CN113378103A - Dynamic tracking method for coherent distribution source under strong impact noise - Google Patents

Dynamic tracking method for coherent distribution source under strong impact noise Download PDF

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CN113378103A
CN113378103A CN202110611610.5A CN202110611610A CN113378103A CN 113378103 A CN113378103 A CN 113378103A CN 202110611610 A CN202110611610 A CN 202110611610A CN 113378103 A CN113378103 A CN 113378103A
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高洪元
刘亚鹏
杜亚男
刘凯龙
张志伟
陈世聪
孙贺麟
刘廷晖
张禹泽
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Abstract

The invention discloses a method for dynamically tracking a coherent distribution source under strong impact noise, and particularly relates to a method for designing a weighted norm fraction low-order correlation matrix under the strong impact noise, designing a maximum likelihood dynamic tracking method based on the weighted norm low-order correlation matrix on the basis of the weighted norm fraction low-order correlation matrix to dynamically track the coherent distribution source, and quickly obtaining a tracking result through a quantum benchmark learning mechanism. The invention designs a coherent distribution source dynamic tracking method based on a quantum pole learning mechanism with higher robustness, designs a weighted norm fraction low-order correlation matrix under strong impact noise, and realizes dynamic tracking by using a maximum likelihood tracking method. The low-order correlation matrix of the weighted norm fraction can be designed, coherent information sources can be distinguished, effective tracking of dynamic targets is achieved under the condition of strong impact noise, the designed quantum benchmark learning mechanism can carry out high-precision solution on the maximum likelihood equation of the low-order correlation matrix of the weighted norm fraction, and tracking results can be obtained quickly and accurately.

Description

Dynamic tracking method for coherent distribution source under strong impact noise
Technical Field
The invention relates to a coherent distribution source dynamic tracking method under strong impact noise, in particular to a coherent distribution source dynamic tracking method based on a quantum marker post learning mechanism under a strong impact noise environment, and belongs to the field of array signal processing.
Background
In recent years, attention has been paid to a high-resolution array signal processing technology, particularly, an array direction finding technology is widely applied to the fields of seismic exploration, radar, passive sonar, wireless communication and the like, and a plurality of high-resolution estimation algorithms are formed. Most of direction-of-arrival estimation algorithms mostly assume that a signal source is a far-field point target, a point target model is an approximation of an actual environment, most direction-finding algorithms usually assume that background noise is Gaussian noise, an angle during high-speed instantaneous sampling is a fixed value, and an ideal result can be obtained by analyzing with second-order or higher-order cumulant. However, because the size of the target depends on the distance from the array receiving antenna, and the influence of the phenomena such as multipath effect and scattering, the signal arrival angle in wireless mobile communication is often expanded within a certain range, a distributed signal source is presented, and meanwhile, the central azimuth angle of the distributed source in the actual environment changes with time, and non-gaussian noise exists, such as sea clutter noise, atmospheric noise, wireless channel noise and the like.
The method has the advantages that coherent distributed source dynamic tracking is carried out by using a maximum likelihood algorithm, high-precision and high-resolution tracking performance can be obtained, coherent information sources can be resolved, but global maximum search needs to be carried out on a multi-dimensional nonlinear optimization problem, how to quickly obtain a search result with high precision is a classic problem of application of the maximum likelihood dynamic tracking method, and the method is solved by using an intelligent optimization algorithm and is a potential solution, but the existing intelligent optimization algorithm has some defects when solving a complex dynamic tracking problem, such as low convergence speed, easiness in falling into a local extreme value and the like, so that a new intelligent optimization algorithm needs to be designed for solving specific problems.
Through the search of the prior art documents, Cai Rui et al propose a novel DOA estimation method based on generalized correlation entropy in the 'electronic and information article' (2020,42(11): 2600-; guo Xiansheng et al proposed a coherent distribution source center DOA tracking method based on subspace updating in the "Fast DOA tracking of coherent distributed sources based on subspace updating" published in CIE Radar (2006:1407-1410), improved the PAST algorithm, and researched the FAPI-based dynamic DOA estimation method, and the method has the characteristics of small calculated amount and good real-time property. But this method is not ideal and cannot resolve coherent sources in low signal-to-noise and strong impulsive noise environments.
The existing literature retrieval results show that the existing coherent distribution source dynamic tracking method mostly adopts subspace tracking and iteration methods, the algorithm is good in real-time performance and small in calculation amount, but mostly cannot directly solve coherent information sources, and has poor performance in the environment of low signal-to-noise ratio and impulse noise, and the technical problem that the existing coherent distribution source dynamic tracking method has poor performance in the background of strong impulse noise and low signal-to-noise ratio and cannot distinguish coherent information sources needs to be solved urgently.
Disclosure of Invention
Aiming at the prior art, the technical problem to be solved by the invention is to provide a coherent distribution source dynamic tracking method under strong impact noise, the method utilizes a quantum pole learning mechanism to carry out efficient solution, has robustness under the environment of strong impact noise, can distinguish coherent information sources, and breaks through some application limitations of the conventional coherent distribution source dynamic tracking method.
In order to solve the technical problem, the invention provides a method for dynamically tracking a coherent distribution source under strong impact noise, which comprises the following steps:
the method comprises the following steps: establishing a generalized array flow pattern of a coherent distribution source, acquiring snapshot sampling data of an array receiving signal, and constructing a maximum likelihood tracking equation based on a weighted norm fraction low-order correlation matrix;
step two: initializing a search space;
step three: initializing all individual quantum states in the whole ecological system and setting parameters;
step four: constructing a fitness function, calculating a fitness function value of each individual in all populations, calculating an average fitness value of each population, setting up an internal pole and an external pole, and calculating an average fitness value of the current generation of the whole ecological system;
step five: realizing an optimization searching process according to a quantum marker post learning mechanism;
step six: judging whether the maximum iteration number G is reached, if not, making G equal to G +1, and returning to the fifth step; if so, stopping loop iteration, outputting an individual and a quantum state representing an external marker post, and entering the next step;
step seven: judging whether the maximum fast beat number K is reachedpIf not, let k be k +1, update the search space of 2P angle parameters at the next snapshot, obtain the next snapshot sampling data, update the weighted norm fraction low-order correlation matrix, return toReturning to the third step; otherwise, carrying out the next step;
step eight: and outputting a dynamic tracking result of the coherent distribution source according to the obtained estimated values of the angle parameters in all the snapshot sampling data.
The invention also includes:
1. establishing a generalized array flow pattern of a coherent distribution source, acquiring snapshot sampling data of an array receiving signal, and constructing a maximum likelihood tracking equation based on a weighted norm fraction low-order correlation matrix, wherein the maximum likelihood tracking equation specifically comprises the following steps:
the array receiving signal model of the coherent distribution source satisfies the following conditions:
x(t)＝B(ψ)s(t)+n(t)
wherein B (psi) [ B (psi) ]1),b(ψ2),…,b(ψP)]Is a generalized array flow pattern matrix of coherently distributed sources,
Figure BDA0003095960960000031
d is the uniform linear array element spacing, lambda is the coherent distribution source propagation wavelength, P is 1,2, …, P is the distribution source number, and M is the receiving array element number; thetapAnd ΔpRespectively representing the central azimuth angle and the angular spread of the p-th coherent distribution source;
constructing a maximum likelihood tracking equation of the kth snapshot based on the updated weighted norm fraction low-order correlation matrix as
Figure BDA0003095960960000032
Wherein P isB(ψ)＝B(ψ)[BH(ψ)B(ψ)]-1BH(psi) is the projection matrix of the generalized array manifold matrix B (psi), superscript H is the matrix conjugate transpose, argmax () represents the variable that finds the largest function value, and trace represents the tracing of the matrix.
2. The initializing search space in the second step specifically comprises: at the kth snapshot, a search space of 2P angular parameters is defined as
Figure BDA0003095960960000033
Wherein the first P uq(k) And vq(k) Searching for q central azimuth angles of kth snapshot respectivelyUpper and lower limits of space, q ═ 1,2, …, P, and the last P uq(k) And vq(k) And respectively taking the upper limit and the lower limit of a corresponding search space definition domain as the initial values of the search space at the time of the 1 st snapshot, wherein q is P +1, P +2, … and 2P.
3. Initializing all individual quantum states in the whole ecological system and setting parameters in the third step specifically as follows:
firstly, the population number in the whole ecological system is set to be NPThe number of individuals in the phi-th population is NφFor the kth snapshot data, the maximum number of iterations
Figure BDA0003095960960000034
Wherein, zeta is a positive integer,
Figure BDA0003095960960000035
to get the function rounded down, in the g-th iteration, the phi-th population is
Figure BDA0003095960960000036
The quantum state of an individual in a 2P-dimensional search space is
Figure BDA0003095960960000037
Where, phi is 1,2, …, NP,
Figure BDA0003095960960000038
When g is 1, each dimension of all individual quantum states of the initial generation is initialized to [0, 1%]A uniform random number in between;
4. constructing a fitness function in the fourth step, calculating the fitness function value of each individual in all the populations, calculating the average fitness value of each population, and setting up an internal pole and an external pole, wherein the calculation of the average fitness value of the current generation of the whole ecological system specifically comprises the following steps:
in the g-th iteration, according to the mapping rule
Figure BDA0003095960960000041
All individuals in the population are combinedEach dimension of the quantum state is mapped into an angle parameter search space range to obtain the phi-th population in the g-th iteration
Figure BDA0003095960960000042
The individual is
Figure BDA0003095960960000043
Where, phi is 1,2, …, NP，
Figure BDA0003095960960000044
q is 1,2, …,2P, in the phi-th population of the g-th iteration
Figure BDA0003095960960000045
Fitness function of an individual is
Figure BDA0003095960960000046
Calculating fitness function values of all individuals in each population according to the fitness functions, and calculating the average fitness value of the phi-th population in the g-th iteration
Figure BDA0003095960960000047
Where, phi is 1,2, …, NPFinding out and recording the individual with the optimal fitness function value in the phi-th population of the g-th iteration as
Figure BDA0003095960960000048
Having a quantum state of
Figure BDA0003095960960000049
Where, phi is 1,2, …, NPSetting the artificial ecological system as an internal marker post, recording and updating the individuals with the optimal fitness function values in the whole ecological system of the g-th iteration
Figure BDA00030959609600000410
Having a quantum state of
Figure BDA00030959609600000411
Setting it as external marker post, calculating the whole ecologyAverage fitness value of system in g-th iteration
Figure BDA00030959609600000412
Where, phi is 1,2, …, NP。
5. The optimization searching process is realized according to a quantum marker post learning mechanism in the fifth step and specifically comprises the following steps:
step 5.1: the method comprises the following steps of learning external benchmarks by individuals in all populations, calculating and evaluating fitness functions, and specifically comprises the following steps: in the phi-th population in the g-th generation
Figure BDA00030959609600000413
The individual has an external learning rate of
Figure BDA00030959609600000414
Wherein, G'rAn initial value representing an external learning rate is shown,
Figure BDA00030959609600000415
represents the mean fitness value of the phi-th population in the g-th generation,
Figure BDA00030959609600000416
represents the first in the phi-th population in the g-th generation
Figure BDA00030959609600000417
Fitness function value of individual, phi 1,2, …, NP，
Figure BDA00030959609600000418
If it is not
Figure BDA00030959609600000419
Then phi in the phi-th population
Figure BDA00030959609600000420
Individual quantum rotation angle vector of
Figure BDA00030959609600000421
Wherein the content of the first and second substances,
Figure BDA00030959609600000422
is [0,1 ]]Uniformly distributed random number, λ0For learning factors during external benchmarking, quantum states are updated using an analog quantum revolving gate:
Figure BDA00030959609600000423
wherein
Figure BDA00030959609600000424
Represents the first in the phi-th population in the g +1 th generation
Figure BDA00030959609600000425
Individual qth quantum rotation angle, where Φ is 1,2, …, NP，
Figure BDA00030959609600000426
q is 1,2, …,2P, and then mapping the updated individual quantum states to updated individuals
Figure BDA00030959609600000427
Then all individuals are subjected to calculation and evaluation of fitness functions;
step 5.2: after all the individuals after the external benchmarking learning are subjected to fitness function calculation and evaluation, if the first population in the phi-th population is
Figure BDA0003095960960000051
If the fitness function value of each individual is not improved, internal benchmarking learning is carried out and fitness function evaluation is carried out, and the method specifically comprises the following steps: in the phi-th population in the g-th generation
Figure BDA0003095960960000052
The internal learning rate of an individual is
Figure BDA0003095960960000053
Wherein, Br' denotes an initial value of the internal learning rate,
Figure BDA0003095960960000054
is the first in the phi-th population in the g-th generation
Figure BDA0003095960960000055
The Euclidean distance between individual quantum states and internal benchmarks, i.e.
Figure BDA0003095960960000056
R is the diameter of the search space, i.e.
Figure BDA0003095960960000057
Wherein the content of the first and second substances,
Figure BDA0003095960960000058
represents the q-dimension quantum state of the benchmark in the phi-th population in the g-th generation,
Figure BDA0003095960960000059
represents the first in the phi-th population in the g-th generation
Figure BDA00030959609600000510
Q-th dimension of individual quantum state, phi 1,2, …, NP，
Figure BDA00030959609600000511
q is 1,2, …,2P if
Figure BDA00030959609600000512
Then phi in the phi-th population
Figure BDA00030959609600000513
Individual quantum rotation angle vector of
Figure BDA00030959609600000514
Wherein the content of the first and second substances,
Figure BDA00030959609600000515
is [0,1 ]]Uniformly distributed random number, λ1For learning factors during internal benchmarking, quantum states are updated using an analog quantum revolving gate:
Figure BDA00030959609600000516
wherein
Figure BDA00030959609600000517
Represents the first in the phi-th population in the g +1 th generation
Figure BDA00030959609600000518
Q-th dimension of quantum rotation angle, phi 1,2, …, NP，
Figure BDA00030959609600000519
q is 1,2, …,2P, and then the updated quantum states are mapped to updated individual states
Figure BDA00030959609600000520
Then all individuals are subjected to calculation and evaluation of fitness functions;
step 5.3: after all the individuals after internal benchmarking learning are subjected to fitness function calculation and evaluation, if the first population is in the phi-th population
Figure BDA00030959609600000521
If the fitness function value of each individual is not improved, self-learning is carried out and fitness function evaluation is carried out, and the method specifically comprises the following steps: phi in the phi th population
Figure BDA00030959609600000522
The self-learning rate of an individual is
Figure BDA00030959609600000523
Wherein S isr' denotes an initial value of the self-learning rate,
Figure BDA00030959609600000524
represents the mean fitness value of the phi-th population in the g-th generation,
Figure BDA00030959609600000525
represents the first in the phi-th population in the g-th generation
Figure BDA00030959609600000526
Fitness function value of individual, phi 1,2, …, NP，
Figure BDA00030959609600000527
If it is not
Figure BDA00030959609600000528
Then Logistic chaos mapping is performed, i.e.
Figure BDA00030959609600000529
Wherein λ is2Is a Logistic parameter, λ2∈[0,4]，φ＝1,2,…,NP，
Figure BDA00030959609600000530
q 1,2, …,2P, and then mapping the updated quantum states to updated individuals
Figure BDA00030959609600000531
Then all individuals are subjected to calculation and evaluation of fitness functions;
step 5.4: calculating the average fitness value of each updated population
Figure BDA00030959609600000532
Where, phi is 1,2, …, NPFinding out and recording the individual with the best fitness function value in the phi-th population of the g +1 th iteration
Figure BDA0003095960960000061
Having a quantum state of
Figure BDA0003095960960000062
Where, phi is 1,2, …, NPEstablishing the new internal marker post as a new internal marker post, recording and updating the individual with the optimal fitness function value in the g +1 th iteration whole ecological system
Figure BDA0003095960960000063
Having a quantum state of
Figure BDA0003095960960000064
Setting it as new external marker post, calculating the updated average adaptability value of whole ecological system
Figure BDA0003095960960000065
Where, phi is 1,2, …, NPIf the average fitness value is not improved or the external pole is not changed compared with the previous generation, the individuals with the best fitness function value and the corresponding quantum state are exchanged among the various populations, namely, the various populations establish a new internal pole again.
6. Step seven, judging whether the maximum fast beat number K is reachedpIf the correlation matrix does not reach the preset value, making k equal to k +1, updating the search space of the 2P angular parameters at the next snapshot, and acquiring the next snapshot sampling data, wherein the updating of the weighted norm fraction low-order correlation matrix specifically comprises:
judging whether the maximum fast beat number K is reachedpIf not, updating the search space of the 2P angle parameters in k +1 times of snapshots
Figure BDA0003095960960000066
Figure BDA0003095960960000067
Wherein the content of the first and second substances,
Figure BDA0003095960960000068
to converge constant, μq(k) For the kth snapshot the central value of the search interval for the qth angular parameter, i.e.
Figure BDA0003095960960000069
Figure BDA00030959609600000610
Is a genetic factor, and is a gene of the genetic factor,
Figure BDA00030959609600000611
is the search radius of the search interval,
Figure BDA00030959609600000612
the estimated value of the qth angle parameter for k-1 snapshots, q is 1,2, …, 2P; acquiring the snapshot sampling data x (k +1) [ [ x ] ] for k +1 times1(k+1),x2(k+1),…,xM(k+1)]TThen the weighted infinite norm normalized signal of the k +1 sample data can be expressed as
Figure BDA00030959609600000613
Wherein, beta is ∈ [0.8,1 ]]As a weighting constant, the increment of the weighted norm fractional low-order correlation matrix constructed by the k-th sampling data can be expressed as
Figure BDA00030959609600000614
Wherein r ism(k+1)＝[r1m(k+1),r2m(k+1),…,rMm(k+1)]TM is 1,2, …, M, i row and l column element
Figure BDA00030959609600000615
Wherein t is a low-order constant, and t is an element [1,2 ]]I ═ 1,2, …, M, l ═ 1,2, …, M, superscript denotes conjugation; constructing an update equation R of a weighted norm fraction low-order correlation matrix after receiving the (k +1) th snapshot sampling dataS(k+1)＝ωRS(k) + (1-omega) R (k +1), wherein RS(k) And R (k +1) is the increment of the weighted norm fraction low-order correlation matrix of the sampling data of the kth snapshot, omega is an updating factor, and k is equal to k + 1.
The invention has the beneficial effects that: aiming at the defects and shortcomings of the existing coherent distributed source dynamic tracking method, the invention provides a coherent distributed source dynamic tracking method based on a quantum pole learning mechanism under strong impact noise, and particularly designs a weighted norm fraction low-order correlation matrix under the strong impact noise, designs a maximum likelihood dynamic tracking method based on the weighted norm low-order correlation matrix on the basis of the weighted norm fraction low-order correlation matrix to carry out coherent distributed source dynamic tracking, and quickly obtains a tracking result through the quantum pole learning mechanism, compared with the prior art, the coherent distributed source dynamic tracking method has the following advantages that:
(1) aiming at the problem that the performance of the existing coherent distributed source dynamic tracking method is deteriorated in a strong impact noise environment, a coherent distributed source dynamic tracking method which is more robust and based on a quantum pole learning mechanism is designed, a weighted norm fraction low-order correlation matrix is designed under the strong impact noise, and dynamic tracking is realized by utilizing a maximum likelihood tracking method.
(2) The coherent distribution source dynamic tracking method provided by the invention designs the weighted norm fraction low-order correlation matrix, can distinguish coherent information sources, realizes effective tracking of dynamic targets under strong impact noise, and can solve the weighted norm fraction low-order correlation matrix maximum likelihood equation with high precision by the designed quantum pole learning mechanism, thereby obtaining the tracking result quickly and accurately.
(3) The effectiveness of the coherent distribution source dynamic tracking method based on the quantum pole learning mechanism under the strong impact noise is proved through simulation verification, the application limit that the performance of the traditional method is deteriorated or even fails under the environment of strong impact noise and low signal-to-noise ratio and the coherent information source cannot be distinguished is broken through, and the accuracy is higher compared with that of the traditional solving method.
Drawings
FIG. 1 is a schematic diagram of a coherent distribution source dynamic tracking method under strong impact noise designed by the present invention.
Fig. 2 is a dynamic tracking result of a designed method for a single coherent distribution source central azimuth angle when α is 0.8 and the generalized signal-to-noise ratio GSNR is 20 dB.
Fig. 3 is a dynamic tracking result of a designed method for a single coherent distribution source angle spread when α is 0.8 and the generalized signal-to-noise ratio GSNR is 20 dB.
Fig. 4 is a dynamic tracking result of the existing method for the central azimuth angle of a single coherent distribution source when α is 0.8 and the generalized signal-to-noise ratio GSNR is 20 dB.
Fig. 5 is a dynamic tracking result of a designed method for two independent source central azimuth angles when α is 1.5 and the generalized signal-to-noise ratio GSNR is 15 dB.
Fig. 6 is a dynamic tracking result of the existing method for the central azimuth angles of two independent information sources when α is 1.5 and the generalized signal-to-noise ratio GSNR is 15 dB.
Fig. 7 is a dynamic tracking result of the designed method for the central azimuth angles of three independent sources when α is 2 and the generalized signal-to-noise ratio GSNR is 15 dB.
Fig. 8 is a dynamic tracking result of the existing method for the central azimuth angles of three independent sources when α is 2 and the generalized signal-to-noise ratio GSNR is 15 dB.
Fig. 9 shows the dynamic tracking result of the designed method for the central azimuth angles of three coherent sources when α is 2 and the generalized SNR is 15 dB.
Fig. 10 shows the dynamic tracking result of the existing method for the central azimuth angles of three coherent sources when α is 2 and the generalized SNR is 15 dB.
Detailed Description
The invention is further described with reference to the drawings and the detailed description.
With reference to fig. 1, the present invention comprises the following steps:
step one, establishing a generalized array flow pattern of a coherent distribution source, acquiring snapshot sampling data of an array receiving signal, and constructing a maximum likelihood tracking equation based on a weighted norm fraction low-order correlation matrix.
The model of the array received signal of the distributed source can be described as the integral of the angular signal density function in the distribution space, i.e.:
Figure BDA0003095960960000081
wherein, x (t) is array receiving signal of distribution source, a (theta) is array guiding vector, theta represents direction of distribution source signal, sp(θ-θpT) is the angular signal density function of the P-th distribution source, n (t) is the noise vector, and P is the number of the distribution sources. For coherent distributed source models, the angular signal density function can be expressed in the form of the product of the random signal amplitude and the spatial distribution function of the distributed source, i.e.: sp(θ-θp,t)＝sp(t)gp(θ-θp) Wherein s isp(t) is the random signal amplitude, gp(θ-θp) Is a spatial distribution function of the distributed source. The spatial distribution function of the coherent distribution source is assumed to be gaussian, i.e.:
Figure BDA0003095960960000082
wherein, DeltapIs an unknown angular distribution parameter, then,
Figure BDA0003095960960000083
wherein psip＝(θp,Δp) Representing the angle parameter, theta, of the p-th coherent distribution sourcepAnd ΔpRespectively representing the central azimuth angle and the angle diffusion of the p-th coherent distribution source, the generalized array flow pattern and the array receiving signal model of the coherent distribution source can be established, namely: x (t) ═ B (ψ) s (t) + n (t), where B (ψ) ═ B (ψ)1),b(ψ2),…,b(ψP)]Is a generalized array flow pattern matrix of coherently distributed sources,
Figure BDA0003095960960000091
d is the uniform linear array element spacing, lambda is the coherent distribution source propagation wavelength, P is 1,2, …, and P, M is the receiving array element number.
Defining the maximum fast beat number as KpAssuming that P coherent distribution sources with wavelength λ are incident on the uniform line array consisting of M array elements, the kth snapshot data received by the uniform line array can be represented as x (K) ═ B (ψ) s (K) + n (K), where K is 1,2, …, K is 1,2, …p，B(ψ)＝[b(ψ1),b(ψ2),…,b(ψP)]In the M multiplied by P dimension generalized array flow pattern, the pth generalized guide vector is
Figure BDA0003095960960000092
p＝1,2,…,P，x(k)＝[x1(k),x2(k),…,xM(k)]TIs the snapshot data of M × 1 dimensional array, where k is the snapshot times, s (k) is [ s ]1(k),s2(k),…,sP(k)]TIs a P x 1 dimensional signal, n (k) is a M x 1 dimensional complex impulse noise distributed following a standard S α S with a characteristic index α, j is a complex unit, and T is a matrix transpose.
The weighted infinite norm normalization signal of the kth snapshot sample data can be expressed as
Figure BDA0003095960960000093
Wherein, beta is ∈ [0.8,1 ]]As a weighting constant, the increment of the weighted norm fractional low-order correlation matrix constructed by the k-th sampling data can be expressed as
Figure BDA0003095960960000094
Wherein r ism(k)＝[r1m(k),r2m(k),…,rMm(k)]TM is 1,2, …, M, i row and l column element
Figure BDA0003095960960000095
Wherein t is a low-order constant, and t is an element [1,2 ]]I ═ 1,2, …, M, l ═ 1,2, …, M, superscript denotes conjugation. RS(k) The updated weighted norm fraction low-order correlation matrix for the sampling data of the kth snapshot, R is obtained at the 1 st snapshotS(1) R (1). Constructing a maximum likelihood tracking equation of the kth snapshot based on the updated weighted norm fraction low-order correlation matrix as
Figure BDA0003095960960000096
Wherein P isB(ψ)＝B(ψ)[BH(ψ)B(ψ)]-1BH(psi) is the projection matrix of the generalized array manifold matrix B (psi), superscript H is the matrix conjugate transpose, argmax () represents the variable that finds the largest function value, and trace represents the tracing of the matrix.
Step two, initializing the search space
At the kth snapshot, a search space of 2P angular parameters is defined as
Figure BDA0003095960960000101
Wherein the first P uq(k) And vq(k) The upper limit and the lower limit of the search space are respectively searched for the q central azimuth angle of the kth snapshot, q is 1,2, …, P, and the last P uq(k) And vq(k) The upper limit and the lower limit of the q-P angle spread search space for the kth snapshot are respectively, and q is P +1, P +2, … and 2P. And respectively taking the upper limit and the lower limit of the corresponding search space definition domain as the initial value of the search space in the 1 st snapshot.
And step three, initializing all individual quantum states in the whole ecological system and setting related parameters.
Firstly, the population number in the whole ecological system is set to be NPThe number of individuals in the phi-th population is NφFor the kth snapshot data, the maximum number of iterations
Figure BDA0003095960960000102
Wherein, zeta is a positive integer,
Figure BDA0003095960960000103
is a rounded down function. In the g-th iteration, the phi-th population is
Figure BDA0003095960960000104
The quantum state of an individual in a 2P-dimensional search space is
Figure BDA0003095960960000105
Where, phi is 1,2, …, NP,
Figure BDA0003095960960000106
When g is 1, each dimension of all individual quantum states of the initial generation is initialized to [0, 1%]A uniform random number in between.
And step four, constructing a fitness function, calculating the fitness function value of each individual in all the populations, calculating the average fitness value of each population, setting up an internal pole and an external pole, and calculating the average fitness value of the current generation of the whole ecological system.
In the g-th iteration, according to the mapping rule
Figure BDA0003095960960000107
Mapping each dimension of each individual quantum state in all the populations into an angle parameter search space range to obtain the phi-th population in the g-th iteration
Figure BDA0003095960960000108
The individual is
Figure BDA0003095960960000109
Where, phi is 1,2, …, NP，
Figure BDA00030959609600001010
q is 1,2, …, 2P. In the phi-th population of the g-th iteration
Figure BDA00030959609600001011
Fitness function of an individual is
Figure BDA00030959609600001012
Calculating fitness function values of all individuals in each population according to the fitness functions, and calculating the average fitness value of the phi-th population in the g-th iteration
Figure BDA00030959609600001013
Where, phi is 1,2, …, NPFinding out and recording the individual with the optimal fitness function value in the phi-th population of the g-th iteration as
Figure BDA00030959609600001014
Having a quantum state of
Figure BDA00030959609600001015
Where, phi is 1,2, …, NPSetting the artificial ecological system as an internal marker post, recording and updating the individuals with the optimal fitness function values in the whole ecological system of the g-th iteration
Figure BDA0003095960960000111
Having a quantum state of
Figure BDA0003095960960000112
Setting the ecological system as an external marker post, and calculating the average fitness value of the whole ecological system in the g iteration
Figure BDA0003095960960000113
Where, phi is 1,2, …, NP。
Step five, realizing an optimization searching process according to a quantum marker post learning mechanism, and specifically comprising the following steps:
(1) and (4) carrying out external benchmark learning and fitness function calculation and evaluation on the individuals in all the populations. The method comprises the following specific steps: in the phi-th population in the g-th generation
Figure BDA0003095960960000114
The individual has an external learning rate of
Figure BDA0003095960960000115
Wherein G isr' denotes an initial value of the external learning rate,
Figure BDA0003095960960000116
represents the mean fitness value of the phi-th population in the g-th generation,
Figure BDA0003095960960000117
represents the first in the phi-th population in the g-th generation
Figure BDA0003095960960000118
Fitness function value of individual, phi 1,2, …, NP，
Figure BDA0003095960960000119
If it is not
Figure BDA00030959609600001110
Then phi in the phi-th population
Figure BDA00030959609600001111
Individual quantum rotation angle vector of
Figure BDA00030959609600001112
Wherein the content of the first and second substances,
Figure BDA00030959609600001113
is [0,1 ]]Uniformly distributed random number, λ0Is a learning factor when external benchmarking learning is carried out. Quantum states are updated using analog quantum turn gates:
Figure BDA00030959609600001114
wherein
Figure BDA00030959609600001115
Represents the first in the phi-th population in the g +1 th generation
Figure BDA00030959609600001116
Individual qth quantum rotation angle, where Φ is 1,2, …, NP，
Figure BDA00030959609600001117
q is 1,2, …,2P, and then mapping the updated individual quantum states to updated individuals
Figure BDA00030959609600001118
All individuals then perform the calculation and evaluation of the fitness function.
(2) After all the individuals after the external benchmarking learning are subjected to fitness function calculation and evaluation, if the first population in the phi-th population is
Figure BDA00030959609600001119
And if the fitness function value of each individual is not improved, performing internal benchmarking learning and evaluating the fitness function. The method comprises the following specific steps: in the phi-th population in the g-th generation
Figure BDA00030959609600001120
The internal learning rate of an individual is
Figure BDA00030959609600001121
Wherein, Br' denotes an initial value of the internal learning rate,
Figure BDA00030959609600001122
is the first in the phi-th population in the g-th generation
Figure BDA00030959609600001123
The Euclidean distance between individual quantum states and internal benchmarks, i.e.
Figure BDA00030959609600001124
R is the diameter of the search space, i.e.
Figure BDA00030959609600001125
Wherein the content of the first and second substances,
Figure BDA00030959609600001126
represents the q-dimension quantum state of the benchmark in the phi-th population in the g-th generation,
Figure BDA00030959609600001127
represents the first in the phi-th population in the g-th generation
Figure BDA00030959609600001128
Q-th dimension of individual quantum state, phi 1,2, …, NP，
Figure BDA00030959609600001129
q is 1,2, …, 2P. If it is not
Figure BDA00030959609600001130
Then phi in the phi-th population
Figure BDA00030959609600001131
Individual quantum rotation angle vector of
Figure BDA00030959609600001132
Wherein the content of the first and second substances,
Figure BDA00030959609600001133
is [0,1 ]]Uniformly distributed random number, λ1Is a learning factor when internal benchmarking learning is carried out. Quantum states are updated using analog quantum turn gates:
Figure BDA0003095960960000121
wherein
Figure BDA0003095960960000122
Represents the first in the phi-th population in the g +1 th generation
Figure BDA0003095960960000123
Q-th dimension of quantum rotation angle, phi 1,2, …, NP，
Figure BDA0003095960960000124
q is 1,2, …, 2P. The updated quantum states are then mapped to updated individual states
Figure BDA0003095960960000125
All individuals then perform the calculation and evaluation of the fitness function.
(3) After all the individuals after internal benchmarking learning are subjected to fitness function calculation and evaluation, if the first population is in the phi-th population
Figure BDA0003095960960000126
If the fitness function value of each individual is not improved, self-learning is carried out and fitness function evaluation is carried out. The method comprises the following specific steps: phi in the phi th population
Figure BDA0003095960960000127
The self-learning rate of an individual is
Figure BDA0003095960960000128
Wherein S isr' denotes an initial value of the self-learning rate,
Figure BDA0003095960960000129
represents the mean fitness value of the phi-th population in the g-th generation,
Figure BDA00030959609600001210
represents the first in the phi-th population in the g-th generation
Figure BDA00030959609600001211
Fitness function value of individual, phi 1,2, …, NP，
Figure BDA00030959609600001212
If it is not
Figure BDA00030959609600001213
Then Logistic chaos mapping is performed, i.e.
Figure BDA00030959609600001214
Wherein λ is2Is a Logistic parameter, λ2∈[0,4]，φ＝1,2,…,NP，
Figure BDA00030959609600001215
q 1,2, …,2P, and then mapping the updated quantum states to updated individuals
Figure BDA00030959609600001216
All individuals then perform the calculation and evaluation of the fitness function.
(4) Calculating the average fitness value of each updated population
Figure BDA00030959609600001217
Where, phi is 1,2, …, NPFinding out and recording the individual with the best fitness function value in the phi-th population of the g +1 th iteration
Figure BDA00030959609600001218
Having a quantum state of
Figure BDA00030959609600001219
Where, phi is 1,2, …, NPEstablishing the new internal marker post as a new internal marker post, recording and updating the individual with the optimal fitness function value in the g +1 th iteration whole ecological system
Figure BDA00030959609600001220
Having a quantum state of
Figure BDA00030959609600001221
Setting it as new external marker post, calculating the updated average adaptability value of whole ecological system
Figure BDA00030959609600001222
Wherein phi is1,2,…,NP. If the average fitness value is not improved or the external pole is not changed compared with the previous generation, the individuals with the best fitness function value and the corresponding quantum state are mutually exchanged among the various populations, namely, the various populations establish a new internal pole again.
Step six, judging whether the maximum iteration times G is reached, if not, making G equal to G +1, and returning to the step five; if so, stopping loop iteration, outputting individual and quantum states representing the external benchmarks and entering the next step.
Step seven, judging whether the maximum fast beat number K is reachedpIf not, making k equal to k +1, updating the search space of the 2P angle parameters at the next snapshot, acquiring the next snapshot sampling data, updating the weighted norm fraction low-order correlation matrix, and returning to the third step; otherwise, the next step is performed. The method comprises the following specific steps:
judging whether the maximum fast beat number K is reachedpIf not, updating the search space of the 2P angle parameters in k +1 times of snapshots
Figure BDA0003095960960000131
Figure BDA0003095960960000132
Wherein the content of the first and second substances,
Figure BDA0003095960960000133
to converge constant, μq(k) For the kth snapshot the central value of the search interval for the qth angular parameter, i.e.
Figure BDA0003095960960000134
Is a genetic factor, and is a gene of the genetic factor,
Figure BDA0003095960960000135
is the search radius of the search interval,
Figure BDA0003095960960000136
for k-1 snapshots q is the estimated value of the qth angular parameter, q is 1,2, …, 2P. Obtain k +1-time snapshot sampling data x (k +1) ═ x1(k+1),x2(k+1),…,xM(k+1)]TThen the weighted infinite norm normalized signal of the k +1 sample data can be expressed as
Figure BDA0003095960960000137
Wherein, beta is ∈ [0.8,1 ]]As a weighting constant, the increment of the weighted norm fractional low-order correlation matrix constructed by the k-th sampling data can be expressed as
Figure BDA0003095960960000138
Wherein r ism(k+1)＝[r1m(k+1),r2m(k+1),…,rMm(k+1)]TM is 1,2, …, M, i row and l column element
Figure BDA0003095960960000139
Wherein t is a low-order constant, and t is an element [1,2 ]]I ═ 1,2, …, M, l ═ 1,2, …, M, superscript denotes conjugation. Constructing an update equation R of a weighted norm fraction low-order correlation matrix after receiving the (k +1) th snapshot sampling dataS(k+1)＝ωRS(k) + (1-omega) R (k +1), wherein RS(k) Updating the updated weighted norm fraction low-order correlation matrix for the k-th snapshot sampling data, wherein R (k +1) is the weighted norm fraction low-order correlation matrix increment of the k + 1-th received snapshot sampling data, omega is an updating factor, k is made to be k +1, and the step III is returned; otherwise, step eight is executed.
And step eight, outputting a dynamic tracking result of the coherent distribution source according to the estimation values of the angle parameters of all the acquired snapshot sampling data.
In fig. 2, fig. 3, fig. 5, fig. 7 and fig. 9, the coherent distributed source dynamic tracking method based on the quantum pole learning mechanism designed by the present invention is denoted as QBOA-INF-ML; the methods involved in FIGS. 4, 6, 8 and 10 are from "Fast DOA tracking of coherent distributed sources on subspaces updating" published in CIE Radar (2006: 1407-.
The simulation experiment parameters of the coherent distribution source dynamic tracking method based on the quantum marker post learning mechanism are set as follows: are all made ofThe number of array elements of the uniform linear array is M equal to 8, the distance d between the array elements is 0.5 lambda, K p400, number of populations NP2, 15 individuals per population, xi 5,
Figure BDA0003095960960000141
G’r＝0.5，B’r＝0.5，S’r＝0.5，λ0＝10，λ1＝3，λ2＝4，
Figure BDA0003095960960000142
β＝1，t＝1.5，ω＝0.95。
coherent distribution source from θ in FIGS. 2, 3 and 41(k)＝[5cos(2πk/400)]°，Δ1The designed method not only can effectively track the central azimuth angle of the coherent distribution source, but also can track the angle spread value of the coherent distribution source.
In FIGS. 5 and 6, the two coherent sources are from θ1(k)＝[50+5cos(2πk/400)]°，Δ1＝1.5°，θ2(k)＝[-50+5cos(2πk/400)]°，Δ2The two coherent distribution sources are independent from each other when the coherent distribution source is incident to the uniform linear array at 3 degrees, and the designed method can effectively track the central azimuth angle of the coherent distribution source under the condition of weak impact noise and shows the tracking performance superior to that of the traditional method.
The three coherent distribution sources in FIGS. 7 and 8 are from θ, respectively1(k)＝[50+5cos(2πk/400)]°，Δ1＝1.5°，θ2(k)＝[5cos(2πk/400)]°，Δ2＝2.5°，θ3(k)＝[-50+5cos(2πk/400)]°，Δ3The three coherent distribution sources are independent from each other when the light enters the uniform linear array at 3.5 degrees, and a simulation graph shows that the designed method can effectively track the central azimuth angle of the coherent distribution source under Gaussian noise and shows the tracking performance superior to that of the traditional method.
The three coherent distribution sources in FIGS. 9 and 10 are from θ, respectively1(k)＝[50+5cos(2πk/400)]°，Δ1＝1.5°，θ2(k)＝[5cos(2πk/400)]°，Δ2＝2.5°，θ3(k)＝[-50+5cos(2πk/400)]°，Δ3The three coherent distribution sources are coherent when the light enters the uniform linear array at 3.5 degrees, and the simulation graph shows that the designed method can effectively track the central azimuth angle of the coherent distribution sources under Gaussian noise, the tracking performance superior to that of the traditional method is shown, the coherent information source can be distinguished, and some application limitations of the traditional method are broken through.

Claims (7)

1. A method for dynamically tracking a coherent distribution source under strong impact noise is characterized by comprising the following steps:
the method comprises the following steps: establishing a generalized array flow pattern of a coherent distribution source, acquiring snapshot sampling data of an array receiving signal, and constructing a maximum likelihood tracking equation based on a weighted norm fraction low-order correlation matrix;
step two: initializing a search space;
step three: initializing all individual quantum states in the whole ecological system and setting parameters;
step four: constructing a fitness function, calculating a fitness function value of each individual in all populations, calculating an average fitness value of each population, setting up an internal pole and an external pole, and calculating an average fitness value of the current generation of the whole ecological system;
step five: realizing an optimization searching process according to a quantum marker post learning mechanism;
step six: judging whether the maximum iteration number G is reached, if not, making G equal to G +1, and returning to the fifth step; if so, stopping loop iteration, outputting an individual and a quantum state representing an external marker post, and entering the next step;
step seven: judging whether the maximum fast beat number K is reachedpIf not, making k equal to k +1, updating the search space of the 2P angle parameters at the next snapshot, acquiring the next snapshot sampling data, updating the weighted norm fraction low-order correlation matrix, and returning to the third step; otherwise, carrying out the next step;
step eight: and outputting a dynamic tracking result of the coherent distribution source according to the obtained estimated values of the angle parameters in all the snapshot sampling data.
2. The method for dynamically tracking the coherent distribution source under the strong impact noise according to claim 1, wherein: step one, establishing a generalized array flow pattern of a coherent distribution source, acquiring snapshot sampling data of an array receiving signal, and constructing a maximum likelihood tracking equation based on a weighted norm fraction low order correlation matrix specifically comprises the following steps:
the array receiving signal model of the coherent distribution source satisfies the following conditions:
x(t)＝B(ψ)s(t)+n(t)
wherein B (psi) [ B (psi) ]1),b(ψ2),…,b(ψP)]Is a generalized array flow pattern matrix of coherently distributed sources,
Figure FDA0003095960950000011
d is the uniform linear array element spacing, lambda is the coherent distribution source propagation wavelength, P is 1,2, …, P is the distribution source number, and M is the receiving array element number; thetapAnd ΔpRespectively representing the central azimuth angle and the angular spread of the p-th coherent distribution source;
constructing a maximum likelihood tracking equation of the kth snapshot based on the updated weighted norm fraction low-order correlation matrix as
Figure FDA0003095960950000021
Wherein P isB(ψ)＝B(ψ)[BH(ψ)B(ψ)]-1BH(psi) is the projection matrix of the generalized array manifold matrix B (psi), superscript H is the matrix conjugate transpose, argmax () represents the variable that finds the largest function value, and trace represents the tracing of the matrix.
3. The method for dynamically tracking the coherent distribution source under the strong impact noise according to claim 1 or 2, wherein: step two, the initializing search space specifically comprises: at the kth snapshot, a search space of 2P angular parameters is defined as
Figure FDA0003095960950000022
Wherein the first P uq(k) And vq(k) The upper limit and the lower limit of the search space are respectively searched for the q central azimuth angle of the kth snapshot, q is 1,2, …, P, and the last P uq(k) And vq(k) And respectively taking the upper limit and the lower limit of a corresponding search space definition domain as the initial values of the search space at the time of the 1 st snapshot, wherein q is P +1, P +2, … and 2P.
4. The method for dynamically tracking the coherent distribution source under the strong impact noise according to claim 3, wherein: step three, initializing all individual quantum states in the whole ecological system and setting parameters specifically comprise:
firstly, the population number in the whole ecological system is set to be NPThe number of individuals in the phi-th population is NφFor the kth snapshot data, the maximum number of iterations
Figure FDA0003095960950000023
Wherein, zeta is a positive integer,
Figure FDA0003095960950000024
to get the function rounded down, in the g-th iteration, the phi-th population is
Figure FDA0003095960950000025
The quantum state of an individual in a 2P-dimensional search space is
Figure FDA0003095960950000026
Where, phi is 1,2, …, NP,
Figure FDA0003095960950000027
When g is 1, each dimension of all individual quantum states of the initial generation is initialized to [0, 1%]A uniform random number in between.
5. The method for dynamically tracking the coherent distribution source under the strong impact noise according to claim 4, wherein: constructing a fitness function, calculating a fitness function value of each individual in all the populations, calculating an average fitness value of each population, and establishing an internal pole and an external pole, wherein the calculation of the average fitness value of the current generation of the whole ecological system specifically comprises the following steps:
in the g-th iteration, according to the mapping rule
Figure FDA0003095960950000028
Mapping each dimension of each individual quantum state in all the populations into an angle parameter search space range to obtain the phi-th population in the g-th iteration
Figure FDA0003095960950000029
The individual is
Figure FDA00030959609500000210
Where, phi is 1,2, …, NP，
Figure FDA00030959609500000211
q is 1,2, …,2P, in the phi-th population of the g-th iteration
Figure FDA00030959609500000212
Fitness function of an individual is
Figure FDA00030959609500000213
Calculating fitness function values of all individuals in each population according to the fitness functions, and calculating the average fitness value of the phi-th population in the g-th iteration
Figure FDA0003095960950000031
Where, phi is 1,2, …, NPFinding out and recording the individual with the optimal fitness function value in the phi-th population of the g-th iteration as
Figure FDA0003095960950000032
Having a quantum state of
Figure FDA0003095960950000033
Where, phi is 1,2, …, NPSetting the artificial ecological system as an internal marker post, recording and updating the individuals with the optimal fitness function values in the whole ecological system of the g-th iteration
Figure FDA0003095960950000034
Having a quantum state of
Figure FDA0003095960950000035
Setting the ecological system as an external marker post, and calculating the average fitness value of the whole ecological system in the g iteration
Figure FDA0003095960950000036
Where, phi is 1,2, …, NP。
6. The method for dynamically tracking the coherent distribution source under the strong impact noise according to claim 5, wherein: the step five, the process of realizing the optimization searching according to the quantum marker post learning mechanism specifically comprises the following steps:
step 5.1: the method comprises the following steps of learning external benchmarks by individuals in all populations, calculating and evaluating fitness functions, and specifically comprises the following steps: in the phi-th population in the g-th generation
Figure FDA0003095960950000037
The individual has an external learning rate of
Figure FDA0003095960950000038
Wherein, G'rAn initial value representing an external learning rate is shown,
Figure FDA0003095960950000039
represents the mean fitness value of the phi-th population in the g-th generation,
Figure FDA00030959609500000310
represents the first in the phi-th population in the g-th generation
Figure FDA00030959609500000311
Fitness function value of individual, phi 1,2, …, NP，
Figure FDA00030959609500000312
If it is not
Figure FDA00030959609500000313
Then phi in the phi-th population
Figure FDA00030959609500000314
Individual quantum rotation angle vector of
Figure FDA00030959609500000315
Wherein the content of the first and second substances,
Figure FDA00030959609500000316
is [0,1 ]]Uniformly distributed random number, λ0For learning factors during external benchmarking, quantum states are updated using an analog quantum revolving gate:
Figure FDA00030959609500000317
wherein
Figure FDA00030959609500000318
Represents the first in the phi-th population in the g +1 th generation
Figure FDA00030959609500000319
Individual qth quantum rotation angle, where Φ is 1,2, …, NP，
Figure FDA00030959609500000320
q is 1,2, …,2P, and then updatedMapping of individual quantum states to updated individuals
Figure FDA00030959609500000321
Then all individuals are subjected to calculation and evaluation of fitness functions;
step 5.2: after all the individuals after the external benchmarking learning are subjected to fitness function calculation and evaluation, if the first population in the phi-th population is
Figure FDA00030959609500000322
If the fitness function value of each individual is not improved, internal benchmarking learning is carried out and fitness function evaluation is carried out, and the method specifically comprises the following steps: in the phi-th population in the g-th generation
Figure FDA00030959609500000323
The internal learning rate of an individual is
Figure FDA00030959609500000324
Wherein, B'rAn initial value representing an internal learning rate is indicated,
Figure FDA00030959609500000325
is the first in the phi-th population in the g-th generation
Figure FDA00030959609500000326
The Euclidean distance between individual quantum states and internal benchmarks, i.e.
Figure FDA0003095960950000041
R is the diameter of the search space, i.e.
Figure FDA0003095960950000042
Wherein the content of the first and second substances,
Figure FDA0003095960950000043
represents the q-dimension quantum state of the benchmark in the phi-th population in the g-th generation,
Figure FDA0003095960950000044
represents the first in the phi-th population in the g-th generation
Figure FDA0003095960950000045
Q-th dimension of individual quantum state, phi 1,2, …, NP，
Figure FDA0003095960950000046
q is 1,2, …,2P if
Figure FDA0003095960950000047
Then phi in the phi-th population
Figure FDA0003095960950000048
Individual quantum rotation angle vector of
Figure FDA0003095960950000049
Wherein the content of the first and second substances,
Figure FDA00030959609500000410
is [0,1 ]]Uniformly distributed random number, λ1For learning factors during internal benchmarking, quantum states are updated using an analog quantum revolving gate:
Figure FDA00030959609500000411
wherein
Figure FDA00030959609500000412
Represents the first in the phi-th population in the g +1 th generation
Figure FDA00030959609500000413
Q-th dimension of quantum rotation angle, phi 1,2, …, NP，
Figure FDA00030959609500000414
q is 1,2, …,2P, and then the updated quantum state is mapped to moreThe new individual is
Figure FDA00030959609500000415
Then all individuals are subjected to calculation and evaluation of fitness functions;
step 5.3: after all the individuals after internal benchmarking learning are subjected to fitness function calculation and evaluation, if the first population is in the phi-th population
Figure FDA00030959609500000416
If the fitness function value of each individual is not improved, self-learning is carried out and fitness function evaluation is carried out, and the method specifically comprises the following steps: phi in the phi th population
Figure FDA00030959609500000417
The self-learning rate of an individual is
Figure FDA00030959609500000418
Wherein, S'rAn initial value of the self-learning rate is represented,
Figure FDA00030959609500000419
represents the mean fitness value of the phi-th population in the g-th generation,
Figure FDA00030959609500000420
represents the first in the phi-th population in the g-th generation
Figure FDA00030959609500000421
Fitness function value of individual, phi 1,2, …, NP，
Figure FDA00030959609500000422
If it is not
Figure FDA00030959609500000423
Then Logistic chaos mapping is performed, i.e.
Figure FDA00030959609500000424
Wherein λ is2Is a Logistic parameter, λ2∈[0,4]，φ＝1,2,…,NP，
Figure FDA00030959609500000425
q 1,2, …,2P, and then mapping the updated quantum states to updated individuals
Figure FDA00030959609500000426
Then all individuals are subjected to calculation and evaluation of fitness functions;
step 5.4: calculating the average fitness value of each updated population
Figure FDA00030959609500000427
Where, phi is 1,2, …, NPFinding out and recording the individual with the best fitness function value in the phi-th population of the g +1 th iteration
Figure FDA00030959609500000428
Having a quantum state of
Figure FDA00030959609500000429
Where, phi is 1,2, …, NPEstablishing the new internal marker post as a new internal marker post, recording and updating the individual with the optimal fitness function value in the g +1 th iteration whole ecological system
Figure FDA00030959609500000430
Having a quantum state of
Figure FDA00030959609500000431
Setting it as new external marker post, calculating the updated average adaptability value of whole ecological system
Figure FDA0003095960950000051
Where, phi is 1,2, …, NPAverage fitness if compared to the previous generationIf the value is not improved or the external pole is not changed, the individual with the best fitness function value and the corresponding quantum state are exchanged among all the groups, namely, all the groups establish a new internal pole again.
7. The method for dynamically tracking the coherent distribution source under the strong impact noise according to claim 6, wherein: seventhly, judging whether the maximum fast beat number K is reachedpIf the correlation matrix does not reach the preset value, making k equal to k +1, updating the search space of the 2P angular parameters at the next snapshot, and acquiring the next snapshot sampling data, wherein the updating of the weighted norm fraction low-order correlation matrix specifically comprises:
judging whether the maximum fast beat number K is reachedpIf not, updating the search space of the 2P angle parameters in k +1 times of snapshots
Figure FDA0003095960950000052
Figure FDA0003095960950000053
Wherein the content of the first and second substances,
Figure FDA0003095960950000054
to converge constant, μq(k) For the kth snapshot the central value of the search interval for the qth angular parameter, i.e.
Figure FDA0003095960950000055
Figure FDA0003095960950000056
Is a genetic factor, and is a gene of the genetic factor,
Figure FDA0003095960950000057
is the search radius of the search interval,
Figure FDA0003095960950000058
the estimated value of the qth angle parameter for k-1 snapshots, q is 1,2, …, 2P; obtaining the sampling number of k +1 times of snapshotsAccording to x (k +1) ═ x1(k+1),x2(k+1),…,xM(k+1)]TThen the weighted infinite norm normalized signal of the k +1 sample data can be expressed as
Figure FDA0003095960950000059
Wherein, beta is ∈ [0.8,1 ]]As a weighting constant, the increment of the weighted norm fractional low-order correlation matrix constructed by the k-th sampling data can be expressed as
Figure FDA00030959609500000510
Wherein r ism(k+1)＝[r1m(k+1),r2m(k+1),…,rMm(k+1)]TM is 1,2, …, M, i row and l column element
Figure FDA00030959609500000511
Wherein t is a low-order constant, and t is an element [1,2 ]]I ═ 1,2, …, M, l ═ 1,2, …, M, superscript denotes conjugation; constructing an update equation R of a weighted norm fraction low-order correlation matrix after receiving the (k +1) th snapshot sampling dataS(k+1)＝ωRS(k) + (1-omega) R (k +1), wherein RS(k) And R (k +1) is the increment of the weighted norm fraction low-order correlation matrix of the sampling data of the kth snapshot, omega is an updating factor, and k is equal to k + 1.
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