizing is carried out to data are received for standard
Change processing, wherein the value of q is determined according to the characteristic index α that impact noise S α S is distributed.
4. the coherent signal parameter Estimation side under a kind of impulsive noise environment according to claim 1 based on uniform circular array
Method, which is characterized in that described that mode excitation transformation is carried out to array output data, comprising:
Wherein, T=J-1CvF/M, F=[w-l,w-l+1,…,wl]H, l=-h ..., 0 ..., h,
wl=[1, exp (j2 π l/M) ..., exp (j2 π l (M-1)/M)]H,
J=diag { J-h(β),…,J-1(β),J0(β),J1(β),…,Jh(β) },
Cv=diag { j-h,…,j-1,j0,j1,…,jh, 2 π r/ λ of h ≈ is the max model number of mode excitation, Jl(β), l=-
H ..., 0 ..., h are l rank Bessel function of the first kind.
5. the coherent signal parameter Estimation side under a kind of impulsive noise environment according to claim 1 based on uniform circular array
Method, which is characterized in that the sparse reconstruct wordbook of construction, comprising:
Under K snap sampling condition, output signal data matrix isDefine output signal
Covariance matrixTo covariance matrixEigenvalues Decomposition is carried out, wherein D big characteristic values
Corresponding characteristic vector is respectively v1,v2,…,vD, utilize ES=span { v1,v2,…vDConstruction signal subspace ES；By information source
The equally spaced division of range (0,360 °) that may be present, Φ=(φ1,φ2,…,φP), wherein the value of P is by dividing precision
It determines, P is greater than far field narrow band signal number D, constructs signal guide vector sparse dictionary collection B (Φ)=[b (φ1) b(φ2) … b
(φP)], b (φp) it is sparse dictionary collection atom, p=1,2 ..., P, b (φp)=exp (jl φp), l=-h ..., 0 ..., h；
Signal subspace ESIt is defined as the initial residual error r of sparse reconstruct0, the number of iterations of the setting t for sparse reconstruct, t=1,2 ..., D,
Initial value sets t=1, sets indexed set U, and initial index integrates as empty set.
6. the coherent signal parameter Estimation side under a kind of impulsive noise environment according to claim 1 based on uniform circular array
Method, which is characterized in that the sparse reconstruct obtains coherent azimuth, comprising:
Residual error r is calculated separately in the t times iterative processt-1In each signal guide vector sparse dictionary collection atom b (φp) (p=1,
2 ..., P) on projection value, the corresponding atom of record maximal projection coefficientIt is added into rope
Draw collection U；Original signal, the approximate solution s of original signal are reconstructed using indexed set Ut=U+rt-1=(UTU)-1UTrt-1, and update residual
Difference is
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