CN114019447A - Broadband direction finding method and system based on focus fraction low-order covariance under impact noise - Google Patents
Broadband direction finding method and system based on focus fraction low-order covariance under impact noise Download PDFInfo
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Abstract
The invention discloses a broadband direction finding method and a broadband direction finding system based on focusing score low-order covariance under impact noise, which comprises the steps of establishing a maximum likelihood broadband signal direction finding model based on focusing score low-order covariance under impact noise; calculating the fitness values of all positions of the squirrels, and initializing local and global optimal quantum positions and global worst quantum positions; e, allocating squirrel positions; updating squirrel quantum position and quantum rotation angle in 4 cases; calculating the fitness values of the new positions of all squirrels, and updating the local and global optimal quantum positions and the global worst quantum position; and mapping the global optimal quantum position of the squirrel group into a global optimal position according to a mapping rule to obtain an incoming wave angle of the broadband signal. The method solves the maximum likelihood broadband direction-finding equation based on the focus fraction low-order covariance by using a continuous quantum squirrel search mechanism, can effectively find the direction in an impact noise environment, and has the advantages of good coherence solving capability, high direction-finding precision and wide application range.
Description
Technical Field
The invention relates to the technical field of array signal processing, in particular to a broadband direction finding method and system based on focusing fraction low-order covariance under impact noise.
Background
Array signal processing has wide application in the fields of communication, radar, sonar and the like, and direction-of-arrival estimation is one of important research directions in the field of array signals. The broadband signal has the advantages of large amount of carried information, easy target signal detection, parameter estimation, characteristic extraction and the like, and the application of the broadband signals such as frequency hopping signals, spread spectrum signals, linear frequency modulation signals and the like in a communication system is more and more extensive. The theory and method of wideband signal direction finding is developed on the basis of narrowband signal direction finding. However, for broadband signals, due to different array flow patterns at different frequencies, signal subspaces corresponding to different frequencies are different, so that the original narrowband signal direction finding method cannot be directly applied to broadband signal direction finding. In addition, the application environment of broadband signal direction finding is more and more complex, so that it is necessary to design a new broadband signal direction finding method which has high solving precision and can be applied to the complex impulse noise environment.
According to the existing literature, the 'broadband DOA estimation method based on corrected subspace orthogonal test', published by the inventor on firepower and command control (2018, vol.43, No.5, pp: 82-86), weights the signal subspace and the noise subspace, and estimates the DOA of the covariance matrix by the corrected subspace orthogonal projection test method, but the method has low solving precision and cannot effectively measure the direction of the broadband signal in the impact noise environment. "Wideband DOA estimation based on coherent signal subspace method" published by Ahmad Z et al in COMPEL International Journal of calculations and Mathematics in electric (2018, Vol.37, No.3, pp: 1271-.
Disclosure of Invention
The invention aims to solve the technical problems that the existing broadband signal direction finding method is carried out under an assumed model of Gaussian noise, direction finding fails under complex environments such as impact noise and the like, the requirement of broadband signal direction finding in complex battlefield environments cannot be met, direction finding precision is not high, and the direction finding effect is poor when a coherent signal source is processed.
The invention solves the technical problems through the following technical means:
the broadband direction finding method based on the focus fraction low-order covariance under noise attack comprises the following steps:
step 1, establishing a maximum likelihood broadband signal direction finding model based on focusing fraction low-order covariance under impact noise;
step 2, initializing continuous quantum squirrel search mechanism parameters;
step 3, calculating the fitness values of all the positions of the squirrels, and initializing a local optimal quantum position, a global optimal quantum position and a global worst quantum position;
step 4, squirrel position distribution: according to the fitness value of the position of the squirrel, sequentially dividing the squirrel into a squirrel on a hazelnut tree, a squirrel on a pecan tree, a squirrel on an oak tree and a squirrel on a common tree;
and 5, updating the quantum positions of the squirrels on the hazelnut tree, the pecan tree, the oak tree and the common tree respectively by using four different modes:
5.1 the squirrel on the hazelnut tree is operated as follows:
the squirrel on the hazelnut tree moves to the direction of the global optimal position, and the ith iteration is performed for t times1The running step of squirrel is
Wherein h ismaxAnd hminA maximum running stride length and a minimum running stride length,
is [0,1 ]]A uniform random number in between, and,
iterating the ith time t +11The p-dimension quantum rotation angle of only squirrel is
Wherein
Is the ith1Local optimal quantum position searched by squirrel till the t-th iteration
The (d) th dimension of (a),
the global worst molecular position searched for by the t-th generation of the population of the mouse of the Pomacea
The (d) th dimension of (a),
the global optimal quantum position searched by the squirrel stopping population for the t generation
P-th dimension of (c)1To adjust the constant, c2Is [0,1 ]]A constant value of (a) to (b),
the mean value is 0, and the variance is 1, the ith number on the hazelnut tree1The p-dimension updating mode of only squirrel quantum position is
abs () is an absolute value operation;
5.2 the squirrel on the hickory tree is operated as follows:
the squirrel on the hickory tree moves to the hazelnut tree and the global optimal position, and the ith iteration is carried out for t +1 times2The p-dimension quantum rotation angle of only squirrel is
Wherein
And
is [0,1 ]]A uniform random number in between, c4Is [0,1 ]]A constant value of (a) to (b),
is the average value of the p-th dimension, beta, of the squirrel quantum position on the hazelnut treet＝c3(1-t)/tmax，c3Is [0,1 ]]A constant value of (a) to (b),
then the ith of the hickory nut2The p-dimension updating mode of only squirrel quantum position is
5.3 squirrels on oak were subjected to the following operations:
the squirrel on the oak moves to the pecan tree and the direction of the global optimal position, and the ith iteration is carried out for t +1 times3The p-dimension quantum rotation angle of only squirrel is
Wherein,
is [0,1 ]]A uniform random number in between, and,
A0is [0,1 ]]Constant of c between c5In order to adjust the constant, the constant is adjusted,
is [0,1 ]]The number of the machines is uniform among the machines,
the p-dimension average value of the squirrel quantum position on the hickory tree is the ith dimension of the oak tree3The p-dimension updating mode of only squirrel quantum position is
5.4 the squirrel on the general tree is subjected to the following operations:
the squirrel on the common tree moves towards the oak tree and the global optimal position, and the ith iteration is carried out for the t times4The Le' vy running step length of only squirrel is
The gamma is a constant and is a linear variable,
and
is [0,1 ]]A uniform random number in between, and,
is a constant; i th iteration at t +14The p-dimension quantum rotation angle of only squirrel is
Is [0,1 ]]A uniform random number in between, and,
is in oak treeThe p-th dimension of the quantum position of the randomly selected squirrel is the i-th dimension of the common tree4The p-dimension updating mode of only squirrel quantum position is
Step 6, calculating the fitness values of the new positions of all squirrels, and updating the local optimal quantum position, the global worst quantum position and the global optimal quantum position;
and 7, mapping the global optimal quantum position of the squirrel group into a global optimal position according to a mapping rule to obtain an incoming wave angle of the broadband signal.
The maximum likelihood broadband signal direction finding model based on the focusing score low-order covariance can effectively estimate the incoming wave direction of a broadband signal in an impact noise environment, has excellent coherent resolving capability, designs a continuous quantum squirrel search mechanism to be applied to broadband signal direction finding, designs four different squirrel quantum position evolution mechanisms, better avoids trapping in local optimization, effectively improves global optimization capability, and ensures the effectiveness and the reliability of broadband signal direction finding. The designed broadband signal direction finding method is wide in application range, and the problem that the existing broadband signal direction finding method is ineffective in complex noise environments such as impact noise and the like in practical engineering application can be effectively solved.
Further, the step 1 specifically comprises: and establishing a maximum likelihood broadband signal direction finding model based on the focusing fraction low-order covariance under the impact noise. Under the impact noise environment, P far-fields exist in the broadband signals respectively at the direction angle theta1,θ2,...,θPThe signal is incident to an antenna array which comprises M array elements in space, the distance between the array elements is d, and the bandwidth of an incident signal is B; with the first array element as the reference array element, the signal received by the mth array element can be expressed as
Wherein,
denotes the incident direction as thetapThe broadband signal of (a) is,
representing impulse noise on the m-th array element, am,pIndicating the signal strength present at the mth array element with different spatial losses from the pth source to the various sensors,
representing the time delay of the p source to the m array element;
will observe the time ToThe array receiving data in the array is divided into L subsections, and each subsection has a time TdI.e. by
The observation data are then subjected to a discrete Fourier transform of K points, provided that the subsegment T is completedCompared with the noise, L groups of mutually uncorrelated narrow-band frequency domain components can be obtained after the correlation time is longer, and then the data after the discrete Fourier transform are uncorrelated, so that the broadband model Z can be obtainedl(fk)＝Aθ(fk)Sl(fk)+Nl(fk)，l＝1,2,...,L，k＝1,2,...,K，θ＝[θ1,θ2,…,θP](ii) a In the formula Zl(fk)＝[Z1l(fk),Z2l(fk),…,ZMl(fk)]T，Sl(fk)＝[S1l(fk),S2l(fk),…,SPl(fk)]T，Nl(fk)＝[N1l(fk),N2l(fk),…,NMl(fk)]TAre respectively
At the l-th time subsection at a frequency fkDiscrete fourier transform of time.
Is a steering matrix of size M × P, which is full rank when P directions are different;
a steering vector called a matrix;
selecting a reference frequency point f0Calculating a reference frequency point f0Corresponding steering matrix is
Guide vector
Calculating the corresponding frequency point f of the array received datakFocus matrix T (f)k)＝V(fk)U(fk)HWherein H represents a conjugate transpose, U (f)k) And V (f)k) Are respectively Aθ(fk)Aθ(f0) Left and right singular vectors of (a);
calculating the corresponding frequency point f by using the received datakFractional low order covariance of time
R(fk) Element R in (1)ab(fk) Can be expressed as
Further, the step 2 specifically comprises: the squirrel population has the scale of
Maximum number of iterations tmaxThe search space dimension is P, and in the t iteration, the quantum position of the ith squirrel is P
The quantum rotation angle of the ith squirrel is
Wherein
vmaxAnd vminThe upper and lower boundaries of the squirrel quantum rotation angle
P is 1,2, …, P, t is the number of iterations, and initially t is 1.
Further, the step 3 specifically comprises: mapping the quantum position of the ith squirrel in the t iteration to a position
The specific mapping rule is
Wherein A isminAnd AmaxRespectively a lower bound and an upper bound of the angle search space; calculating the position of the ith squirrel in the t iteration
Fitness value of
Determining the local optimal quantum position searched by the ith squirrel till the tth iteration to be
And the global optimal quantum positions searched by all squirrels till the t iteration are
And global minimum quantum position
Further, the step 4 specifically includes: according to the fitness value of the position of the squirrel, the squirrels are divided into the squirrels on hazelnut trees, the squirrels on pecan trees, the squirrels on oak trees and the squirrels on common trees in sequence from big to small. Front with larger adaptability value
Only the squirrel is set as the squirrel on the hazelnut tree, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the hickory, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the mountain oak, and the fitness value is ranked as the second
To
Is/are as follows
Only the squirrel is set as the squirrel on the general tree, and
corresponding to the method, the invention also provides a broadband direction finding system based on the focus score low-order covariance under the condition of establishing impact noise, which is characterized by comprising the following steps:
the broadband signal direction-finding model establishing module is used for establishing a maximum likelihood broadband signal direction-finding model based on the focusing fraction low-order covariance under the impact noise;
the initialization module is used for initializing continuous quantum squirrel search mechanism parameters;
the fitness value calculation module is used for calculating the fitness values of the positions of all squirrels and initializing a local optimal quantum position, a global optimal quantum position and a global worst quantum position;
position assignment module for squirrel position assignment: according to the fitness value of the position of the squirrel, sequentially dividing the squirrel into a squirrel on a hazelnut tree, a squirrel on a pecan tree, a squirrel on an oak tree and a squirrel on a common tree;
the updating module is used for respectively updating the quantum positions of the squirrels on the hazelnut trees, the pecan trees, the oak trees and the common trees by using four different modes:
5.1 the squirrel on the hazelnut tree is operated as follows:
the squirrel on the hazelnut tree moves to the direction of the global optimal position, and the ith iteration is performed for t times1The running step of squirrel is
Wherein h ismaxAnd hminA maximum running stride length and a minimum running stride length,
is [0,1 ]]A uniform random number in between, and,
iterating the ith time t +11The p-dimension quantum rotation angle of only squirrel is
Wherein
Is the ith1Local optimal quantum position searched by squirrel till the t-th iteration
The (d) th dimension of (a),
the global worst molecular position searched for by the t-th generation of the population of the mouse of the Pomacea
The (d) th dimension of (a),
global searched for by the t-th generation of the stock squirrelOptimal quantum position
P-th dimension of (c)1To adjust the constant, c2Is [0,1 ]]A constant value of (a) to (b),
the mean value is 0, and the variance is 1, the ith number on the hazelnut tree1The p-dimension updating mode of only squirrel quantum position is
abs () is an absolute value operation;
5.2 the squirrel on the hickory tree is operated as follows:
the squirrel on the hickory tree moves to the hazelnut tree and the global optimal position, and the ith iteration is carried out for t +1 times2The p-dimension quantum rotation angle of only squirrel is
Wherein
And
is [0,1 ]]A uniform random number in between, c4Is [0,1 ]]A constant value of (a) to (b),
is the average value of the p-th dimension, beta, of the squirrel quantum position on the hazelnut treet＝c3(1-t)/tmax，c3Is [0,1 ]]A constant value of (a) to (b),
then the ith of the hickory nut2The p-dimension updating mode of only squirrel quantum position is
5.3 squirrels on oak were subjected to the following operations:
the squirrel on the oak moves to the pecan tree and the direction of the global optimal position, and the ith iteration is carried out for t +1 times3The p-dimension quantum rotation angle of only squirrel is
Wherein,
is [0,1 ]]A uniform random number in between, and,
A0is [0,1 ]]Constant of c between c5In order to adjust the constant, the constant is adjusted,
is [0,1 ]]The number of the machines is uniform among the machines,
the p-dimension average value of the squirrel quantum position on the hickory tree is the ith dimension of the oak tree3The p-dimension updating mode of only squirrel quantum position is
5.4 the squirrel on the general tree is subjected to the following operations:
the squirrel on the common tree moves towards the oak tree and the global optimal position, and the ith iteration is carried out for the t times4The Le' vy running step length of only squirrel is
The gamma is a constant and is a linear variable,
and
is [0,1 ]]A uniform random number in between, and,
is a constant; i th iteration at t +14The p-dimension quantum rotation angle of only squirrel is
Is [0,1 ]]A uniform random number in between, and,
the p-th dimension of the squirrel quantum position randomly selected on the oak tree is the ith dimension on the common tree4The p-dimension updating mode of only squirrel quantum position is
The new position fitness value calculation module is used for calculating the fitness values of new positions of all squirrels and updating the local optimal quantum position, the global worst quantum position and the global optimal quantum position;
and the mapping module is used for mapping the global optimal quantum position of the squirrel group into a global optimal position according to the mapping rule so as to obtain the incoming wave angle of the broadband signal.
Further, the broadband signal direction finding model establishing module specifically includes: and establishing a maximum likelihood broadband signal direction finding model based on the focusing fraction low-order covariance under the impact noise. Under the impact noise environment, P far-fields exist in the broadband signals respectively at the direction angle theta1,θ2,...,θPThe signal is incident to an antenna array which comprises M array elements in space, the distance between the array elements is d, and the bandwidth of an incident signal is B; with the first array element as the reference array element, the signal received by the mth array element can be expressed as
Wherein,
denotes the incident direction as thetapThe broadband signal of (a) is,
representing impulse noise on the m-th array element, am,pIndicating the signal strength present at the mth array element with different spatial losses from the pth source to the various sensors,
representing the time delay of the p source to the m array element;
will observe the time ToThe array receiving data in the array is divided into L subsections, and each subsection has a time TdI.e. by
The observation data are then subjected to a discrete Fourier transform of K points, provided that the subsegment T is completedCompared with the noise, L groups of mutually uncorrelated narrow-band frequency domain components can be obtained after the correlation time is longer, and then the data after the discrete Fourier transform are uncorrelated, so that the broadband model Z can be obtainedl(fk)＝Aθ(fk)Sl(fk)+Nl(fk)，l＝1,2,...,L，k＝1,2,...,K，θ＝[θ1,θ2,…,θP](ii) a In the formula Zl(fk)＝[Z1l(fk),Z2l(fk),…,ZMl(fk)]T，Sl(fk)＝[S1l(fk),S2l(fk),…,SPl(fk)]T，Nl(fk)＝[N1l(fk),N2l(fk),…,NMl(fk)]TAre respectively
At the l-th time subsection at a frequency fkDiscrete Fourier transform of time。
Is a steering matrix of size M × P, which is full rank when P directions are different;
a steering vector called a matrix;
selecting a reference frequency point f0Calculating a reference frequency point f0Corresponding steering matrix is
Guide vector
Calculating the corresponding frequency point f of the array received datakFocus matrix T (f)k)＝V(fk)U(fk)HWherein H represents a conjugate transpose, U (f)k) And V (f)k) Are respectively Aθ(fk)Aθ(f0) Left and right singular vectors of (a);
calculating the corresponding frequency point f by using the received datakFractional low order covariance of time
R(fk) Element R in (1)ab(fk) Can be expressed as
Further, the initialization module specifically includes: the squirrel population has the scale of
Maximum number of iterations tmaxThe search space dimension is P, and in the t iteration, the quantum position of the ith squirrel is P
The quantum rotation angle of the ith squirrel is
Wherein
vmaxAnd vminThe upper and lower boundaries of the squirrel quantum rotation angle
P is 1,2, …, P, t is the number of iterations, and initially t is 1.
Further, the fitness value calculating module specifically includes: mapping the quantum position of the ith squirrel in the t iteration to a position
The specific mapping rule is
Wherein A isminAnd AmaxRespectively a lower bound and an upper bound of the angle search space; calculating the position of the ith squirrel in the t iteration
Fitness value of
Determining the local optimal quantum position searched by the ith squirrel till the tth iteration to be
And the global optimal quantum positions searched by all squirrels till the t iteration are
And global minimum quantum position
Further, the position allocation module specifically includes: according to the fitness value of the position of the squirrel, the squirrels are divided into the squirrels on hazelnut trees, the squirrels on pecan trees, the squirrels on oak trees and the squirrels on common trees in sequence from big to small. Front with larger adaptability value
Only the squirrel is set as the squirrel on the hazelnut tree, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the hickory, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the mountain oak, and the fitness value is ranked as the second
To
Is/are as follows
Only the squirrel is set as the squirrel on the general tree, and
the invention has the advantages that: the method constructs a new focusing score low-order covariance under the impact noise, designs the maximum likelihood broadband signal direction finding method based on the focusing score low-order covariance, can effectively find the direction under the impact noise environment, and has good decoherence capability. A continuous quantum squirrel search mechanism is designed to solve a maximum likelihood broadband signal direction-finding equation based on the focus fraction low-order covariance, so that the solving precision is improved under the condition of reducing the calculated amount, and the broadband signal direction-finding result is more accurate. Four different squirrel quantum position evolution mechanisms are designed, so that the squirrel quantum position evolution mechanisms can be better prevented from falling into local optimization, the global optimization capability is effectively improved, and the effectiveness and the reliability of broadband signal direction finding are ensured. The designed broadband signal direction finding method is wide in application range, and the problem that the existing broadband signal direction finding method is ineffective in complex noise environments such as impact noise and the like in practical engineering application can be effectively solved. According to simulation results, the broadband signal direction finding method can effectively estimate the direction of arrival of the independent source and the coherent source under the impact noise.
Drawings
FIG. 1 is a flow diagram of a broadband direction finding method in an embodiment of the invention;
FIG. 2 is a diagram illustrating a result of broadband direction finding of two independent sources using the method of the present embodiment when an impact noise characteristic index is 1.5 according to the present embodiment;
FIG. 3 is a diagram illustrating a result of broadband direction finding of two coherent sources using the method of this embodiment when the impulse noise characteristic index is 1.5 according to an embodiment of the present invention
In fig. 2 and fig. 3, the maximum likelihood broadband signal direction finding method based on the focus score low-order covariance of the continuous quantum squirrel search mechanism designed by the invention is abbreviated as "CQSA-FFLOC-ML", and the maximum likelihood broadband direction finding method based on the particle swarm optimization is abbreviated as "PSO-ML".
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention particularly relates to a maximum likelihood broadband direction finding method based on focus fraction low-order covariance under an impact noise environment, a direction finding equation is solved through a continuous quantum squirrel mechanism, and the broadband signal direction finding method can effectively find directions of an independent source and a coherent source under the impact noise.
Fig. 1 introduces a block diagram of the broadband direction finding system of the present invention, and the detailed flow is as follows:
the method comprises the following steps: and establishing a maximum likelihood broadband signal direction finding model based on the focusing fraction low-order covariance under the impact noise. Under the impact noise environment, P far-field broadband signals are respectivelyAt an angle of orientation theta1,θ2,...,θPThe signal is incident on an antenna array which comprises M array elements in space, the spacing of the array elements is d, and the bandwidth of the incident signal is B. With the first array element as the reference array element, the signal received by the mth array element can be expressed as
M1, 2. Wherein,
denotes the incident direction as thetapThe broadband signal of (a) is,
representing impulse noise on the m-th array element, am,pIndicating the signal strength present at the mth array element with different spatial losses from the pth source to the various sensors,
representing the time delay for the p-th source to reach the m-th array element.
Will observe the time ToThe array receiving data in the array is divided into L subsections, and each subsection has a time TdI.e. by
The observation data are then subjected to a discrete Fourier transform of K points, provided that the subsegment T is completedCompared with the noise, L groups of mutually uncorrelated narrow-band frequency domain components can be obtained after the correlation time is longer, and then the data after the discrete Fourier transform are uncorrelated, so that the broadband model Z can be obtainedl(fk)＝Aθ(fk)Sl(fk)+Nl(fk)，l＝1,2,...,L，k＝1,2,...,K，θ＝[θ1,θ2,…,θP]. In the formula Zl(fk)＝[Z1l(fk),Z2l(fk),…,ZMl(fk)]T，Sl(fk)＝[S1l(fk),S2l(fk),…,SPl(fk)]T，Nl(fk)＝[N1l(fk),N2l(fk),…,NMl(fk)]TAre respectively
At the l-th time subsection at a frequency fkDiscrete fourier transform of time.
Is a steering matrix of size M × P, which is full rank when P directions are different;
referred to as the steering vector of the matrix.
Selecting a reference frequency point f0Calculating a reference frequency point f0Corresponding steering matrix is
Guide vector
Calculating the corresponding frequency point f of the array received datakFocus matrix T (f)k)＝V(fk)U(fk)HWherein H represents a conjugate transpose, U (f)k) And V (f)k) Are respectively Aθ(fk)Aθ(f0) Left and right singular vectors.
Calculating the corresponding frequency point f by using the received datakFractional low order covariance of time
R(fk) Element R in (1)ab(fk) Can be expressed as
Step two: initializing continuous quantum squirrel search mechanism parameters. The squirrel population has the scale of
Maximum number of iterations tmaxThe search space dimension is P, and in the t iteration, the quantum position of the ith squirrel is P
The quantum rotation angle of the ith squirrel is
Wherein
vmaxAnd vminThe upper and lower boundaries of the squirrel quantum rotation angle
P is 1,2, …, P, t is iteration number, initialLet t be 1 at the beginning.
Step three: and calculating the fitness value of the positions of all squirrels. Mapping the quantum position of the ith squirrel in the t iteration to a position
The specific mapping rule is
Wherein A isminAnd AmaxThe lower and upper bounds of the angle search space are respectively. Calculating the position of the ith squirrel in the t iteration
Fitness value of
Determining the local optimal quantum position searched by the ith squirrel till the tth iteration to be
And the global optimal quantum positions searched by all squirrels till the t iteration are
And global minimum quantum position
Step four: squirrel position assignment: according to the fitness value of the position of the squirrel, the squirrels are divided into the squirrels on hazelnut trees, the squirrels on pecan trees, the squirrels on oak trees and the squirrels on common trees in sequence from big to small. Front with larger adaptability value
The squirrel is set on hazelnut treeSquirrel, fitness value ranked as
To
Is/are as follows
Only the squirrel is set as the squirrel on the hickory, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the mountain oak, and the fitness value is ranked as the second
To
Is/are as follows
Only the squirrel is set as the squirrel on the general tree, and
step five: the quantum positions of squirrels on hazelnut trees, pecan trees, oak trees and common trees are updated in four different ways.
(1) The following operations were performed on squirrels on hazelnuts:
the squirrel on the hazelnut tree moves to the direction of the global optimal position, and the ith iteration is performed for t times1The running step of squirrel is
Wherein h ismaxAnd hminA maximum running stride length and a minimum running stride length,
is [0,1 ]]A uniform random number in between, and,
iterating the ith time t +11The p-dimension quantum rotation angle of only squirrel is
Wherein
Is the ith1Local optimal quantum position searched by squirrel till the t-th iteration
The (d) th dimension of (a),
the global worst molecular position searched for by the t-th generation of the population of the mouse of the Pomacea
The (d) th dimension of (a),
the global optimal quantum position searched by the squirrel stopping population for the t generation
P-th dimension of (c)1To adjust the constant, c2Is [0,1 ]]A constant value of (a) to (b),
the mean value is 0, and the variance is 1, the ith number on the hazelnut tree1The p-dimension updating mode of only squirrel quantum position is
abs () is an absolute value operation.
(2) The squirrel on the hickory tree was operated as follows:
the squirrel on the hickory tree moves to the hazelnut tree and the global optimal position, and the ith iteration is carried out for t +1 times2The p-dimension quantum rotation angle of only squirrel is
Wherein
And
is [0,1 ]]A uniform random number in between, c4Is [0,1 ]]A constant value of (a) to (b),
is the average value of the p-th dimension, beta, of the squirrel quantum position on the hazelnut treet＝c3(1-t)/tmax，c3Is [0,1 ]]A constant value of (a) to (b),
then the ith of the hickory nut2The p-dimension updating mode of only squirrel quantum position is
(3) Squirrels on oak were subjected to the following procedure:
the squirrel on the oak moves to the pecan tree and the direction of the global optimal position, and the ith iteration is carried out for t +1 times3The p-dimension quantum rotation angle of only squirrel is
Wherein,
is [0,1 ]]Uniform random betweenThe number of the first and second groups is,
A0is [0,1 ]]Constant of c between c5In order to adjust the constant, the constant is adjusted,
is [0,1 ]]The number of the machines is uniform among the machines,
the p-dimension average value of the squirrel quantum position on the hickory tree is the ith dimension of the oak tree3The p-dimension updating mode of only squirrel quantum position is
(4) The following operations were performed on squirrels on common trees:
the squirrel on the common tree moves towards the oak tree and the global optimal position, and the ith iteration is carried out for the t times4The Le' vy running step length of only squirrel is
The gamma is a constant and is a linear variable,
and
is [0,1 ]]A uniform random number in between, and,
is a constant. I th iteration at t +14The p-dimension quantum rotation angle of only squirrel is
Is [0,1 ]]A uniform random number in between, and,
the p-th dimension of the squirrel quantum position randomly selected on the oak tree is the ith dimension on the common tree4The p-dimension updating mode of only squirrel quantum position is
Step six: calculating the fitness value of the new positions of all squirrels, and updating the local optimal quantum position of the ith squirrel
Updating global optimal quantum positions of the entire squirrel population
And global minimum quantum position
If i squirrels iterate the quantum position for the t +1 th time
The adaptability is better than
The degree of adaptability of
Otherwise
Updating the local optimal quantum position with the maximum fitness value in the t +1 generation until the global optimal quantum position reaches the t +1 iteration
Using the quantum position with the minimum fitness value to update until the t +1 th iteration isGlobal minimum quantum position of stop
Step seven: judging whether the maximum iteration times is reached, if not, making t equal to t +1, and returning to the fourth step to continue; if the signal is obtained, mapping the global optimal quantum position of the squirrel group into the global optimal position according to the mapping rule, and obtaining the incoming wave angle of the broadband signal.
The specific parameters of the model are set as follows:
the broadband far-field signal has the lowest frequency of 80MHz and the highest frequency of 120MHz, the antenna array is a uniform linear array, the number of the antennas is 8, the number of fast beats is 2048, the number of the information sources is 2, the incident angles of the signals are 40 degrees and 10 degrees respectively, the incident signals adopt linear frequency modulation signals, and the fractional low-order covariance characteristic index p10.9, 40, 64 and 600 monte carlo experiments.
The parameters based on the continuous quantum squirrel search mechanism are set as follows: squirrel population size
Maximum number of iterations tmaxConstant c is adjusted to 1001＝2，c2＝0.01，c3＝0.5，c4＝0.5，c5＝2，A0＝9，Γ＝1.5，
vmax＝0.1，vmax＝-0.1，hmax＝2.7182，hmin＝1。
Parameter settings for Particle Swarm Optimization refer to "Particle Swarm Optimization" 2002 published by Kennedy J and Eberhart R at Icnn95-International Conference on Neural Networks.
Fig. 2 shows simulation comparison curves of root mean square errors of the impulse noise characteristic index of 1.5 and the maximum likelihood broadband signal direction finding method based on the particle swarm optimization according to the two independent sources, under different generalized signal-to-noise ratios, and it can be seen from fig. 2 that the direction finding performance of the broadband signal direction finding method provided by the invention is excellent.
Fig. 3 shows a simulation comparison curve of root mean square errors of the impulse noise characteristic index of 1.5, regarding two coherent sources, the designed wideband signal direction finding method of the present invention and the maximum likelihood wideband signal direction finding method based on the particle swarm optimization under different generalized signal-to-noise ratios, and it can be seen from fig. 3 that the designed wideband signal direction finding method of the present invention has excellent coherent resolving capability under the impulse noise.
The embodiment utilizes a continuous quantum squirrel search mechanism to carry out direction finding on the broadband signal under the background of impact noise, and overcomes the defects of direction finding failure, low direction finding precision and the like of the traditional broadband direction finding method under the background of impact noise. The method comprises the steps of establishing a maximum likelihood broadband signal direction finding model based on focusing fraction low-order covariance under impact noise; initializing continuous quantum squirrel search mechanism parameters; calculating the fitness values of all positions of the squirrels, and initializing a local optimal quantum position, a global worst quantum position and a global optimal quantum position; e, allocating squirrel positions; updating the quantum positions and quantum rotation angles of a squirrel on a hazelnut tree, a squirrel on a pecan tree, a squirrel on an oak tree and a squirrel on a common tree; calculating the fitness values of the new positions of all squirrels, and updating the local optimal quantum position, the global worst quantum position and the global optimal quantum position; judging whether the maximum times are reached; and mapping the global optimal quantum position of the squirrel group into a global optimal position according to a mapping rule to obtain an incoming wave angle of the broadband signal. The method solves the maximum likelihood broadband direction-finding equation based on the focus fraction low-order covariance by using a continuous quantum squirrel search mechanism, can effectively find the direction in an impact noise environment, and has the advantages of good coherence solving capability, high direction-finding precision and wide application range.
Based on the above method, this embodiment further discloses a broadband direction finding system based on a focus score low-order covariance under noise attack, which includes:
broadband signal direction findingAnd the model establishing module is used for establishing a maximum likelihood broadband signal direction finding model based on the focusing fraction low-order covariance under the impact noise. Under the impact noise environment, P far-fields exist in the broadband signals respectively at the direction angle theta1,θ2,...,θPThe signal is incident on an antenna array which comprises M array elements in space, the spacing of the array elements is d, and the bandwidth of the incident signal is B. With the first array element as the reference array element, the signal received by the mth array element can be expressed as
Wherein,
denotes the incident direction as thetapThe broadband signal of (a) is,
representing impulse noise on the m-th array element, am,pIndicating the signal strength present at the mth array element with different spatial losses from the pth source to the various sensors,
representing the time delay for the p-th source to reach the m-th array element.
Will observe the time ToThe array receiving data in the array is divided into L subsections, and each subsection has a time TdI.e. by
The observation data are then subjected to a discrete Fourier transform of K points, provided that the subsegment T is completedCompared with the noise, L groups of mutually uncorrelated narrow-band frequency domain components can be obtained after the correlation time is longer, and then the data after the discrete Fourier transform are uncorrelated, so that the broadband model Z can be obtainedl(fk)＝Aθ(fk)Sl(fk)+Nl(fk)，l＝1,2,...,L，k＝1,2,...,K，θ＝[θ1,θ2,…,θP]. In the formula Zl(fk)＝[Z1l(fk),Z2l(fk),…,ZMl(fk)]T，Sl(fk)＝[S1l(fk),S2l(fk),…,SPl(fk)]T，Nl(fk)＝[N1l(fk),N2l(fk),…,NMl(fk)]TAre respectively
At the l-th time subsection at a frequency fkDiscrete fourier transform of time.
Is a steering matrix of size M × P, which is full rank when P directions are different;
referred to as the steering vector of the matrix.
Selecting a reference frequency point f0Calculating a reference frequency point f0Corresponding steering matrix is
Guide vector
Calculating the corresponding frequency point f of the array received datakFocus matrix T (f)k)＝V(fk)U(fk)HWherein H represents a conjugate transpose, U (f)k) And V (f)k) Are respectively Aθ(fk)Aθ(f0) Left and right singular vectors.
Calculating the corresponding frequency point f by using the received datakFractional low order covariance of time
R(fk) Element R in (1)ab(fk) Can be expressed as
And the initialization module initializes the continuous quantum squirrel search mechanism parameters. The squirrel population has the scale of
Maximum number of iterations tmaxThe search space dimension is P, and in the t iteration, the quantum position of the ith squirrel is P
The quantum rotation angle of the ith squirrel is
Wherein
vmaxAnd vminThe upper and lower boundaries of the squirrel quantum rotation angle
P is 1,2, …, P, t is the number of iterations, and initially t is 1.
And the fitness value calculating module is used for calculating the fitness values of the positions of all squirrels. Mapping the quantum position of the ith squirrel in the t iteration to a position
The specific mapping rule is
Wherein A isminAnd AmaxThe lower and upper bounds of the angle search space are respectively. Calculating the position of the ith squirrel in the t iteration
Fitness value of
Determining the local optimal quantum position searched by the ith squirrel till the tth iteration to be
And the global optimal quantum positions searched by all squirrels till the t iteration are
And global minimum quantum position
Position assignment module for squirrel position assignment: according to the fitness value of the position of the squirrel, sequentially dividing the squirrel into a squirrel on a hazelnut tree, a squirrel on a pecan tree, a squirrel on an oak tree and a common squirrelSquirrel on the tree. Front with larger adaptability value
Only the squirrel is set as the squirrel on the hazelnut tree, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the hickory, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the mountain oak, and the fitness value is ranked as the second
To
Is/are as follows
Only the squirrel is set as the squirrel on the general tree, and
and the updating module is used for respectively updating the quantum positions of the squirrels on the hazelnut tree, the pecan tree, the oak tree and the common tree in four different modes.
(1) The following operations were performed on squirrels on hazelnuts:
the squirrel on the hazelnut tree moves to the direction of the global optimal position, and the ith iteration is performed for t times1The running step of squirrel is
Wherein h ismaxAnd hminA maximum running stride length and a minimum running stride length,
a uniform random number in between, and,
iterating the ith time t +11The p-dimension quantum rotation angle of only squirrel is
Wherein
Is the ith1Local optimal quantum position searched by squirrel till the t-th iteration
The (d) th dimension of (a),
the global worst molecular position searched for by the t-th generation of the population of the mouse of the Pomacea
The (d) th dimension of (a),
the global optimal quantum position searched by the squirrel stopping population for the t generation
P-th dimension of (c)1To adjust the constant, c2Is [0,1 ]]A constant value of (a) to (b),
the mean value is 0, and the variance is 1, the ith number on the hazelnut tree1The p-dimension updating mode of only squirrel quantum position is
abs () is an absolute value operation.
(2) The squirrel on the hickory tree was operated as follows:
the squirrel on the hickory tree moves to the hazelnut tree and the global optimal position, and the ith iteration is carried out for t +1 times2The p-dimension quantum rotation angle of only squirrel is
Wherein
And
is [0,1 ]]A uniform random number in between, c4Is [0,1 ]]A constant value of (a) to (b),
is the average value of the p-th dimension, beta, of the squirrel quantum position on the hazelnut treet＝c3(1-t)/tmax，c3Is [0,1 ]]A constant value of (a) to (b),
then the ith of the hickory nut2The p-dimension updating mode of only squirrel quantum position is
(3) Squirrels on oak were subjected to the following procedure:
the squirrel on the oak moves to the pecan tree and the direction of the global optimal position, and the ith iteration is carried out for t +1 times3The p-dimension quantum rotation angle of only squirrel is
Wherein,
is [0,1 ]]A uniform random number in between, and,
A0is [0,1 ]]Constant of c between c5In order to adjust the constant, the constant is adjusted,
is [0,1 ]]The number of the machines is uniform among the machines,
the p-dimension average value of the squirrel quantum position on the hickory tree is the ith dimension of the oak tree3The p-dimension updating mode of only squirrel quantum position is
(4) The following operations were performed on squirrels on common trees:
the squirrel on the common tree moves towards the oak tree and the global optimal position, and the ith iteration is carried out for the t times4The Le' vy running step length of only squirrel is
The gamma is a constant and is a linear variable,
and
is [0,1 ]]A uniform random number in between, and,
is a constant. I th iteration at t +14The p-dimension quantum rotation angle of only squirrel is
Is [0,1 ]]A uniform random number in between, and,
the p-th dimension of the squirrel quantum position randomly selected on the oak tree is the ith dimension on the common tree4The p-dimension updating mode of only squirrel quantum position is
A new position fitness value calculating module for calculating the fitness values of the new positions of all squirrels and updating the local optimal quantum position of the ith squirrel
Updating global optimal quantum positions of the entire squirrel population
And global minimum quantum position
If i squirrels iterate the quantum position for the t +1 th time
The adaptability is better than
The degree of adaptability of
Otherwise
Global updating is carried out until the t +1 th iteration by using the local optimal quantum position with the maximum fitness value in the t +1 th generationOptimal quantum position
Using the quantum position with the minimum fitness value to update the global minimum quantum position until the t +1 th iteration
The mapping module is used for judging whether the maximum iteration times is reached, if not, making t equal to t +1, and returning to the step four to continue; if the signal is obtained, mapping the global optimal quantum position of the squirrel group into the global optimal position according to the mapping rule, and obtaining the incoming wave angle of the broadband signal.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. The broadband direction finding method based on the focus fraction low-order covariance under noise attack is characterized by comprising the following steps of:
step 1, establishing a maximum likelihood broadband signal direction finding model based on focusing fraction low-order covariance under impact noise;
step 2, initializing continuous quantum squirrel search mechanism parameters;
step 3, calculating the fitness values of all the positions of the squirrels, and initializing a local optimal quantum position, a global optimal quantum position and a global worst quantum position;
step 4, squirrel position distribution: according to the fitness value of the position of the squirrel, sequentially dividing the squirrel into a squirrel on a hazelnut tree, a squirrel on a pecan tree, a squirrel on an oak tree and a squirrel on a common tree;
and 5, updating the quantum positions of the squirrels on the hazelnut tree, the pecan tree, the oak tree and the common tree respectively by using four different modes:
5.1 the squirrel on the hazelnut tree is operated as follows:
the squirrel on the hazelnut tree moves to the direction of the global optimal position, and the ith iteration is performed for t times1The running step of squirrel is
Wherein h ismaxAnd hminA maximum running stride length and a minimum running stride length,
is [0,1 ]]A uniform random number in between, and,
iterating the ith time t +11The p-dimension quantum rotation angle of only squirrel is
Wherein
Is the ith1Local optimal quantum position searched by squirrel till the t-th iteration
The (d) th dimension of (a),
the global worst molecular position searched for by the t-th generation of the population of the mouse of the Pomacea
The (d) th dimension of (a),
the global optimal quantum position searched by the squirrel stopping population for the t generation
P-th dimension of (c)1To adjust the constant, c2Is [0,1 ]]A constant value of (a) to (b),
the mean value is 0, and the variance is 1, the ith number on the hazelnut tree1The p-dimension updating mode of only squirrel quantum position is
abs () is an absolute value operation;
5.2 the squirrel on the hickory tree is operated as follows:
the squirrel on the hickory tree moves to the hazelnut tree and the global optimal position, and the ith iteration is carried out for t +1 times2The p-dimension quantum rotation angle of only squirrel is
Wherein
And
is [0,1 ]]A uniform random number in between, c4Is [0,1 ]]A constant value of (a) to (b),
is the average value of the p-th dimension, beta, of the squirrel quantum position on the hazelnut treet＝c3(1-t)/tmax，c3Is [0,1 ]]A constant value of (a) to (b),
then the ith of the hickory nut2Pth dimension updating method of squirrel quantum position onlyIs of the formula
5.3 squirrels on oak were subjected to the following operations:
the squirrel on the oak moves to the pecan tree and the direction of the global optimal position, and the ith iteration is carried out for t +1 times3The p-dimension quantum rotation angle of only squirrel is
Wherein,
is [0,1 ]]A uniform random number in between, and,
A0is [0,1 ]]Constant of c between c5In order to adjust the constant, the constant is adjusted,
is [0,1 ]]The number of the machines is uniform among the machines,
the p-dimension average value of the squirrel quantum position on the hickory tree is the ith dimension of the oak tree3The p-dimension updating mode of only squirrel quantum position is
5.4 the squirrel on the general tree is subjected to the following operations:
the squirrel on the common tree moves towards the oak tree and the global optimal position, and the ith iteration is carried out for the t times4The Le' vy running step length of only squirrel is
The gamma is a constant and is a linear variable,
and
is [0,1 ]]A uniform random number in between, and,
is a constant; i th iteration at t +14The p-dimension quantum rotation angle of only squirrel is
Is [0,1 ]]A uniform random number in between, and,
the p-th dimension of the squirrel quantum position randomly selected on the oak tree is the ith dimension on the common tree4The p-dimension updating mode of only squirrel quantum position is
Step 6, calculating the fitness values of the new positions of all squirrels, and updating the local optimal quantum position, the global worst quantum position and the global optimal quantum position;
and 7, mapping the global optimal quantum position of the squirrel group into a global optimal position according to a mapping rule to obtain an incoming wave angle of the broadband signal.
2. The broadband direction finding method based on focus score low-order covariance under impact noise according to claim 1, wherein the step 1 specifically comprises: and establishing a maximum likelihood broadband signal direction finding model based on the focusing fraction low-order covariance under the impact noise. At the moment of impactUnder the noise environment, P far-fields exist in the broadband signals respectively at the direction angle theta1,θ2,...,θPThe signal is incident to an antenna array which comprises M array elements in space, the distance between the array elements is d, and the bandwidth of an incident signal is B; with the first array element as the reference array element, the signal received by the mth array element can be expressed as
Wherein,
denotes the incident direction as thetapThe broadband signal of (a) is,
representing impulse noise on the m-th array element, am,pIndicating the signal strength present at the mth array element with different spatial losses from the pth source to the various sensors,
representing the time delay of the p source to the m array element;
will observe the time ToThe array receiving data in the array is divided into L subsections, and each subsection has a time TdI.e. by
The observation data are then subjected to a discrete Fourier transform of K points, provided that the subsegment T is completedCompared with the noise, L groups of mutually uncorrelated narrow-band frequency domain components can be obtained after the correlation time is longer, and then the data after the discrete Fourier transform are uncorrelated, so that the broadband model Z can be obtainedl(fk)＝Aθ(fk)Sl(fk)+Nl(fk)，l＝1,2,...,L，k＝1,2,...,K，θ＝[θ1,θ2,…,θP](ii) a In the formula Zl(fk)＝[Z1l(fk),Z2l(fk),…,ZMl(fk)]T，Sl(fk)＝[S1l(fk),S2l(fk),…,SPl(fk)]T，Nl(fk)＝[N1l(fk),N2l(fk),…,NMl(fk)]TAre respectively
At the l-th time subsection at a frequency fkDiscrete fourier transform of time.
Is a steering matrix of size M × P, which is full rank when P directions are different;
a steering vector called a matrix;
selecting a reference frequency point f0Calculating a reference frequency point f0Corresponding steering matrix is
Guide vector
Calculating the corresponding frequency point f of the array received datakFocus matrix T (f)k)＝V(fk)U(fk)HWherein H represents a conjugate transpose, U (f)k) And V (f)k) Are respectively Aθ(fk)Aθ(f0) Left and right singular vectors of (a);
calculating the corresponding frequency point f by using the received datakFractional low order covariance of time
R(fk) Element R in (1)ab(fk) Can be expressed as
Wherein, a is 1,2, a, M, b is 1,2, a, M, p1Is a fractional low-order covariance feature index, 0 < p11 ≦ E () representing the mathematical expectation; determining each frequency point fkThe corresponding received data focus score low order covariance is Rc(fk)＝T(fk)R(fk)T(fk)HFinally, the reference frequency point f is obtained0Corresponding received data focus score low order covariance of
Combining a maximum likelihood direction finding method to design a maximum likelihood direction finding equation based on focusing fraction low order covariance to obtain an angle estimation value of
Wherein
Is a reference frequency point f0And tr () represents the trace-finding operation of the matrix.
3. The broadband direction finding method based on focus score low-order covariance under impact noise according to claim 2, wherein the step 2 is specifically: the squirrel population has the scale of
Maximum number of iterations tmaxThe search space dimension is P, and in the t iteration, the quantum position of the ith squirrel is P
The quantum rotation angle of the ith squirrel is
Wherein
vmaxAnd vminThe upper and lower boundaries of the squirrel quantum rotation angle
P is 1,2, …, P, t is the number of iterations, and initially t is 1.
4. The broadband direction finding method based on focus score low-order covariance under impact noise according to claim 3, wherein the step 3 is specifically: mapping the quantum position of the ith squirrel in the t iteration to a position
The specific mapping rule is
Wherein A isminAnd AmaxRespectively a lower bound and an upper bound of the angle search space; calculating the position of the ith squirrel in the t iteration
Fitness value of
Determining the local optimal quantum position searched by the ith squirrel till the tth iteration to be
And the global optimal quantum positions searched by all squirrels till the t iteration are
And global minimum quantum position
p＝1,2,…,P。
5. The broadband direction finding method based on focus score low-order covariance under impact noise according to claim 4, wherein the step 4 is specifically: according to the fitness value of the position of the squirrel, the squirrels are divided into the squirrels on hazelnut trees, the squirrels on pecan trees, the squirrels on oak trees and the squirrels on common trees in sequence from big to small. Front with larger adaptability value
Only the squirrel is set as the squirrel on the hazelnut tree, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the hickory, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the mountain oak, and the fitness value is ranked as the second
To
Is/are as follows
Only the squirrel is set as the squirrel on the general tree, and
6. a broadband direction finding system based on focus score low order covariance under noise attack, comprising:
the broadband signal direction-finding model establishing module is used for establishing a maximum likelihood broadband signal direction-finding model based on the focusing fraction low-order covariance under the impact noise;
the initialization module is used for initializing continuous quantum squirrel search mechanism parameters;
the fitness value calculation module is used for calculating the fitness values of the positions of all squirrels and initializing a local optimal quantum position, a global optimal quantum position and a global worst quantum position;
position assignment module for squirrel position assignment: according to the fitness value of the position of the squirrel, sequentially dividing the squirrel into a squirrel on a hazelnut tree, a squirrel on a pecan tree, a squirrel on an oak tree and a squirrel on a common tree;
the updating module is used for respectively updating the quantum positions of the squirrels on the hazelnut trees, the pecan trees, the oak trees and the common trees by using four different modes:
5.1 the squirrel on the hazelnut tree is operated as follows:
the squirrel on the hazelnut tree moves to the direction of the global optimal position, and the ith iteration is performed for t times1The running step of squirrel is
Wherein h ismaxAnd hminA maximum running stride length and a minimum running stride length,
is [0,1 ]]BetweenThe number of the uniform random numbers of (a),
iterating the ith time t +11The p-dimension quantum rotation angle of only squirrel is
Wherein
Is the ith1Local optimal quantum position searched by squirrel till the t-th iteration
The (d) th dimension of (a),
the global worst molecular position searched for by the t-th generation of the population of the mouse of the Pomacea
The (d) th dimension of (a),
the global optimal quantum position searched by the squirrel stopping population for the t generation
P-th dimension of (c)1To adjust the constant, c2Is [0,1 ]]A constant value of (a) to (b),
the mean value is 0, and the variance is 1, the ith number on the hazelnut tree1The p-dimension updating mode of only squirrel quantum position is
abs () is an absolute value operation;
5.2 the squirrel on the hickory tree is operated as follows:
the squirrel on the hickory tree moves to the hazelnut tree and the global optimal position, and the ith iteration is carried out for t +1 times2The p-dimension quantum rotation angle of only squirrel is
Wherein
And
is [0,1 ]]A uniform random number in between, c4Is [0,1 ]]A constant value of (a) to (b),
is the average value of the p-th dimension, beta, of the squirrel quantum position on the hazelnut treet＝c3(1-t)/tmax，c3Is [0,1 ]]A constant value of (a) to (b),
then the ith of the hickory nut2The p-dimension updating mode of only squirrel quantum position is
5.3 squirrels on oak were subjected to the following operations:
the squirrel on the oak moves to the pecan tree and the direction of the global optimal position, and the ith iteration is carried out for t +1 times3The p-dimension quantum rotation angle of only squirrel is
Wherein,
is [0,1 ]]A uniform random number in between, and,
A0is [0,1 ]]Constant of c between c5In order to adjust the constant, the constant is adjusted,
is [0,1 ]]The number of the machines is uniform among the machines,
the p-dimension average value of the squirrel quantum position on the hickory tree is the ith dimension of the oak tree3The p-dimension updating mode of only squirrel quantum position is
5.4 the squirrel on the general tree is subjected to the following operations:
the squirrel on the common tree moves towards the oak tree and the global optimal position, and the ith iteration is carried out for the t times4The Le' vy running step length of only squirrel is
The gamma is a constant and is a linear variable,
and
is [0,1 ]]A uniform random number in between, and,
is a constant; i th iteration at t +14The p-dimension quantum rotation angle of only squirrel is
Is [0,1 ]]Is uniformly followed byThe number of the machines is increased,
the p-th dimension of the squirrel quantum position randomly selected on the oak tree is the ith dimension on the common tree4The p-dimension updating mode of only squirrel quantum position is
The new position fitness value calculation module is used for calculating the fitness values of new positions of all squirrels and updating the local optimal quantum position, the global worst quantum position and the global optimal quantum position;
and the mapping module is used for mapping the global optimal quantum position of the squirrel group into a global optimal position according to the mapping rule so as to obtain the incoming wave angle of the broadband signal.
7. The broadband direction-finding system based on the focus score low-order covariance under the impulsive noise of claim 6, wherein the broadband signal direction-finding model establishing module is specifically: and establishing a maximum likelihood broadband signal direction finding model based on the focusing fraction low-order covariance under the impact noise. Under the impact noise environment, P far-fields exist in the broadband signals respectively at the direction angle theta1,θ2,...,θPThe signal is incident to an antenna array which comprises M array elements in space, the distance between the array elements is d, and the bandwidth of an incident signal is B; with the first array element as the reference array element, the signal received by the mth array element can be expressed as
Wherein,
denotes the incident direction as thetapThe broadband signal of (a) is,
representing impulse noise on the m-th array element, am,pIndicating the signal strength present at the mth array element with different spatial losses from the pth source to the various sensors,
representing the time delay of the p source to the m array element;
will observe the time ToThe array receiving data in the array is divided into L subsections, and each subsection has a time TdI.e. by
The observation data are then subjected to a discrete Fourier transform of K points, provided that the subsegment T is completedCompared with the noise, L groups of mutually uncorrelated narrow-band frequency domain components can be obtained after the correlation time is longer, and then the data after the discrete Fourier transform are uncorrelated, so that the broadband model Z can be obtainedl(fk)＝Aθ(fk)Sl(fk)+Nl(fk)，l＝1,2,...,L，k＝1,2,...,K，θ＝[θ1,θ2,…,θP](ii) a In the formula Zl(fk)＝[Z1l(fk),Z2l(fk),…,ZMl(fk)]T，Sl(fk)＝[S1l(fk),S2l(fk),…,SPl(fk)]T，Nl(fk)＝[N1l(fk),N2l(fk),…,NMl(fk)]TAre respectively
At the l-th time subsection at a frequency fkDiscrete fourier transform of time.
Is a steering matrix of size M × P whenWhen the P directions are different, the matrix is full rank;
a steering vector called a matrix;
selecting a reference frequency point f0Calculating a reference frequency point f0Corresponding steering matrix is
Guide vector
Calculating the corresponding frequency point f of the array received datakFocus matrix T (f)k)＝V(fk)U(fk)HWherein H represents a conjugate transpose, U (f)k) And V (f)k) Are respectively Aθ(fk)Aθ(f0) Left and right singular vectors of (a);
calculating the corresponding frequency point f by using the received datakFractional low order covariance of time
R(fk) Element R in (1)ab(fk) Can be expressed as
Wherein, a is 1,2, a, M, b is 1,2, a, M, p1Is a fractional low-order covariance feature index, 0 < p11 ≦ E () representing the mathematical expectation; determining each frequency point fkThe corresponding received data focus score low order covariance is Rc(fk)＝T(fk)R(fk)T(fk)HFinally, the reference frequency point f is obtained0Corresponding received data focus score low order covariance of
Design basis combined with maximum likelihood direction finding methodIn the maximum likelihood direction-finding equation of the focus fraction low-order covariance, the angle estimation value is obtained as
Wherein
Is a reference frequency point f0And tr () represents the trace-finding operation of the matrix.
8. The broadband direction-finding system based on focus score low-order covariance under impulse noise of claim 7, wherein the initialization module is specifically configured to: the squirrel population has the scale of
Maximum number of iterations tmaxThe search space dimension is P, and in the t iteration, the quantum position of the ith squirrel is P
The quantum rotation angle of the ith squirrel is
Wherein
vmaxAnd vminThe upper and lower boundaries of the squirrel quantum rotation angle
P is 1,2, …, P, t is the number of iterations, and initially t is 1.
9. The broadband direction finding system based on focus score low-order covariance under impact noise according to claim 8, wherein the fitness value calculating module is specifically: mapping the quantum position of the ith squirrel in the t iteration to bitsDevice for placing
The specific mapping rule is
Wherein A isminAnd AmaxRespectively a lower bound and an upper bound of the angle search space; calculating the position of the ith squirrel in the t iteration
Fitness value of
Determining the local optimal quantum position searched by the ith squirrel till the tth iteration to be
And the global optimal quantum positions searched by all squirrels till the t iteration are
And global minimum quantum position
p＝1,2,…,P。
10. The broadband direction finding system based on focus score low-order covariance under impact noise according to claim 9, wherein the location assignment module is specifically: according to the fitness value of the position of the squirrel, the squirrels are divided into the squirrels on hazelnut trees, the squirrels on pecan trees, the squirrels on oak trees and the squirrels on common trees in sequence from big to small. Front M with larger fitness value1Only the squirrel is set as the squirrel on the hazelnut tree, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the hickory, and the fitness value is ranked as the first
To
Is/are as follows
Only the squirrel is set as the squirrel on the mountain oak, and the fitness value is ranked as the second
To
Is/are as follows
Only the squirrel is set as the squirrel on the general tree, and
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