CN113552530A - Near-field and far-field source mixed direction finding method based on quantum mouse group - Google Patents

Near-field and far-field source mixed direction finding method based on quantum mouse group Download PDF

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CN113552530A
CN113552530A CN202110723576.0A CN202110723576A CN113552530A CN 113552530 A CN113552530 A CN 113552530A CN 202110723576 A CN202110723576 A CN 202110723576A CN 113552530 A CN113552530 A CN 113552530A
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CN113552530B (en
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高洪元
张禹泽
杜亚男
刘亚鹏
白浩川
赵海军
刘廷晖
刘凯龙
刘家威
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Harbin Engineering University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/04—Details
    • G01S3/12—Means for determining sense of direction, e.g. by combining signals from directional antenna or goniometer search coil with those from non-directional antenna
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/04—Details
    • G01S3/10—Means for reducing or compensating for quadrantal, site, or like errors
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae

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Abstract

The invention discloses a near-field and far-field source mixed direction finding method based on a quantum rat group, which is characterized in that a separation operator is constructed on the basis of obtaining a far-field source angle, a far-field source fourth-order cumulant matrix can be obtained through the operator, a pure near-field source fourth-order cumulant matrix is obtained through fourth-order cumulant matrix difference, and a related process of parameter search is carried out through a quantum rat group mechanism, so that the technical problems of angle ambiguity and low efficiency of a far-field and near-field signal source separation method existing in the conventional mixed source direction finding method are solved. The method can quickly obtain a more accurate direction finding result of the mixed source, has no quantization error, can expand the aperture of the array through the fourth-order cumulant matrix, improves the direction finding precision, has higher speed and higher precision compared with the traditional near-field and far-field source mixed direction finding method, and breaks through the application limit of the existing method.

Description

Near-field and far-field source mixed direction finding method based on quantum mouse group
Technical Field
The invention relates to a near-field and far-field source mixed direction finding method in a Gaussian noise environment, in particular to a near-field and far-field source mixed direction finding method based on a quantum rat swarm, and belongs to the field of array signal processing.
Background
Passive source localization estimates target parameters of the source using an array signal processing correlation algorithm, through a steering vector matrix and an observed source vector of the sensor array, for example: and parameters such as an azimuth angle, a pitch angle and a distance are reached. Passive source localization belongs to the field of array signal processing, and has wide application in radar, information warfare, seismology, and many military or living fields in microphone arrays, and thus has received wide attention of people.
The classical direction finding method aims at a near-field source or a far-field source signal, however, in an actual engineering problem, a far-field source signal source and a near-field source signal source may exist at the same time, the situation is called as a mixed source, the angle and distance of the near-field source need to be estimated in the direction finding of the mixed source, and for the far-field source, the angle parameter estimation is simplified, so that the traditional far-field source or near-field source positioning method cannot be directly applied to the direction finding of the mixed source, and the direction finding method of the mixed source needs further intensive research.
When the traditional noise subspace algorithm is used for positioning the mixed source, a spectral peak searching process is used, quantization errors exist if a larger spectral peak searching interval is selected, on the contrary, the searching time is longer if a smaller spectral peak searching interval is selected, and the contradiction exists between the estimation precision and the searching time.
Through the search of the prior art document, the inventor finds that Two fourth-order cumulant matrixes are constructed in the "Passive Localization of Mixed Near-Field and Far-Field Sources Using Two-stage MUSIC Algorithm [ J ]" published by the Limb-L.et al in Signal Processing (2010.58(1): 108-) -120 ], the first four-order cumulant matrix only comprises the angle information of the Mixed source, and the angle parameter is obtained by Using the MUSIC Algorithm, the second four-order cumulant matrix comprises the angle and distance information, the search function can be reduced to one dimension by substituting the estimated angle information of all Far-Field Signal Sources and Near-Field Signal Sources into a Two-dimensional MUSIC spectrum peak search function, the Near-Field source distance parameter is estimated, but the method has serious performance reduction and even failure when the angles of the Far-Field source and the Near-Field source are close, angle ambiguity exists, and the calculated amount of the Algorithm is larger due to the construction of the Two fourth-order cumulant matrixes, and the direction finding result has quantization error; he J et al, Signal Processing (2012,60(4):2066-2070.), published "Efficient application of MUSIC algorithm under the existence of far-field and near-field sources [ J ], propose to use oblique projection technique to separate far-field and near-field sources, reduce the amount of calculation and avoid the problem of estimation error due to angular ambiguity, but this method only uses the anti-diagonal line elements of the covariance matrix of the array received data when estimating the parameters of the near-field sources, which results in unsatisfactory azimuth and distance estimation performance of the near-field sources.
The retrieval results of the existing documents show that the existing near-field and far-field source mixed direction finding method has the defects of high calculation complexity, incapability of realizing high-efficiency separation of near-field and far-field source sources and the like, so that a new mixed source separation method is designed, and a new near-field and far-field source mixed direction finding method is further provided.
Disclosure of Invention
Aiming at the prior art, the technical problem to be solved by the invention is to provide a near-field and far-field source mixed direction-finding method which has higher precision and avoids the problem of angle blurring based on a quantum rat group.
In order to solve the technical problem, the invention provides a near-field and far-field source mixed direction-finding method based on a quantum rat group, which comprises the following steps:
the method comprises the following steps: establishing a mathematical model of a uniform symmetric linear array receiving signal under Gaussian noise, which specifically comprises the following steps:
supposing that a uniform linear array consisting of 2N +1 isotropic omnidirectional antennas is arranged, K narrow-band signal sources with the wavelength of lambda have the direction angle of thetak(K1, 2, …, K) is incident on the linear array, assuming the first K1(0≤K1Not more than K) signal sources are far-field signal sources, and K-K is arranged behind the far-field signal sources1The signal source is a near-field source, the distance between adjacent array elements is d, and under the assumption that the signal is a narrow-band signal, for the t-th snapshot, the array element receiving data is x (t) ═ A (theta, r) s (t) + n (t) ═ AF(θ)sF(t)+AF(θ,r)sN(t) + n (t), where the data vector x (t) received by the line array is [ x (t) ]-N(t),x-(N-1)(t),…,x0(t),x1(t),…,xN(t)]TIs (2N +1) × 1 dimension; array noise vector n (t) ═ n-N(t),…,n0(t),n1(t),…,nN(t)]TIs (2N +1) × 1 dimension;
Figure BDA0003137562990000021
is K1 X 1 dimension far field source vector;
Figure BDA0003137562990000022
is (K-K)1) A x 1-dimensional near-field source vector;
Figure BDA0003137562990000023
is (2N + 1). times.K1Array-fashion steering matrix of dimensional far-field sources, where AF(theta) the kth column steering vector of the steering matrix
Figure BDA0003137562990000024
(2N+1)×(K-K1) The steering matrix of the near-field signal source of dimension is
Figure BDA0003137562990000025
Wherein A isN(theta, r) a k-th column steering vector of the steering matrix,
Figure BDA0003137562990000026
step two: design target fitness function F1，F2，F3The method specifically comprises the following steps:
1. design solution of far-field source angle target fitness function F1：
For the t-th snapshot array element receiving vector x (t), a covariance matrix can be constructed
Figure BDA0003137562990000027
Wherein the superscript 'H' represents the conjugate transpose of the matrix, T is the maximum snapshot number of samples, and R is subjected to feature decomposition
Figure BDA0003137562990000031
Wherein the signal subspace UsIs (2N +1) x K dimension, noise subspace UnA diagonal matrix V of dimensions (2N +1) × (2N +1-K), K × KsThe elements on the main diagonal of the diagonal matrix are K large eigenvalues, and the diagonal matrix V with (2N +1-K) x (2N +1-K) dimensionsnThe elements on the main diagonal line of the system consist of the remaining 2N +1-K smaller eigenvalues;
constructing fitness function for solving far field angle
Figure BDA0003137562990000032
Wherein: theta is the vector to be estimated, trace is the trace-solving function,
Figure BDA0003137562990000033
a mapping matrix that is a steering matrix;
2. design solution near-field source angle target fitness function F2：
Constructing a fourth-order cumulant matrix C only containing information source angle information1，C1In
Figure BDA0003137562990000034
An element can be represented as
Figure BDA0003137562990000035
Wherein: c1Is a matrix of (2N +1) × (2N +1) dimensions,
Figure BDA0003137562990000036
Figure BDA0003137562990000037
Figure BDA0003137562990000038
where superscript'. indicates conjugation, E represents the mean, sk(t) represents the envelope of the kth information source at the tth snapshot;
constructing virtual steering vector matrix of far-field information source
Figure BDA0003137562990000039
Wherein
Figure BDA00031375629900000310
For the k-th far-field source angle estimate,
Figure BDA00031375629900000311
constructing a separation operator
Figure BDA00031375629900000312
Therein is marked'+' expressing the pseudo-inverse of the matrix, the fourth-order cumulant matrix of the far-field source
Figure BDA00031375629900000313
Difference C by fourth order cumulant matrix3＝C1-C2Obtaining a fourth-order cumulant matrix C of a near-field source3. To C3Performing feature decomposition
Figure BDA00031375629900000314
Wherein, UC,nIs (2N +1) × (2N +1-K + K1) Dimensional noise subspace, UC,sIs (2N +1) × (K-K)1) Dimension signal subspace, (K-K)1)×(K-K1) Diagonal matrix V of dimensionC,sThe element on the main diagonal is composed of (K-K)1) Formed by a larger eigenvalue, (2N +1-K + K)1)×(2N+1-K+K1) Diagonal matrix V of dimensionC,nThe elements on the main diagonal are composed of the rest 2N +1-K + K1The smaller characteristic values are formed;
constructing fitness function for solving near field angle
Figure BDA00031375629900000315
Wherein:
Figure BDA00031375629900000316
in order to be able to estimate the vector,
Figure BDA00031375629900000318
is a mapping matrix of the virtual steering vector matrix,
Figure BDA00031375629900000317
3. design and solve target fitness function F of near-field source distance3：
Constructing fitness function for solving near-field source distance
Figure BDA0003137562990000041
Wherein:
Figure BDA0003137562990000042
is a vector formed by the estimated value of the near-field source angle, and r is the vector to be estimatedThe vector is counted and the vector is calculated,
Figure BDA0003137562990000043
a mapping matrix that is a steering matrix, satisfying the following relationship:
Figure BDA0003137562990000044
4. in order to separately obtain the angle of the far-field source, the angle of the near-field source and the distance of the near-field source, the maximum fitness function value F according to the quantum rat swarm mechanism needs to be calculated in sequence ξ1,2, 3, 1;
step three: initializing a quantum mouse group, experience factors and environment factors according to the value of xi, and simultaneously selecting corresponding FξAs a fitness function for a quantum rat population algorithm;
step four: the optimization searching process of the quantum individual is realized by using an analog quantum revolving door through an environmental factor and an experience factor;
step five: updating the optimal position of the g +1 th generation of quantum, and updating experience factors and environment factors;
step six: judging the magnitude relation between G +1 and G, if G +1 is less than G, making the iteration number G equal to G +1, and returning to the step four; if G +1 equals G, the mapping state of the optimal quantum position is output
Figure BDA0003137562990000045
As output parameter
Figure BDA0003137562990000046
Step seven: if xi < 3, xi +1, and returning to the third step; if xi is 3, the obtained product
Figure BDA0003137562990000047
As an estimate of the far-field angle,
Figure BDA0003137562990000048
as the near-field angle estimation value,
Figure BDA0003137562990000049
as a near field distance estimate.
The invention also includes:
1. initializing a quantum mouse group, experience factors and environment factors according to the value of xi, and simultaneously selecting corresponding FξThe fitness function of the quantum rat group algorithm is specifically as follows:
dimension of the mouse quantum site is SξInitializing quantum mouse group space, wherein the number of individuals in the quantum mouse group is M, the maximum iteration number is G, the iteration number is G, and in the G-th iteration, the M-th quantum mouse is in SξThe quantum locations in the dimensional search space are
Figure BDA00031375629900000410
The S (S is 1,2, …, S) of the quantum position of the primary quantum mouse group when g is 1ξ) Dimension initialization to [0,1 ]]The quantum position of the mouse individual can obtain the corresponding mapping state position through the mapping relation, namely the mapping state position
Figure BDA00031375629900000411
The mapping rule is as follows:
Figure BDA00031375629900000412
wherein
Figure BDA00031375629900000413
Figure BDA00031375629900000414
In order to solve the upper limit of the s-dimension variable of the mouse mapping state position when the xi fitness function F (xi) is solved,
Figure BDA00031375629900000415
to solve the xi fitness function F (xi) the lower limit of the S-dimension variable of the mouse mapping state position, S is 1,2, …, Sξ；
Calculating the fitness value of the quantum position of the rat swarm and obtaining the quantum optimal position, p, of the rat swarmgRepresents the optimum found up to the g-th generationThe quantum position of the quantum well is determined,
Figure BDA00031375629900000416
obtaining the mapping state position of the quantum position of the initial mouse group through a mapping equation
Figure BDA0003137562990000051
Substituting into fitness function FξCalculating and calculating the first generation experience factor of the mth mouse
Figure BDA0003137562990000052
Initializing fitness function value corresponding to mth mouse
Figure BDA0003137562990000053
pgInitializing to a quantum position with the maximum fitness function value in the first generation population, and sequencing M quantum mice according to experience factors of the first generation quantum mice, wherein the experience factor of the mouse with the number of 1 is T1 1On the basis, the optimal empirical factor of the initial generation is obtained
Figure BDA0003137562990000054
Wherein upsilon is in [0,1 ]]Random numbers uniformly distributed among them;
environmental factors of the m-th mouse in the g-th generation
Figure BDA0003137562990000055
The specific expression of (a) is as follows:
Figure BDA0003137562990000056
wherein: m is 1,2, … M,
Figure BDA0003137562990000057
is the optimal empirical factor of the g generation.
2. Fourthly, the quantum individual optimizing search process is realized through the environment factor and the experience factor by using the analog quantum revolving door, and the method specifically comprises the following steps:
step 4.1: defining the comprehensive factor of the m-th mouse in the g-th generation
Figure BDA0003137562990000058
Wherein:
Figure BDA0003137562990000059
environmental factors of the m-th mouse in the g-th generation,
Figure BDA00031375629900000510
is the experience factor of the m-th mouse in the g-th generation, w1And w2Weight factors of experience factor and environment factor respectively, and satisfy w1+w 21, the individual combination factors of the M (M-1, 2, … M) th rat were obtained
Figure BDA00031375629900000511
Thereafter, the individual transfer probability of the mth mouse was calculated:
Figure BDA00031375629900000512
step 4.2: two quantum rotation angles, p, are defined and calculated1(0≤p1≦ 1) as global search probability when
Figure BDA00031375629900000513
At this time, the mth rat performs the first quantum rotation angle of the dimension s for the mth rat quantum position
Figure BDA00031375629900000514
Wherein
Figure BDA00031375629900000515
Is a comprehensive factor of the mth mouse in the g iteration, g is the current iteration frequency, h (h is more than 0 and less than 1) is a control factor, upsilon3Is at [0,1 ]]Random numbers uniformly distributed among them; when in use
Figure BDA00031375629900000516
At this time, the m-th mouse holdsAnd (3) performing a second quantum rotation angle, wherein a global search is required to make the individuals of the rat father population face the current global optimal solution pgPerforming a change to affect a step length and an adjustment direction of a quantum rotation angle of the quantum rotation angle using a global optimal solution; for the mth mouse quantum position, the rotation angle of the second quantum is
Figure BDA00031375629900000517
Wherein: s is 1,2, …, Sξ，υ4Is at [0,1 ]]Random numbers uniformly distributed among them;
step 4.3: generation of quantum positions of mth mouse generation by simulating variation process using simulated quantum revolving door
Figure BDA00031375629900000518
The mth dimension of the mouse offspring is calculated as
Figure BDA00031375629900000519
Figure BDA0003137562990000061
Step 4.4: calculating mouse offspring
Figure BDA0003137562990000062
The quantum position vector maps the corresponding fitness value of the state and generates the quantum position from the father generation
Figure BDA0003137562990000063
And daughter quantum positions
Figure BDA0003137562990000064
In a total of 2M quantum positions, selecting the optimal M quantum positions as next generation quantum individual quantum positions
Figure BDA0003137562990000065
Calculating mouse offspring
Figure BDA0003137562990000066
The quantum position vector maps the corresponding fitness value of the state and generates the quantum position from the father generation
Figure BDA0003137562990000067
And daughter quantum positions
Figure BDA0003137562990000068
In a total of 2M quantum positions, selecting the optimal M quantum positions as next generation quantum individual quantum positions
Figure BDA0003137562990000069
3. Step five, updating the optimal position of the g +1 th generation of quantum, and updating experience factors and environment factors, specifically:
step 5.1: computing new generation of mth individual quantum position vector
Figure BDA00031375629900000610
Mapping state
Figure BDA00031375629900000611
In the fitness function FξLower fitness value
Figure BDA00031375629900000612
Obtaining a transition empirical factor
Figure BDA00031375629900000613
Sorting the transition experience factors to obtain the maximum value thereof
Figure BDA00031375629900000614
The corresponding quantum position is
Figure BDA00031375629900000615
Will be provided with
Figure BDA00031375629900000616
And Fξ(pg) Make a comparison if
Figure BDA00031375629900000617
Then
Figure BDA00031375629900000618
If it is
Figure BDA00031375629900000619
Then p isg+1＝pgThe mapping state of the optimal quantum position of the g +1 th generation is
Figure BDA00031375629900000620
Step 5.2: the idea of differential evolution is adopted, variation operation is carried out by using experience factors among individuals, and the experience factor of the mth mouse is updated according to the following rules:
Figure BDA00031375629900000621
wherein: rho is an empirical evaporation coefficient, and the distribution interval of rho is [0,1 ]]And Δ T is an empirical variable,
Figure BDA00031375629900000622
wherein: upsilon is2Represents the scaling factor, v2Is [0,1 ]]Uniformly distributed random numbers in between, z1And z2For randomly introduced quantum mouse individuals to perform mutation operations, z1＝(1,2,…,M),z2＝(1,2,…,M)；
Step 5.3: updated experience factor for mth mouse
Figure BDA00031375629900000623
Make a judgment if
Figure BDA00031375629900000624
Then
Figure BDA00031375629900000625
For M mice experience factor
Figure BDA00031375629900000626
Arranged from large to small to obtainTo obtain its maximum value T1 g+1On the basis, the optimal empirical factor of the g +1 th generation is obtained
Figure BDA00031375629900000627
Wherein: upsilon is5Is at [0,1 ]]Uniformly distributed random numbers in between.
The invention has the beneficial effects that: aiming at the defects and shortcomings of the existing near-field and far-field source mixed direction finding method, a new near-field and far-field source mixed direction finding method is designed, mixed source signals are separated by designing a new separation operator, a related special fourth-order cumulant matrix is constructed by combining the related knowledge of high-order cumulant to estimate the angle of a near-field source, and finally the near-field source angle information is substituted to realize distance estimation. The designed method has higher direction finding precision and avoids the problem of angle blurring.
Compared with the prior art, the invention designs the high-efficiency near-field and far-field source mixed direction finding method aiming at the problems of angle ambiguity existing in the existing near-field and far-field source mixed direction finding method or array aperture loss existing in near-field source estimation, realizes the separation of the near-field and far-field sources by constructing the separation operator and combining the four-order cumulant matrix, has the inhibiting effect on Gaussian background noise due to the four-order cumulant matrix, has excellent separation performance, can effectively solve the information source, can still effectively perform the near-field and far-field source mixed direction finding when the angles of the near-field source and the far-field source are closer, and has higher estimation precision due to no array aperture loss, so that the designed method is more suitable for engineering practice.
The near-field and far-field source mixed direction finding method based on the quantum rat swarm mechanism can quickly obtain a relatively accurate mixed source direction finding result, does not have quantization error, can expand the array aperture through a fourth-order cumulant matrix, and improves the direction finding precision. Simulation experiments prove the effectiveness of the near-field and far-field source mixed direction-finding method based on the quantum rat swarm mechanism, and compared with the traditional near-field and far-field source mixed direction-finding method, the method has the advantages of higher speed and higher precision, and breaks through the application limitation of the existing method.
Drawings
FIG. 1 is a flow chart of a near-field and far-field source mixed direction finding method based on quantum rat swarm designed by the invention;
FIG. 2 is a plot of root mean square error versus signal-to-noise ratio for a far-field angle estimate;
FIG. 3 is a plot of success probability versus signal-to-noise ratio for far-field angle estimation;
FIG. 4 is a plot of root mean square error versus signal-to-noise ratio for near field angle estimates;
FIG. 5 is a plot of estimated success probability versus signal-to-noise ratio for near-field angle estimation;
FIG. 6 is a plot of root mean square error versus signal-to-noise ratio for near field distance estimates;
FIG. 7 is a plot of estimated success probability versus signal-to-noise ratio for near-field distance estimation.
Detailed Description
The invention is further described with reference to the drawings and the detailed description.
With reference to fig. 1, a near-field and far-field source hybrid direction finding method based on quantum rat population of the present invention includes the following steps:
step one, establishing a mathematical model of a uniform symmetric linear array receiving signal under Gaussian noise.
Supposing that a uniform linear array consisting of 2N +1 isotropic omnidirectional antennas is arranged, K narrow-band signal sources with the wavelength of lambda have the direction angle of thetak(K1, 2, …, K) is incident on the linear array, assuming the first K1(0≤K1Not more than K) signal sources are far-field signal sources, and K-K is arranged behind the far-field signal sources1Each source is a near field source. The distance between adjacent array elements is d, and under the assumption that the signal is a narrow-band signal, for the t-th snapshot, the array element receiving data is x (t) ═ a (θ, r) s (t) + n (t) ═ aF(θ)sF(t)+AF(θ,r)sN(t) + n (t), where the data vector x (t) received by the line array is [ x (t) ]-N(t),x-(N-1)(t),…,x0(t),x1(t),…,xN(t)]TIs (2N +1) × 1 dimension; array noise vector n (t) ═ n-N(t),…,n0(t),n1(t),…,nN(t)]TIs (2N +1) × 1 dimension;
Figure BDA0003137562990000071
is K1X 1 dimension far field source vector;
Figure BDA0003137562990000072
is (K-K)1) A x 1-dimensional near-field source vector;
Figure BDA0003137562990000073
is (2N + 1). times.K1Array-fashion steering matrix of dimensional far-field sources, where AF(theta) the kth column steering vector of the steering matrix
Figure BDA0003137562990000074
(2N+1)×(K-K1) The steering matrix of the near-field signal source of dimension is
Figure BDA0003137562990000081
Wherein A isN(theta, r) a k-th column steering vector of the steering matrix,
Figure BDA0003137562990000082
step two, designing a target fitness function F1，F2，F3The method comprises the following specific steps:
1. design solution of far-field source angle target fitness function F1。
For the t-th snapshot array element receiving vector x (t), a covariance matrix can be constructed
Figure BDA0003137562990000083
Where the superscript 'H' represents the conjugate transpose of the matrix and T is the maximum snapshot number. Performing characteristic decomposition on R
Figure BDA0003137562990000084
Wherein the signal subspace UsIs (2N +1) x K dimension, noise subspace UnA diagonal matrix V of dimensions (2N +1) × (2N +1-K), K × KsIts main pairThe elements on the angular line are composed of K larger eigenvalues, and the diagonal matrix V with (2N +1-K) x (2N +1-K) dimensionsnThe elements on its main diagonal are made up of the remaining 2N +1-K smaller eigenvalues.
Constructing fitness function for solving far field angle
Figure BDA0003137562990000085
Wherein: theta is the vector to be estimated, trace is the trace-solving function,
Figure BDA0003137562990000086
a mapping matrix that is a steering matrix.
2. Design solution near-field source angle target fitness function F2。
Constructing a fourth-order cumulant matrix C only containing information source angle information1，C1In
Figure BDA0003137562990000087
An element can be represented as
Figure BDA0003137562990000088
Wherein: c1Is a matrix of (2N +1) × (2N +1) dimensions,
Figure BDA0003137562990000089
Figure BDA00031375629900000810
Figure BDA00031375629900000811
where superscript'. indicates conjugation, E represents the mean, sk(t) represents the envelope of the kth source at the tth snapshot.
Constructing virtual steering vector matrix of far-field information source
Figure BDA00031375629900000812
Wherein
Figure BDA00031375629900000813
Is as followsk far-field source angle estimates,
Figure BDA00031375629900000814
constructing a separation operator
Figure BDA00031375629900000815
Wherein the superscript '+' represents the pseudo-inverse of the matrix, and the far-field source obtains the fourth-order cumulant matrix
Figure BDA0003137562990000091
Difference C by fourth order cumulant matrix3＝C1-C2Obtaining a fourth-order cumulant matrix C of a near-field source3. To C3Performing feature decomposition
Figure BDA0003137562990000092
Wherein, UC,nIs (2N +1) × (2N +1-K + K1) Dimensional noise subspace, UC,sIs (2N +1) × (K-K)1) Dimension signal subspace, (K-K)1)×(K-K1) Diagonal matrix V of dimensionC,sThe element on the main diagonal is composed of (K-K)1) Formed by a larger eigenvalue, (2N +1-K + K)1)×(2N+1-K+K1) Diagonal matrix V of dimensionC,nThe elements on the main diagonal are composed of the rest 2N +1-K + K1The smaller eigenvalues.
Constructing fitness function for solving near field angle
Figure BDA0003137562990000093
Wherein:
Figure BDA00031375629900000914
in order to be able to estimate the vector,
Figure BDA00031375629900000916
is a mapping matrix of the virtual steering vector matrix,
Figure BDA00031375629900000915
3. designing and solving target fitness function of near-field source distanceF3。
Constructing fitness function for solving near-field source distance
Figure BDA0003137562990000094
Wherein:
Figure BDA0003137562990000095
is a vector formed by the estimated values of the near-field source angles, r is a vector to be estimated,
Figure BDA0003137562990000096
a mapping matrix that is a steering matrix, satisfying the following relationship:
Figure BDA0003137562990000097
4. in order to separately obtain the angle of the far-field source, the angle of the near-field source and the distance of the near-field source, the maximum fitness function value F according to the quantum rat swarm mechanism needs to be calculated in sequenceξXi is 1,2, 3, and xi is 1 initially.
Step three: initializing a quantum mouse group, experience factors and environment factors according to the value of xi, and simultaneously selecting corresponding FξThe fitness function of the quantum rat group algorithm comprises the following specific steps
Dimension of the mouse quantum site is SξA quantum rat population space was initialized. The number of individuals in the quantum mouse group is M, the maximum iteration number is G, and the number of iterations is G. In the g iteration, m number of mice in SξThe quantum locations in the dimensional search space are
Figure BDA0003137562990000098
The S (S is 1,2, …, S) of the quantum position of the primary quantum mouse group when g is 1ξ) Dimension initialization to [0,1 ]]The quantum position of the mouse individual can obtain the corresponding mapping state position through the mapping relation, namely the mapping state position
Figure BDA0003137562990000099
The mapping rule is as follows:
Figure BDA00031375629900000910
wherein
Figure BDA00031375629900000911
Figure BDA00031375629900000912
In order to solve the upper limit of the s-dimension variable of the mouse mapping state position when the xi fitness function F (xi) is solved,
Figure BDA00031375629900000913
to solve the xi fitness function F (xi) the lower limit of the S-dimension variable of the mouse mapping state position, S is 1,2, …, Sξ。
Calculating the fitness value of the quantum position of the rat swarm and obtaining the quantum optimal position, p, of the rat swarmgIndicating the optimal quantum position found up to the g-th generation,
Figure BDA0003137562990000101
obtaining the mapping state position of the quantum position of the initial mouse group through a mapping equation
Figure BDA0003137562990000102
Substituting into fitness function FξCalculating and calculating the first generation experience factor of the mth mouse
Figure BDA0003137562990000103
Initializing fitness function value corresponding to mth mouse
Figure BDA0003137562990000104
pgAnd initializing the quantum position with the maximum fitness function value in the first generation population. Sorting M quantum mice according to experience factors of the first generation quantum mice, wherein the experience factor of the mice numbered 1 is T1 1On the basis, the optimal empirical factor of the initial generation is obtained
Figure BDA0003137562990000105
Wherein upsilon is in [0,1 ]]Uniformly distributed random numbers in between.
The second part of the environmental factors, humidity, brightness, etc. of the environment have an effect on the mouse. Environmental factors of the m-th mouse in the g-th generation
Figure BDA0003137562990000106
The specific expression of (a) is as follows:
Figure BDA0003137562990000107
wherein: m is 1,2, … M,
Figure BDA0003137562990000108
is the optimal empirical factor of the g generation.
Step four: and (3) realizing the optimization searching process of the quantum individuals by using an analog quantum revolving gate through an environmental factor and an experience factor. Comprises the following specific steps
1. Defining the comprehensive factor of the m-th mouse in the g-th generation
Figure BDA0003137562990000109
Wherein:
Figure BDA00031375629900001010
environmental factors of the m-th mouse in the g-th generation,
Figure BDA00031375629900001011
is the experience factor of the m-th mouse in the g-th generation, w1And w2Weight factors of experience factor and environment factor respectively, and satisfy w1+w 21. Obtaining the comprehensive factor of the M (M-1, 2, … M) mice
Figure BDA00031375629900001012
Thereafter, the individual transfer probability of the m-th mouse was calculated
Figure BDA00031375629900001013
2. Two quantum rotation angles, p, are defined and calculated1(0≤p1Less than or equal to 1) as a global search summaryRate of change
Figure BDA00031375629900001014
At this time, the mth mouse executes a first quantum rotation angle, the first quantum rotation angle enables the individuals of the parent mouse group located in the better quantum interval to change only in a very small range, and the step length of the quantum rotation angle is influenced by using the comprehensive factors of the mouse individuals and the current iteration times. For the mth mouse quantum position, the rotation angle of the first quantum in the s-dimension is
Figure BDA00031375629900001015
Wherein
Figure BDA00031375629900001016
Is a comprehensive factor of the mth mouse in the g iteration, g is the current iteration frequency, h (h is more than 0 and less than 1) is a control factor, upsilon3Is at [0,1 ]]Uniformly distributed random numbers in between. When in use
Figure BDA00031375629900001017
At this time, the mth mouse executes the second quantum rotation angle, because the combination factor of the mth mouse is smaller, and the mouse is located at a poor quantum position, the global search needs to be performed for the two quantum rotation angles to make the individuals of the parent mouse group face the current global optimal solution pgThe variation is performed using a global optimal solution to affect the step size and the adjustment direction of the quantum rotation angle. For the mth mouse quantum position, the rotation angle of the second quantum is
Figure BDA0003137562990000111
Wherein: s is 1,2, …, Sξ，υ4Is at [0,1 ]]Uniformly distributed random numbers in between.
3. Generation of quantum positions of mth mouse generation by simulating variation process using simulated quantum revolving door
Figure BDA0003137562990000112
The mth dimension of the mouse offspring is calculated as
Figure BDA0003137562990000113
4. Calculating mouse offspring
Figure BDA0003137562990000114
The quantum position vector maps the corresponding fitness value of the state and generates the quantum position from the father generation
Figure BDA0003137562990000115
And daughter quantum positions
Figure BDA0003137562990000116
In a total of 2M quantum positions, selecting the optimal M quantum positions as next generation quantum individual quantum positions
Figure BDA0003137562990000117
Calculating mouse offspring
Figure BDA0003137562990000118
The quantum position vector maps the corresponding fitness value of the state and generates the quantum position from the father generation
Figure BDA0003137562990000119
And daughter quantum positions
Figure BDA00031375629900001110
In a total of 2M quantum positions, selecting the optimal M quantum positions as next generation quantum individual quantum positions
Figure BDA00031375629900001111
Step five: updating the optimal position of the g +1 th generation of quantum, and updating an empirical factor and an environmental factor, wherein the method comprises the following specific steps of:
1. computing new generation of mth individual quantum position vector
Figure BDA00031375629900001112
Mapping state
Figure BDA00031375629900001113
In the fitness function FξLower fitness value
Figure BDA00031375629900001114
Obtaining a transition empirical factor
Figure BDA00031375629900001115
Sorting the transition experience factors to obtain the maximum value thereof
Figure BDA00031375629900001116
The corresponding quantum position is
Figure BDA00031375629900001117
Will be provided with
Figure BDA00031375629900001118
And Fξ(pg) Make a comparison if
Figure BDA00031375629900001119
Then
Figure BDA00031375629900001120
If it is
Figure BDA00031375629900001121
Then p isg+1＝pgThe mapping state of the optimal quantum position of the g +1 th generation is
Figure BDA00031375629900001122
2. The idea of differential evolution is adopted, and the variation operation is carried out by using empirical factors among a plurality of individuals. The experience factor for the mth mouse is updated according to the following rules:
Figure BDA00031375629900001123
wherein: rho is an empirical evaporation coefficient, and the distribution interval of rho is [0,1 ]]And Δ T is an empirical variable,
Figure BDA00031375629900001124
wherein: upsilon is2Represents the scaling factor, v2Is [0,1 ]]Uniformly distributed random numbers in between, z1And z2For randomly introduced quantum mouse individuals to perform mutation operations, z1＝(1,2,…,M),z2＝(1,2,…,M)。
3. Updated experience factor for mth mouse
Figure BDA00031375629900001125
Make a judgment if
Figure BDA00031375629900001126
Then
Figure BDA00031375629900001127
For M mice experience factor
Figure BDA00031375629900001128
Arranged from large to small to obtain the maximum value T1 g+1On the basis, the optimal empirical factor of the g +1 th generation is obtained
Figure BDA00031375629900001129
Wherein: upsilon is5Is at [0,1 ]]Uniformly distributed random numbers in between.
Step six: judging the magnitude relation between G +1 and G, if G +1 is less than G, making the iteration number G equal to G +1, and returning to the step four; if G +1 equals G, then outputting the mapping state of the optimal quantum position
Figure BDA0003137562990000121
As output parameter
Figure BDA0003137562990000122
Step seven: if xi < 3, xi +1, and returning to the third step; if xi is 3, the obtained product
Figure BDA0003137562990000123
As far field angleThe value of the estimated value is,
Figure BDA0003137562990000124
as the near-field angle estimation value,
Figure BDA0003137562990000125
as a near field distance estimate.
In FIGS. 2 to 7, the Near-field source ESPRIT-like algorithm mentioned in "Near sources localization using symmetry superbras [ J ]" published in IEEE Signal Processing Letters,2007,4(4): 409-. The second-order accumulation-based oblique projection algorithm mentioned in "Efficient application of MUSIC algorithm under the correlation of far-field and near-field sources [ J ]" also in accordance with He J et al Signal Processing (2012,60(4):2066-2070 ]) works well and also achieves source separation of near-field and far-field, using the second-order accumulation-based oblique projection algorithm as the second comparison object.
In simulation experiments, the fast beat number is 300, the signal-to-noise ratio is increased from 0dB to 20dB, and the incident angle of a far-field source is assumed to be theta1At 25 °, the angle of incidence and distance of the near field source is (θ)2,r2) The frequency of the signal source is 471MHz (13 degrees and 10m), the uniform symmetrical linear array is composed of 9 sensors, the array element distance d is 0.25 lambda, the narrow-band point source non-Gaussian stationary random process with equal power is adopted by no matter the far-field signal source or the near-field signal source, and the global search probability p10.01, 100 maximum iteration number G, and weight factor w1＝0.8，w20.2, 50 for the population size M, 0.1 for the control factor h, 0.2 for the empirical evaporation coefficient p, S1＝K1，S2＝K-K1，S3＝K-K1，
Figure BDA0003137562990000126
Figure BDA0003137562990000127
And the absolute value of the difference between the specified estimation parameter and the actual parameter is less than 0.2, and the estimation is judged to be successful. In a Gaussian complex white noise environment, comparing the variation curves of the root mean square error of angle and distance estimation and the estimation success probability along with the root mean square error, it can be known from fig. 2 that the root mean square error of the far-field source angle estimation of the calculation method is not much different from the oblique projection algorithm, but is stronger than the ESPRIT-like algorithm, the estimation success probability is improved by more than 10% compared with the ESPRIT-like algorithm from fig. 3, and it can be known from fig. 4, fig. 5, fig. 6 and fig. 7 that the angle and distance estimation performance of the designed algorithm at a near-field source is stronger than the ESPRIT-like algorithm and the oblique projection algorithm, and the root mean square error and the success probability are both obviously improved. The method designed by the invention has the advantages over the traditional near-field and far-field source mixed direction-finding method.

Claims (4)

1. A near-field and far-field source mixed direction-finding method based on quantum rat groups is characterized by comprising the following steps:
the method comprises the following steps: establishing a mathematical model of a uniform symmetric linear array receiving signal under Gaussian noise, which specifically comprises the following steps:
supposing that a uniform linear array consisting of 2N +1 isotropic omnidirectional antennas is arranged, K narrow-band signal sources with the wavelength of lambda have the direction angle of thetak(K1, 2, …, K) is incident on the linear array, assuming the first K1(0≤K1Not more than K) signal sources are far-field signal sources, and K-K is arranged behind the far-field signal sources1The signal source is a near-field source, the distance between adjacent array elements is d, and under the assumption that the signal is a narrow-band signal, for the t-th snapshot, the array element receiving data is x (t) ═ A (theta, r) s (t) + n (t) ═ AF(θ)sF(t)+AF(θ,r)sN(t) + n (t), where the data vector x (t) received by the line array is [ x (t) ]-N(t),x-(N-1)(t),…,x0(t),x1(t),…,xN(t)]TIs (2N +1) × 1 dimension; array noise vector n (t) ═ n-N(t),…,n0(t),n1(t),…,nN(t)]TIs (2N +1) × 1 dimension;
Figure FDA0003137562980000011
is K1X 1 dimension far field source vector;
Figure FDA0003137562980000012
is (K-K)1) A x 1-dimensional near-field source vector;
Figure FDA0003137562980000013
is (2N + 1). times.K1Array-fashion steering matrix of dimensional far-field sources, where AF(theta) the kth column steering vector of the steering matrix
Figure FDA0003137562980000014
(2N+1)×(K-K1) The steering matrix of the near-field signal source of dimension is
Figure FDA0003137562980000015
Wherein A isN(theta, r) a k-th column steering vector of the steering matrix,
Figure FDA0003137562980000016
step two: design target fitness function F1，F2，F3The method specifically comprises the following steps:
1. design solution of far-field source angle target fitness function F1：
For the t-th snapshot array element receiving vector x (t), a covariance matrix can be constructed
Figure FDA0003137562980000017
Wherein the superscript 'H' represents the conjugate transpose of the matrix, T is the maximum snapshot number of samples, and R is subjected to feature decomposition
Figure FDA0003137562980000018
Wherein the signal subspace UsIs (2N +1) x K dimension, noise subspace UnA diagonal matrix V of dimensions (2N +1) × (2N +1-K), K × KsThe elements on the main diagonal are larger by KA diagonal matrix V of (2N +1-K) × (2N +1-K) dimensions formed by eigenvaluesnThe elements on the main diagonal line of the system consist of the remaining 2N +1-K smaller eigenvalues;
constructing fitness function for solving far field angle
Figure FDA0003137562980000019
Wherein: theta is the vector to be estimated, trace is the trace-solving function,
Figure FDA00031375629800000110
a mapping matrix that is a steering matrix;
2. design solution near-field source angle target fitness function F2：
Constructing a fourth-order cumulant matrix C only containing information source angle information1，C1In
Figure FDA00031375629800000111
An element can be represented as
Figure FDA00031375629800000112
Wherein: c1Is a matrix of (2N +1) × (2N +1) dimensions,
Figure FDA00031375629800000113
Figure FDA0003137562980000021
Figure FDA0003137562980000022
where superscript'. indicates conjugation, E represents the mean, sk(t) represents the envelope of the kth information source at the tth snapshot;
constructing virtual steering vector matrix of far-field information source
Figure FDA0003137562980000023
Wherein
Figure FDA0003137562980000024
For the k-th far-field source angle estimate,
Figure FDA0003137562980000025
constructing a separation operator
Figure FDA0003137562980000026
Wherein the superscript '+' represents the pseudo-inverse of the matrix, and the far-field source obtains the fourth-order cumulant matrix
Figure FDA0003137562980000027
Difference C by fourth order cumulant matrix3＝C1-C2Obtaining a fourth-order cumulant matrix C of a near-field source3. To C3Performing feature decomposition
Figure FDA0003137562980000028
Wherein, UC,nIs (2N +1) × (2N +1-K + K1) Dimensional noise subspace, UC,sIs (2N +1) × (K-K)1) Dimension signal subspace, (K-K)1)×(K-K1) Diagonal matrix V of dimensionC,sThe element on the main diagonal is composed of (K-K)1) Formed by a larger eigenvalue, (2N +1-K + K)1)×(2N+1-K+K1) Diagonal matrix V of dimensionC,nThe elements on the main diagonal are composed of the rest 2N +1-K + K1The smaller characteristic values are formed;
constructing fitness function for solving near field angle
Figure FDA0003137562980000029
Wherein:
Figure FDA00031375629800000210
in order to be able to estimate the vector,
Figure FDA00031375629800000211
is a mapping matrix of the virtual steering vector matrix,
Figure FDA00031375629800000212
3. design and solve target fitness function F of near-field source distance3：
Constructing fitness function for solving near-field source distance
Figure FDA00031375629800000213
Wherein:
Figure FDA00031375629800000214
is a vector formed by the estimated values of the near-field source angles, r is a vector to be estimated,
Figure FDA00031375629800000215
a mapping matrix that is a steering matrix, satisfying the following relationship:
Figure FDA00031375629800000216
4. in order to separately obtain the angle of the far-field source, the angle of the near-field source and the distance of the near-field source, the maximum fitness function value F according to the quantum rat swarm mechanism needs to be calculated in sequenceξ1,2, 3, 1;
step three: initializing a quantum mouse group, experience factors and environment factors according to the value of xi, and simultaneously selecting corresponding FξAs a fitness function for a quantum rat population algorithm;
step four: the optimization searching process of the quantum individual is realized by using an analog quantum revolving door through an environmental factor and an experience factor;
step five: updating the optimal position of the g +1 th generation of quantum, and updating experience factors and environment factors;
step six: judging the magnitude relation between G +1 and G, if G +1 is less than G, making the iteration number G equal to G +1, and returning to the step four; if G +1 equals G, the mapping state of the optimal quantum position is output
Figure FDA00031375629800000217
As output parameter
Figure FDA00031375629800000218
Step seven: if xi < 3, xi +1, and returning to the third step; if xi is 3, the obtained product
Figure FDA0003137562980000031
As an estimate of the far-field angle,
Figure FDA0003137562980000032
as the near-field angle estimation value,
Figure FDA0003137562980000033
as a near field distance estimate.
2. The method of claim 1, wherein the method comprises the following steps: initializing a quantum mouse group, experience factors and environment factors according to the value of xi, and simultaneously selecting corresponding FξThe fitness function of the quantum rat group algorithm is specifically as follows:
dimension of the mouse quantum site is SξInitializing quantum mouse group space, wherein the number of individuals in the quantum mouse group is M, the maximum iteration number is G, the iteration number is G, and in the G-th iteration, the M-th quantum mouse is in SξThe quantum locations in the dimensional search space are
Figure FDA0003137562980000034
The S (S is 1,2, …, S) of the quantum position of the primary quantum mouse group when g is 1ξ) Dimension initialization to [0,1 ]]The quantum position of the mouse individual can obtain the corresponding mapping state position through the mapping relation, namely the mapping state position
Figure FDA0003137562980000035
Mapping rulesComprises the following steps:
Figure FDA0003137562980000036
wherein
Figure FDA0003137562980000037
Figure FDA0003137562980000038
In order to solve the upper limit of the s-dimension variable of the mouse mapping state position when the xi fitness function F (xi) is solved,
Figure FDA0003137562980000039
to solve the xi fitness function F (xi) the lower limit of the S-dimension variable of the mouse mapping state position, S is 1,2, …, Sξ；
Calculating the fitness value of the quantum position of the rat swarm and obtaining the quantum optimal position, p, of the rat swarmgIndicating the optimal quantum position found up to the g-th generation,
Figure FDA00031375629800000310
obtaining the mapping state position of the quantum position of the initial mouse group through a mapping equation
Figure FDA00031375629800000311
Substituting into fitness function FξCalculating and calculating the first generation experience factor of the mth mouse
Figure FDA00031375629800000312
Initializing fitness function value corresponding to mth mouse
Figure FDA00031375629800000313
pgInitializing to a quantum position with the maximum fitness function value in the first generation population, and sequencing M quantum mice according to experience factors of the first generation quantum mice, wherein the experience factor of the mouse with the number of 1 is T1 1On the basis, the optimal empirical factor of the initial generation is obtained
Figure FDA00031375629800000314
Wherein upsilon is in [0,1 ]]Random numbers uniformly distributed among them;
environmental factors of the m-th mouse in the g-th generation
Figure FDA00031375629800000315
The specific expression of (a) is as follows:
Figure FDA00031375629800000316
wherein: m is 1,2, … M,
Figure FDA00031375629800000317
is the optimal empirical factor of the g generation.
3. A method of mixed near-field and far-field source direction finding based on quantum mouse population according to claim 1 or 2, characterized by: fourthly, the optimization searching process of the quantum individuals is realized by using the simulated quantum revolving door through the environmental factors and the experience factors, and the optimization searching process specifically comprises the following steps:
step 4.1: defining the comprehensive factor of the m-th mouse in the g-th generation
Figure FDA00031375629800000318
Wherein:
Figure FDA00031375629800000319
environmental factors of the m-th mouse in the g-th generation,
Figure FDA0003137562980000041
is the experience factor of the m-th mouse in the g-th generation, w1And w2Weight factors of experience factor and environment factor respectively, and satisfy w1+w21, the individual combination factors of the M (M-1, 2, … M) th rat were obtained
Figure FDA0003137562980000042
Thereafter, the individual transfer probability of the mth mouse was calculated:
Figure FDA0003137562980000043
step 4.2: two quantum rotation angles, p, are defined and calculated1(0≤p1≦ 1) as global search probability when
Figure FDA0003137562980000044
At this time, the mth rat performs the first quantum rotation angle of the dimension s for the mth rat quantum position
Figure FDA0003137562980000045
Wherein
Figure FDA0003137562980000046
Is a comprehensive factor of the mth mouse in the g iteration, g is the current iteration frequency, h (h is more than 0 and less than 1) is a control factor, upsilon3Is at [0,1 ]]Random numbers uniformly distributed among them; when in use
Figure FDA0003137562980000047
At this time, the mth mouse executes the second quantum rotation angle, and the global search for the second quantum rotation angle is required to make the individuals of the parent mouse group face the current global optimal solution pgPerforming a change to affect a step length and an adjustment direction of a quantum rotation angle of the quantum rotation angle using a global optimal solution; for the mth mouse quantum position, the rotation angle of the second quantum is
Figure FDA0003137562980000048
Wherein: s is 1,2, …, Sξ，υ4Is at [0,1 ]]Random numbers uniformly distributed among them;
step 4.3: generation of quantum positions of mth mouse generation by simulating variation process using simulated quantum revolving door
Figure FDA0003137562980000049
The mth dimension of the mouse offspring is calculated as
Figure FDA00031375629800000410
Figure FDA00031375629800000411
Step 4.4: calculating mouse offspring
Figure FDA00031375629800000412
The quantum position vector maps the corresponding fitness value of the state and generates the quantum position from the father generation
Figure FDA00031375629800000413
And daughter quantum positions
Figure FDA00031375629800000414
In a total of 2M quantum positions, selecting the optimal M quantum positions as next generation quantum individual quantum positions
Figure FDA00031375629800000415
Calculating mouse offspring
Figure FDA00031375629800000416
The quantum position vector maps the corresponding fitness value of the state and generates the quantum position from the father generation
Figure FDA00031375629800000417
And daughter quantum positions
Figure FDA00031375629800000418
In a total of 2M quantum positions, selecting the optimal M quantum positions as next generation quantum individual quantum positions
Figure FDA00031375629800000419
4. The method of claim 3, wherein the method comprises the following steps: fifthly, updating the optimal position of the g +1 th generation quantum, and updating experience factors and environment factors, specifically:
step 5.1: computing new generation of mth individual quantum position vector
Figure FDA00031375629800000420
Mapping state
Figure FDA00031375629800000421
In the fitness function FξLower fitness value
Figure FDA0003137562980000051
Obtaining a transition empirical factor
Figure FDA0003137562980000052
Sorting the transition experience factors to obtain the maximum value thereof
Figure FDA0003137562980000053
The corresponding quantum position is
Figure FDA0003137562980000054
Will be provided with
Figure FDA0003137562980000055
And Fξ(pg) Make a comparison if
Figure FDA0003137562980000056
Then
Figure FDA0003137562980000057
If it is
Figure FDA0003137562980000058
Then p isg+1＝pgThe mapping state of the optimal quantum position of the g +1 th generation is
Figure FDA0003137562980000059
Step 5.2: the idea of differential evolution is adopted, variation operation is carried out by using experience factors among individuals, and the experience factor of the mth mouse is updated according to the following rules:
Figure FDA00031375629800000510
wherein: rho is an empirical evaporation coefficient, and the distribution interval of rho is [0,1 ]]And Δ T is an empirical variable,
Figure FDA00031375629800000511
wherein: upsilon is2Represents the scaling factor, v2Is [0,1 ]]Uniformly distributed random numbers in between, z1And z2For randomly introduced quantum mouse individuals to perform mutation operations, z1＝(1,2,…,M),z2＝(1,2,…,M)；
Step 5.3: updated experience factor for mth mouse
Figure FDA00031375629800000512
Make a judgment if
Figure FDA00031375629800000513
Then
Figure FDA00031375629800000514
For M mice experience factor
Figure FDA00031375629800000515
Arranged from large to small to obtain the maximum value T1 g+1On the basis, the optimal empirical factor of the g +1 th generation is obtained
Figure FDA00031375629800000516
Wherein: upsilon is5Is at [0,1 ]]Uniformly distributed random numbers in between.
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