CN109669156A - Circle battle array model space dynamic direction-finding method under impact noise based on quantum emperor butterfly - Google Patents
Circle battle array model space dynamic direction-finding method under impact noise based on quantum emperor butterfly 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
- G01S3/46—Systems for determining direction or deviation from predetermined direction using antennas spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems
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Abstract
The present invention relates to the circle battle array model space dynamic direction-finding methods under a kind of impact noise based on quantum emperor butterfly, under impulsive noise environment, devise a kind of index core covariance matrix, utilize the index core covariance matrix maximum likelihood dynamic direction-finding method of circle battle array model space, dynamic direction finding is carried out to information source, and using the quantum emperor butterfly search mechanisms optimal angle that searchable index core covariance matrix maximum likelihood equations is estimated in the region of search, reduce calculation amount and then gradually reducing search space.Dynamic direction-finding method designed by the present invention, under the complex environments such as Gaussian noise, weak impact noise and thump noise can effective direction finding, in the case where low signal-to-noise ratio fewer snapshots and coherent have superior DOA estimate performance.
Description
Technical field
The present invention relates to a kind of circle battle array model space dynamic direction-finding method based on quantum emperor butterfly, belongs at array signal
Reason field.
Background technique
It is always array signal processing that direction finding, which is also referred to as direction of arrival angle (Direction of Arrival, DOA) estimation,
The Hot Contents in field, the extensive application in the systems such as communication, radar and sonar.Uniform circular array (Uniform
Circular Array, UCA) due to special array structure and good Measure direction performance, it is standby in many direction findings application
Favored.The array structure of uniform circular array makes its array prevalence more complicated, does not have the vandermonde matrix of even linear array
Form, many be suitable for the Direction Finding Algorithm of linear array can not graft application to circle battle array direction finding apply.
In order to make the excellent DOA algorithm for estimating applied to linear array can be applied to round battle array, and the operation of reduction DOA estimation
Amount, the estimation of mode space transform algorithm receive the extensive concern of scholar.Mode space transform is to pass through transformation for the battle array of circle battle array
Column prevalence is transformed into the form of similar linear array, realizes the Mutual coupling of input signal.
Existing technical literature retrieval discovery, high book man of virtue and ability it is equal " electronics and information journal " (2007, Vol.29, No.12,
Pp.2832-2835 one kind is proposed in " the pattern space matrix reconstruction algorithm based on uniform circular array ") delivered not by signal phase
The DOA estimation method that closing property influences, and reduce calculation amount to a certain extent.But this method has lost array aperture, estimates
It is not high to count precision, not dynamic direction finding, and direction finding is failed under impulsive noise environment.Zhao great Yong etc. is in " journal of Shandong university (work
Learn version) " in (2010, Vol.40, No.1, pp.133-138) " dynamic DOA tracking " under the impact noise background delivered to grain
Swarm optimization improves, and has studied the dynamic DOA estimation method based on maximum likelihood algorithm, and this method is avoiding fractional lower-order
While square matrix repetitive assignment, the calculation amount of multi-dimensional search is reduced to a certain extent.But this method is only capable of at 180 °
Carry out direction estimation in angular range, and the low order matrix impact and noise resistance ability used has to be hoisted, and this method is made
Particle swarm algorithm is easily trapped into " precocity " convergence, needs biggish population scale and the number of iterations, solving precision is not high.
Existing document shows that existing dynamic direction-finding method uses subspace tracking class method mostly, and such methods have
Calculation amount is small, the good advantage of real-time, but it estimates that performance is poor in the case where low signal-to-noise ratio, and does not have solution in itself
Relevant ability is needed to pre-process covariance matrix with the decorrelation LMSs technology such as space smoothing, complex steps, and is being rushed
It hits Measure direction performance under noise background to deteriorate seriously, or even failure.The present invention devises under a kind of impact noise based on quantum emperor
The circle battle array model space dynamic direction-finding method of butterfly devises a kind of index core covariance matrix under impulsive noise environment, utilizes
The index core covariance matrix maximum likelihood dynamic direction-finding method of circle battle array model space carries out dynamic direction finding to information source, and uses
Quantum emperor's butterfly search mechanisms optimal angle that searchable index core covariance matrix maximum likelihood equations is estimated in the region of search,
Reduce calculation amount and then gradually reducing search space.Dynamic direction-finding method designed by the present invention, in Gaussian noise, weak punching
Hit under the complex environments such as noise and thump noise can effective direction finding, in low signal-to-noise ratio, the feelings of fewer snapshots and coherent
Under condition there is superior DOA to estimate performance.
Summary of the invention
For the above-mentioned prior art, the technical problem to be solved in the present invention is to provide one kind in Gaussian noise, weak impulse noise
Under the complex environments such as sound and thump noise can effective direction finding, in the case where low signal-to-noise ratio fewer snapshots and coherent
Circle battle array model space dynamic direction-finding method based on quantum emperor butterfly under impact noise with superior DOA estimation performance.
In order to solve the above technical problems, the circle battle array model space based on quantum emperor butterfly is dynamic under a kind of impact noise of the present invention
State direction-finding method, comprising the following steps:
Step 1: obtaining the snapshot data of array received, defines transformation matrixBuilding array signal becomes through model space
Index core covariance matrix after changing constructs the maximum likelihood direction finding equation based on index core covariance matrix, specifically:
Assuming that n-th of narrowband far field information source is from azimuth angle thetan, pitch angleIt is incident on the radius being made of M array element
For on the uniform circular array of r, the mathematical model of n=1,2 ..., N, incident wavelength λ, the kth time snapshot data of array received areX (k)=[x1(k),x2(k),...,xM(k)]TArray received snapshot data arrow is tieed up for M × 1
Amount,For M × N-dimensional array manifold matrix, θ=[θ1,θ2,...,θN] andThe azimuth of respectively N number of information source and pitch angle vector,
It is n-th of steering vector of array manifold matrix, wherein n=1,2 ..., N；
J is imaginary unit；T indicates that transposition, s (k) are the signal phasor that N × 1 is tieed up, and n (k) is that the dimension of M × 1 obeys the mark that characteristic index is α
The impact noise vector of quasi- S α S distribution, whole information sources are coplanar with array, i.e. pitch angle
The max model that uniform circular array can excite For downward bracket function, the π r/ of β=2 λ；Definition transformation square
Battle arrayForJ=diag { j in formula-LJ-L(-β),...,jLJL(- β) }, wherein Jl() is the l rank first kind
Bessel function；Diag { Θ } indicates the diagonal matrix being made of the element in vector Θ, F=[w in formula-L,w-L+1,...,
wL], wherein l=-L ..., 0 ..., L；H table
Show conjugate transposition；WithPremultiplication x (k) is obtainedY (k)=[y1(k),y2(k),...,
y2L+1(k)]T, wherein array manifoldWith generalized circular matrix structure, then uniform circular array is converted to
Virtual uniform linear array；Index core covariance matrix of the 1st snap sampled data after mode space transform beThe i-th row d arranges an element in matrix
Wherein, i=1,2 ..., 2L+1；D=1,2 ..., 2L+1；η is index nuclear constant；* conjugation is indicated；Construction is assisted based on index core
The maximum likelihood direction finding equation of variance matrix isWherein PB(θ)=B (θ) [BH(θ)B(θ)-1]
BH(θ) is orthogonal intersection cast shadow matrix,For the index core covariance matrix of kth time snap sampling, argmax () indicates to find tool
There is the variable of maximal function value, trace representing matrix seeks mark；
Step 2: the region of search of initialization emperor butterfly, specifically:
In kth time snap, the region of search of N number of orientation angles is defined asIts
In, un(k) and gnIt (k) is respectively upper and lower bound that kth time snap n-th ties up the orientation angles region of search, the 1st snap search
The initial value in section takes the upper and lower bound of region of search domain respectively；N=1,2 ..., N；
Step 3: quantum position, interim quantum position and the position of every emperor butterfly, construction in initialization emperor butterfly population
Fitness function calculates the fitness of every emperor butterfly position, determines global optimum's quantum position of emperor butterfly population, really
The termination the number of iterations of quantitative sub- emperor butterfly search mechanisms, specifically:
The population scale of emperor butterfly isIt is initialized in quantum domain by random deviceThe quantum position of emperor butterfly
It is set to the quantum bit of interim quantum position, the t times iteration, the h emperor butterflyWherein, The interim quantum bit of the t times iteration, the h emperor butterfly is set toWherein,The t times iteration, the h emperor
The position of butterfly isIt is the mapping state of the t times iteration, the h sub- position of emperor's regulated stream flow, mapping mode isWherein,T is the number of iterations；It defines the t times
The quantum rotation angle of the h emperor butterfly of iteration isWherein,It is right
In the angle estimation of kth time snap, the termination the number of iterations of quantum emperor's butterfly search mechanisms takes kth time all dimension fields of search of snap
Between the upper limit and the difference integral multiple of lower limit maximum value, i.e.,Wherein,Round numbers；For to
Lower bracket function, the number of iterations is set as 1 when initial；
The t times iteration, the h emperor butterfly positionFitness function beRoot
The fitness function value that every emperor butterfly position is calculated according to fitness function, by emperor butterfly population to t on behalf of only searched
Rope to the maximum position of fitness value be recorded as global optimum position Corresponding global optimum's amount
Sub- position is
Step 4: emperor butterfly population is divided into two subgroups, using in two different policy update subgroups 1 and subgroup 2
The interim quantum position of emperor butterfly, specifically:
SelectionEmperor butterfly forms subgroup 1, whereinp1For constant, indicate in subgroup 1 shared by emperor butterfly
Ratio, it is remainingEmperor butterfly constitutes subgroup 2；
In subgroup 1, in the t times iteration, ifH1Emperor butterfly n-th ties up interim quantum position
Update mode isOtherwise, h1The update mode that emperor butterfly n-th ties up interim quantum position isIts
In,WithIt is equally distributed random number between [0,1]；p2For constant, the migration period is indicated； For emperor's butterfly label randomly selected in subgroup 1；For emperor's butterfly mark randomly selected in subgroup 2
Number；
In subgroup 2, ifH2The update mode that emperor butterfly n-th ties up interim quantum position isOtherwise, h2The update mode that emperor butterfly n-th ties up interim quantum position isWherein,For [0,
1] equally distributed random number between；p3For constant, mobility is indicated；
For emperor's butterfly label randomly selected in subgroup 2；For the n-th dimension of emperor's butterfly population global optimum's quantum position；
Step 5: two subgroups of recombination are a population, update the quantum position and position of every emperor butterfly, calculate every
The fitness value of new position, updates global optimum's quantum position and global optimum position where emperor butterfly, specifically:
Generate equally distributed random number between one [0,1]Ifp4Probability is adjusted for emperor butterfly, is made
The h emperor butterfly n-th, which is updated, with simulation Quantum rotating gate ties up quantum position:It is no
Then,Wherein,For the h the n-th Wei Liangzixuanzhuanjiao of emperor butterfly；Between [0,1]
The random number of even distribution；Obtaining the h dimension of emperor butterfly n-th position according to mapping relations is
According to fitness functionThe fitness of new position where calculating all emperor butterflies,
The global optimum position and global optimum's quantum position that emperor butterfly population is updated according to fitness function value, fromA quantum bit
It sets i.e.WithMiddle selectionAt the beginning of evolution of a outstanding quantum position as next iteration emperor butterfly
Beginning quantum position, and be denoted as
Step 6: judge whether to reach required maximum number of iterations: if not up to, the number of iterations is enabled to add 1, returning to step
Rapid four continue cycling through；Otherwise, emperor butterfly population global optimum position and global optimum's quantum position are exported and is entered in next step；
Step 7: the region of search of the N number of orientation angles of snap next time is updated, judges whether to reach maximum number of snapshots: if
Not up to, continue to obtain snap next time and sample the data after mode space transform, more new index core covariance matrix enables fast
Umber of beats adds 1, return step three；Otherwise, the estimated value that lower dynamic object is sampled according to obtained all snaps, exports dynamic direction finding
As a result, specifically:
In+1 snap of kth, N number of orientation angles region of search is updated to
Wherein The central value of the orientation angles region of search is tieed up for+1 snap of kth n-th, i.e., For gene, ω is the convergence factor that convergence rate is influenced in the region of search,The estimated value of orientation angles is tieed up for kth time snap n-th,For the search radius of the region of search, n=1,2 ..., N；
Judge whether to reach maximum number of snapshots: if not up to, continuing to obtain snap sampling next time through mode space transform
Data y (k+1)=[y afterwards1(k+1),y2(k+1),...,y2L+1(k+1)]T, and then the update side of index core covariance matrix
Cheng WeiWherein
The i-th row d arranges an element in matrixWherein i=1,
2,...,2L+1；D=1,2 ..., 2L+1；Number of snapshots are enabled to add 1, return step three；Otherwise, according to obtaining
All snaps sample the estimated value of lower dynamic object, export the result of dynamic direction finding.
The invention has the advantages that: compared with prior art the invention has the following advantages that
(1) uniform circular array is converted to virtual uniform line by mode space transform under impulsive noise environment by the present invention
Battle array, and angle estimation, institute are carried out to dynamic object using the maximum likelihood dynamic direction-finding method based on index core covariance matrix
Design method can carry out dynamic direction finding to independent source, coherent source and mixing source, and dynamic Measure direction performance is excellent, and can carry out impulse noise
The 360 ° omni-directional tracking of dynamic object under acoustic environment.
(2) the dynamic direction-finding method designed by the present invention, devises index core covariance matrix, in low signal-to-noise ratio, small fast
Under umber of beats, Gaussian noise, weak impact noise and thump noise situations can effectively dynamic direction finding, have wide range of applications.
(3) quantum emperor butterfly searching method is devised and then can index core covariance matrix maximum likelihood equations to array
High-precision solution is carried out, there is fast convergence rate, the high advantage of convergence precision.
Search speed of the present invention is fast, and tracking accuracy is high, can be under Gaussian noise, weak impact noise and thump noise dynamically
Direction finding has wide range of applications.
Detailed description of the invention
Fig. 1 is the circle battle array model space dynamic direction-finding method schematic diagram based on quantum emperor butterfly under impact noise；
It is 0.95 that Fig. 2, which is characterized index, the dynamic direction finding result of two independent sources when broad sense Signal to Noise Ratio (SNR)=15dB；
It is 1.8 that Fig. 3, which is characterized index, the dynamic direction finding result of three independent sources when broad sense Signal to Noise Ratio (SNR)=15dB；
It is 1.8 that Fig. 4, which is characterized index, the dynamic direction finding result of three coherents when broad sense Signal to Noise Ratio (SNR)=15dB；
It is 1.8 that Fig. 5, which is characterized index, the dynamic direction finding result of three compound informations when broad sense Signal to Noise Ratio (SNR)=15dB；
Fig. 6 is that i.e. characteristic index is 2 under Gaussian noise, the dynamic direction finding of three independent sources when Signal to Noise Ratio (SNR)=10dB
As a result.
Specific embodiment
The specific embodiment of the invention is described further with reference to the accompanying drawing.
As shown in Figure 1, technical solution of the present invention includes the following steps:
Step 1: obtaining the snapshot data of array received, defines transformation matrixBuilding array signal becomes through model space
Index core covariance matrix after changing constructs the maximum likelihood direction finding equation based on index core covariance matrix.
Assuming that n-th of narrowband far field information source is from azimuth angle thetan, pitch angleIt is incident on the radius being made of M array element
For on the uniform circular array of r, n=1,2 ..., N, incident wavelength λ, then the mathematical modulo of the kth time snapshot data of array received
Type isX (k)=[x1(k),x2(k),...,xM(k)]TArray received number of snapshots are tieed up for M × 1
According to vector,For M × N-dimensional array manifold matrix, θ=[θ1,
θ2,...,θN] andThe azimuth of respectively N number of information source and pitch angle vector,It is n-th of steering vector of array manifold matrix.Wherein, n=1,
2,...,N；J is imaginary unit；T indicates transposition.S (k) is N × 1
The signal phasor of dimension, n (k) are the impact noise vector that the dimension of M × 1 obeys the standard S α S distribution that characteristic index is α.It is discussed herein
Be all information sources situation all coplanar with array, i.e. pitch angle
The max model that uniform circular array can excite For downward bracket function；The π r/ of β=2 λ.Definition transformation square
Battle arrayForJ=diag { j in formula-LJ-L(-β),...,jLJL(- β) }, wherein Jl() is the l rank first kind
Bessel function；Diag { Θ } indicates the diagonal matrix being made of the element in vector Θ, F=[w in formula-L,w-L+1,...,
wL], wherein l=-L ..., 0 ..., L；H
Indicate conjugate transposition.WithPremultiplication x (k) can be obtainedY (k)=[y1(k),y2
(k),...,y2L+1(k)]T, wherein array manifoldWith Vandermonde matrix structure,
Uniform circular array has been converted into virtual uniform linear array at this time.1st index of the snap sampled data after mode space transform
Core covariance matrix isThe i-th row d arranges an element in matrixWherein, i=1,2 ..., 2L+1；D=1,2 ..., 2L+1；η is index nuclear constant；*
Indicate conjugation.Constructing the maximum likelihood direction finding equation based on index core covariance matrix isIts
Middle PB(θ)=B (θ) [BH(θ)B(θ)-1]BH(θ) is orthogonal intersection cast shadow matrix,For the index core covariance of kth time snap sampling
Matrix, argmax () indicate that searching has the variable of maximal function value, and trace representing matrix seeks mark.
Step 2: the region of search of initialization emperor butterfly.
In kth time snap, the region of search of N number of orientation angles is defined asIts
In, un(k) and gnIt (k) is respectively upper and lower bound that kth time snap n-th ties up the orientation angles region of search, the 1st snap search
The initial value in section takes the upper and lower bound of region of search domain respectively；N=1,2 ..., N.
Step 3: quantum position, interim quantum position and the position of every emperor butterfly, construction in initialization emperor butterfly population
Fitness function calculates the fitness of every emperor butterfly position, determines global optimum's quantum position of emperor butterfly population, really
The termination the number of iterations of quantitative sub- emperor butterfly search mechanisms.
The population scale of emperor butterfly isIt is initialized in quantum domain by random deviceThe quantum position of emperor butterfly
It is set to the quantum bit of interim quantum position, the t times iteration, the h emperor butterflyWherein, The interim quantum bit of the t times iteration, the h emperor butterfly is set toWherein,The t times iteration, the h emperor
The position of butterfly isIt is the mapping state of the t times iteration, the h sub- position of emperor's regulated stream flow, mapping mode isWherein,T is the number of iterations.It defines the t times
The quantum rotation angle of the h emperor butterfly of iteration isWherein,It is right
In the angle estimation of kth time snap, the termination the number of iterations of quantum emperor's butterfly search mechanisms takes kth time all dimension fields of search of snap
Between the upper limit and the difference integral multiple of lower limit maximum value, i.e.,Wherein,Round numbers；For to
Lower bracket function.The number of iterations is set as 1 when initial.
The t times iteration, the h emperor butterfly positionFitness function beRoot
The fitness function value that every emperor butterfly position is calculated according to fitness function, by emperor butterfly population to t on behalf of only searched
Rope to the maximum position of fitness value be recorded as global optimum position Corresponding global optimum's amount
Sub- position is
Step 4: emperor butterfly population is divided into two subgroups, using in two different policy update subgroups 1 and subgroup 2
The interim quantum position of emperor butterfly.
SelectionEmperor butterfly forms subgroup 1, whereinp1For constant, indicate in subgroup 1 shared by emperor butterfly
Ratio.It is remainingEmperor butterfly constitutes subgroup 2.
In subgroup 1, in the t times iteration, ifH1Emperor butterfly n-th ties up interim quantum position
Update mode isOtherwise, h1The update mode that emperor butterfly n-th ties up interim quantum position isIts
In,WithIt is equally distributed random number between [0,1]；p2For constant, the migration period is indicated； For emperor's butterfly label randomly selected in subgroup 1；For emperor's butterfly mark randomly selected in subgroup 2
Number.
In subgroup 2, ifH2The update mode that emperor butterfly n-th ties up interim quantum position isOtherwise, h2The update mode that emperor butterfly n-th ties up interim quantum position isWherein,For [0,
1] equally distributed random number between；p3For constant, mobility is indicated；
For emperor's butterfly label randomly selected in subgroup 2；For the n-th dimension of emperor's butterfly population global optimum's quantum position.
Step 5: two subgroups of recombination are a population, update the quantum position and position of every emperor butterfly, calculate every
The fitness value of new position, updates global optimum's quantum position and its corresponding global optimum position where emperor butterfly.
Generate equally distributed random number between one [0,1]Ifp4Probability is adjusted for emperor butterfly, is made
The h emperor butterfly n-th, which is updated, with simulation Quantum rotating gate ties up quantum position:It is no
Then,Wherein,For the h the n-th Wei Liangzixuanzhuanjiao of emperor butterfly；Between [0,1]
The random number of even distribution；Obtaining the h dimension of emperor butterfly n-th position according to mapping relations is
According to fitness functionThe fitness of new position where calculating all emperor butterflies,
The global optimum position and global optimum's quantum position of emperor butterfly population are updated according to fitness function value.FromA quantum bit
It sets i.e.WithMiddle selectionAt the beginning of evolution of a outstanding quantum position as next iteration emperor butterfly
Beginning quantum position, and be denoted as
Step 6: judge whether to reach required maximum number of iterations: if not up to, the number of iterations is enabled to add 1, returning to step
Rapid four continue cycling through；Otherwise, emperor butterfly population global optimum position and global optimum's quantum position are exported and is entered in next step.
Step 7: the region of search of the N number of orientation angles of snap next time is updated, judges whether to reach maximum number of snapshots: if
Not up to, continue to obtain snap next time and sample the data after mode space transform, more new index core covariance matrix enables fast
Umber of beats adds 1, return step three；Otherwise, the estimated value that lower dynamic object is sampled according to obtained all snaps, exports dynamic direction finding
As a result.
In+1 snap of kth, N number of orientation angles region of search is updated to
Wherein
The central value of the orientation angles region of search is tieed up for+1 snap of kth n-th, i.e., To lose
The factor is passed, ω is the convergence factor that convergence rate is influenced in the region of search,Estimating for orientation angles is tieed up for kth time snap n-th
Evaluation,For the search radius of the region of search, n=1,2 ..., N.
Judge whether to reach maximum number of snapshots: if not up to, continuing to obtain snap sampling next time through mode space transform
Data y (k+1)=[y afterwards1(k+1),y2(k+1),...,y2L+1(k+1)]T, and then the update side of index core covariance matrix
Cheng WeiWherein
The i-th row d arranges an element in matrixWherein i=1,
2,...,2L+1；D=1,2 ..., 2L+1；Number of snapshots are enabled to add 1, return step three；Otherwise, according to obtaining
All snaps sample the estimated value of lower dynamic object, export the result of dynamic direction finding.
In the case where characteristic index is 2 i.e. Gaussian noise, SNR represents signal-to-noise ratio, and SNR represents broad sense signal-to-noise ratio in the case of other.Punching
The parameter setting for hitting the circle battle array model space dynamic direction-finding method under noise based on quantum emperor butterfly is as follows:
In circle battle array model space direction-finding system, the array number M=16 of uniform circular array, array element spacingCircle battle array half
Diameter isMutual coupling parameter setting situation: maximum number of snapshots K=500, the initial ranging of each orientation angles
Section is [0 °, 360 °], convergence factor ω=0.995, search radiusHeredity, the factorUpdating factor μ=
0.95.The parameter setting situation of quantum emperor's butterfly search mechanisms: population scalep1=0.5, migrate period p2=1.2,
MobilityEmperor butterfly adjusts probability
In Fig. 2, two independent sources are from θ1(k)=[120+10sin (2 π k/500)] ° and θ2(k)=[- 120+10sin (2
π k/500)] a ° direction is incident on uniform circular array, and impact noise characteristic index is 0.95, and broad sense signal-to-noise ratio is 15dB.From analogous diagram 2
In as can be seen that under thump noise, designed method in most cases can effectively to dynamic arrival bearing into
Line trace.
In Fig. 3, three independent sources are from θ1(k)=[120+10sin (2 π k/500)] °, θ2(k)=[0+10sin (2 π k/
] ° and θ 500)3(k)=[- 120+10sin (2 π k/500)] uniform circular array is incident in a ° direction, and impact noise characteristic index is
1.8, broad sense signal-to-noise ratio is 15dB.As can be seen that designed method can effectively move independent source from analogous diagram 3
State tracking.
In Fig. 4, three coherents are from θ1(k)=[120+10sin (2 π k/500)] °, θ2(k)=[0+10sin (2 π k/
] ° and θ 500)3(k)=[- 120+10sin (2 π k/500)] uniform circular array is incident in a ° direction, and impact noise characteristic index is
1.8, broad sense signal-to-noise ratio is 15dB.As can be seen that designed method can effectively move coherent from analogous diagram 4
State tracking.
In Fig. 5, three compound informations are from θ1(k)=[120+10sin (2 π k/500)] °, θ2(k)=[0+10sin (2 π k/
] ° and θ 500)3(k)=[- 120+10sin (2 π k/500)] uniform circular array is incident in a ° direction, wherein θ1(k) and θ2(k) it is concerned with,
θ2(k) and θ3(k) independent, impact noise characteristic index is 1.8, and broad sense signal-to-noise ratio is 15dB.As can be seen that institute from analogous diagram 5
The method of design effectively can carry out dynamically track to compound information.
In Fig. 6, under Gaussian noise, three coherents are from θ1(k)=[120+10sin (2 π k/500)] °, θ2(k)=
[0+10sin (2 π k/500)] ° and θ3(k)=[- 120+10sin (2 π k/500)] uniform circular array is incident in a ° direction, and signal-to-noise ratio is
10dB.From in analogous diagram 6 as can be seen that designed method under low signal-to-noise ratio can effectively to dynamic arrival bearing carry out with
Track.
Claims (1)
1. the circle battle array model space dynamic direction-finding method under a kind of impact noise based on quantum emperor butterfly, which is characterized in that including
Following steps:
Step 1: obtaining the snapshot data of array received, defines transformation matrixArray signal is constructed after mode space transform
Index core covariance matrix, construct the maximum likelihood direction finding equation based on index core covariance matrix, specifically:
Assuming that n-th of narrowband far field information source is from azimuth angle thetan, pitch angleBeing incident on the radius that one is made of M array element is r's
On uniform circular array, the mathematical model of n=1,2 ..., N, incident wavelength λ, the kth time snapshot data of array received areX (k)=[x1(k),x2(k),...,xM(k)]TArray received snapshot data arrow is tieed up for M × 1
Amount,For M × N-dimensional array manifold matrix, θ=[θ1,θ2,...,θN] andThe azimuth of respectively N number of information source and pitch angle vector,
It is n-th of steering vector of array manifold matrix, wherein n=1,2 ..., N；M=1,2 ..., M-1；J is imaginary unit；T indicates that transposition, s (k) are the signal phasor that N × 1 is tieed up, and n (k) is that the dimension of M × 1 obeys feature
The impact noise vector that the standard S α S that index is α is distributed, whole information sources are coplanar with array, i.e. pitch angle
The max model that uniform circular array can excite For downward bracket function, the π r/ of β=2 λ；Define transformation matrix
ForJ=diag { j in formula-LJ-L(-β),...,jLJL(- β) }, wherein Jl() is l rank first kind shellfish plug
That function；Diag { Θ } indicates the diagonal matrix being made of the element in vector Θ, F=[w in formula-L,w-L+1,...,wL],
In, l=-L ..., 0 ..., L；M=1,2 ..., M-1；H is indicated altogether
Yoke transposition；WithPremultiplication x (k) is obtainedY (k)=[y1(k),y2(k),...,y2L+1
(k)]T, wherein array manifoldWith generalized circular matrix structure, then uniform circular array is converted to
Virtual uniform linear array；Index core covariance matrix of the 1st snap sampled data after mode space transform beThe i-th row d arranges an element in matrix
Wherein, i=1,2 ..., 2L+1；D=1,2 ..., 2L+1；η is index nuclear constant；* conjugation is indicated；Construction is assisted based on index core
The maximum likelihood direction finding equation of variance matrix isWherein PB(θ)=B (θ) [BH(θ)B(θ)-1]
BH(θ) is orthogonal intersection cast shadow matrix,For the index core covariance matrix of kth time snap sampling, argmax () indicates to find tool
There is the variable of maximal function value, trace representing matrix seeks mark；
Step 2: the region of search of initialization emperor butterfly, specifically:
In kth time snap, the region of search of N number of orientation angles is defined asWherein, un
(k) and gnIt (k) is respectively upper and lower bound that kth time snap n-th ties up the orientation angles region of search, the 1st snap region of search
Initial value take the upper and lower bound of region of search domain respectively；N=1,2 ..., N；
Step 3: quantum position, interim quantum position and the position of every emperor butterfly, construction adapt in initialization emperor butterfly population
Function is spent, the fitness of every emperor butterfly position is calculated, determines global optimum's quantum position of emperor butterfly population, determines amount
The termination the number of iterations of sub- emperor butterfly search mechanisms, specifically:
The population scale of emperor butterfly isIt is initialized in quantum domain by random deviceThe quantum position of emperor butterfly and face
When quantum position, the quantum bit of the t times iteration, the h emperor butterfly is set toWherein, N=1,2 ..., N；The interim quantum bit of the t times iteration, the h emperor butterfly is set to
Wherein,N=1,2 ..., N；The position of the t times iteration, the h emperor butterfly isIt is the mapping state of the t times iteration, the h sub- position of emperor's regulated stream flow, mapping mode isWherein,N=1,2 ..., N；T is the number of iterations；It defines the t times
The quantum rotation angle of the h emperor butterfly of iteration isWherein,N=1,2 ..., N；It is right
In the angle estimation of kth time snap, the termination the number of iterations of quantum emperor's butterfly search mechanisms takes kth time all dimension fields of search of snap
Between the upper limit and the difference integral multiple of lower limit maximum value, i.e.,Wherein,Round numbers；For to
Lower bracket function, the number of iterations is set as 1 when initial；
The t times iteration, the h emperor butterfly positionFitness function beAccording to adaptation
Degree function calculates the fitness function value of every emperor butterfly position, by emperor butterfly population to t on behalf of only being searched
The maximum position of fitness value is recorded as global optimum position Corresponding global optimum's quantum position
For
Step 4: being divided into two subgroups for emperor butterfly population, uses emperor in two different policy update subgroups 1 and subgroup 2
The interim quantum position of butterfly, specifically:
SelectionEmperor butterfly forms subgroup 1, whereinp1For constant, emperor's butterfly proportion in subgroup 1 is indicated,
It is remainingEmperor butterfly constitutes subgroup 2；
In subgroup 1, in the t times iteration, ifH1Emperor butterfly n-th ties up the update of interim quantum position
Mode isOtherwise, h1The update mode that emperor butterfly n-th ties up interim quantum position isWherein,WithIt is equally distributed random number between [0,1]；p2For constant, the migration period is indicated；N=1,
2,...,N；For emperor's butterfly label randomly selected in subgroup 1；For emperor's butterfly label randomly selected in subgroup 2；
In subgroup 2, ifH2The update mode that emperor butterfly n-th ties up interim quantum position isIt is no
Then, h2The update mode that emperor butterfly n-th ties up interim quantum position isWherein,Between [0,1] uniformly
The random number of distribution；p3For constant, mobility is indicated；N=1,2 ..., N；For in subgroup 2
Randomly selected emperor butterfly label；For the n-th dimension of emperor's butterfly population global optimum's quantum position；
Step 5: two subgroups of recombination are a population, update the quantum position and position of every emperor butterfly, calculate every emperor
The fitness value of new position, updates global optimum's quantum position and global optimum position where butterfly, specifically:
Generate equally distributed random number between one [0,1]Ifp4Probability is adjusted for emperor butterfly, uses mould
Quasi- Quantum rotating gate updates the h emperor butterfly n-th and ties up quantum position:It is no
Then,Wherein,For the h the n-th Wei Liangzixuanzhuanjiao of emperor butterfly；Between [0,1]
The random number of even distribution；N=1,2 ..., N；Obtaining the h dimension of emperor butterfly n-th position according to mapping relations is
According to fitness functionThe fitness of new position where calculating all emperor butterflies, according to
Fitness function value updates the global optimum position and global optimum's quantum position of emperor butterfly population, fromA quantum position isWithMiddle selectionEvolution primary quantity of a outstanding quantum position as next iteration emperor butterfly
Sub- position, and be denoted as
Step 6: judge whether to reach required maximum number of iterations: if not up to, enabling the number of iterations add 1, return step four
It continues cycling through；Otherwise, emperor butterfly population global optimum position and global optimum's quantum position are exported and is entered in next step；
Step 7: the region of search of the N number of orientation angles of snap next time is updated, judges whether to reach maximum number of snapshots: if not reaching
It arrives, continues to obtain snap next time and sample the data after mode space transform, more new index core covariance matrix enables number of snapshots
Add 1, return step three；Otherwise, the estimated value that lower dynamic object is sampled according to obtained all snaps, exports dynamic direction finding knot
Fruit, specifically:
In+1 snap of kth, N number of orientation angles region of search is updated toWherein For
+ 1 snap of kth n-th ties up the central value of the orientation angles region of search, i.e., For heredity
The factor, ω are the convergence factor that convergence rate is influenced in the region of search,The estimation of orientation angles is tieed up for kth time snap n-th
Value,For the search radius of the region of search, n=1,2 ..., N；
Judge whether to reach maximum number of snapshots: if not up to, continuing to obtain snap sampling next time after mode space transform
Data y (k+1)=[y1(k+1),y2(k+1),...,y2L+1(k+1)]T, and then the renewal equation of index core covariance matrix isWhereinMatrix
In the i-th row d arrange elementWherein i=1,2 ..., 2L+
1；D=1,2 ..., 2L+1；Number of snapshots are enabled to add 1, return step three；Otherwise, all fast according to what is obtained
The estimated value for sampling lower dynamic object is clapped, the result of dynamic direction finding is exported.
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