CN109270485B - Space-time direction finding method based on quantum cell membrane optimization mechanism - Google Patents

Space-time direction finding method based on quantum cell membrane optimization mechanism Download PDF

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CN109270485B
CN109270485B CN201811017339.7A CN201811017339A CN109270485B CN 109270485 B CN109270485 B CN 109270485B CN 201811017339 A CN201811017339 A CN 201811017339A CN 109270485 B CN109270485 B CN 109270485B
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CN109270485A (en
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高洪元
孙贺麟
池鹏飞
刁鸣
张世铂
陈梦晗
侯阳阳
吕阔
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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
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/16—Systems for determining direction or deviation from predetermined direction using amplitude comparison of signals derived sequentially from receiving antennas or antenna systems having differently-oriented directivity characteristics or from an antenna system having periodically-varied orientation of directivity characteristic
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention belongs to the field of array signal processing, and particularly relates to a space-time direction finding method based on a quantum cell membrane optimization mechanism, which comprises the following steps of: acquiring signal time domain data, performing signal snapshot sampling and performing time domain delay on the sampled data; constructing a maximum likelihood estimation equation of maximum likelihood estimation, initializing a quantum substance group, and constructing an adaptability function; selecting elite quantum individuals, and carrying out local search on the elite quantum individuals; dividing quantum individual types; high concentration fat-soluble quantum individual free diffusion; high concentration non-fat soluble quantum individual exercise; low concentration quantum individual motion; generating a new generation quantum substance group; and judging whether the maximum iteration times are reached. The space-time direction finding method based on the quantum cell membrane optimization mechanism solves the problem of large calculated amount of the maximum likelihood estimation method, can quickly obtain a relatively accurate joint estimation result of the signal angle and the frequency, and is easy to process in real time in engineering application.

Description

Space-time direction finding method based on quantum cell membrane optimization mechanism
Technical Field
The invention belongs to the field of array signal processing, and particularly relates to a space-time direction finding method based on a quantum cell membrane optimization mechanism.
Background
The direction finding technology is an important branch in the array signal processing technology, most of the direction finding technology is estimation of one-dimensional signal parameters of azimuth angles, but estimation of multidimensional parameters is relatively close to practical application, and one important research direction is space-time direction finding.
Among many direction-finding methods, the direction-finding method using the principle of maximum likelihood estimation is simple in principle, can be used for direction-finding of coherent sources, and is strong in robustness and stability, but in practical application, the calculation amount required by two-dimensional search is large due to complex implementation process, and if the multi-dimensional search method is low in efficiency, the direction-finding result may not be converged, and only one approximate extremum of a likelihood function may be found, so that convergence to a global optimal solution is difficult to ensure, and practical application of the method is limited. The rotation-invariant subspace method has the advantages of small calculation amount, no need of spectral peak search, but high-dimensional singular value decomposition and additional parameter pairing operation.
Through the search discovery of the prior art document, zhang Zhicheng and the like in the 'joint estimation of the direction of arrival and the frequency by using a state space model' published in optical precision engineering, a system matrix is proposed, which comprises the information of the direction of arrival and the frequency of a signal through constructing a state space model, and the estimated value of the system matrix is subjected to characteristic decomposition to obtain the direction of arrival and the frequency of the signal, but the estimation error is larger. Hu Xuelong in the "double rotation subspace method in signal frequency direction joint estimation" published in university of Yangzhou university journal, a signal frequency and direction joint estimation method based on subspace two-time rotation transformation is provided, the operation amount is small, the number of signals can be identified, but the method is sensitive to the correlation among signal to noise ratio, snapshot number and information sources.
In summary, the literature indicates that for the space-time direction finding problem, a method which is rapid and accurate, has excellent performance and can perform angle and frequency effective joint estimation on a coherent source is lacked.
Disclosure of Invention
Aiming at the problems that the existing maximum likelihood direction finding method is large in calculated amount and high in system complexity, and the combined estimation of frequency and azimuth angle is difficult to realize rapidly and accurately, the invention designs a space-time direction finding method based on a quantum cell membrane optimization mechanism. The method uses the principle of maximum likelihood estimation, utilizes the global optimizing capability of a cell membrane optimizing mechanism to be strong, introduces the quantum principle on the basis of the cell membrane optimizing mechanism, and uses a quantum revolving gate to evolve a quantum individual. The method can obtain accurate estimation results of the azimuth angle and the frequency of the signal in a short time.
A space-time direction finding method based on a quantum cell membrane optimization mechanism comprises the following steps:
(1) Acquiring signal time domain data, performing signal snapshot sampling and performing time domain delay on the sampled data;
(2) Constructing a maximum likelihood estimation equation of maximum likelihood estimation, initializing a quantum substance group, and constructing an adaptability function;
(3) Selecting elite quantum individuals, and carrying out local search on the elite quantum individuals;
(4) Dividing quantum individual types;
(5) High concentration fat-soluble quantum individual free diffusion;
(6) High concentration non-fat soluble quantum individual exercise;
(7) Low concentration quantum individual motion;
(8) Generating a new generation quantum substance group;
(9) And judging whether the maximum iteration times are reached.
The steps of obtaining signal time domain data, sampling signal snapshot and carrying out time domain delay on the sampled data include:
there are I azimuth angles θ= (θ) 1 ,θ 2 ,…,θ I ) Frequency ω= (ω) 1 ,ω 2 ,…,ω I ) Is incident on a uniform linear array containing M array elements with a spacing eta, each array element has a delay device with K-level time domain delay of sigma, wherein theta i An included angle between the i-th signal arrival direction and the normal line direction of the linear array;
the ith signal at time t is represented by a complex envelope:
Figure BDA0001786102110000021
where j is an imaginary unit, u i (t) is the amplitude of the signal,
Figure BDA0001786102110000022
is the phase of the signal;
the ith signal reaching the mth array element at the moment t is as follows:
s i (t-τ mi )＝s i (t)exp(-jω i τ mi )
wherein ,τmi The spatial delay relative to the reference element for the ith signal to reach the mth element;
the m-th array element position is delta m The following steps are:
Figure BDA0001786102110000023
wherein c is the propagation speed of the signal;
in an ideal state, each array element in the array is not affected by inconsistent channels or mutual coupling factors, and the data received by the mth array element at the moment t is:
Figure BDA0001786102110000024
wherein nm (t) represents gaussian white noise at the mth element at time t;
the output data of the signals after time domain delay generated by the kth-stage delayer of the mth array element is as follows:
Figure BDA0001786102110000025
writing the data vector into a matrix form to obtain the data vector received by the mth array element at the moment t, wherein the data vector is as follows:
Y m (t)＝A m S(t)+N m (t)
wherein ,Am Is an array flow pattern matrix, S (t) is a signal vector, N m (t) is a noise vector, m=1, 2, …, M
Y is set to m (t) arranged as a matrix
Figure BDA0001786102110000031
And further simplifying to obtain:
Y(t)＝A (θ,ω) S(t)+N(t)
wherein the noise matrix
Figure BDA0001786102110000032
M x K row and I column space-time two-dimensional array flow pattern matrix>
Figure BDA0001786102110000033
The sampling data of the U-th snapshot sampling is Y (U), u=1, 2, …, U, and a covariance matrix of the sampling data is constructed:
Figure BDA0001786102110000034
wherein U is the total number of snapshots, and H represents conjugate transpose operation.
The constructing a maximum likelihood estimation equation for maximum likelihood estimation, initializing a quantum substance group, and constructing an fitness function, including:
constructing an orthogonal projection matrix by adopting a space-time two-dimensional maximum likelihood method:
Figure BDA0001786102110000035
wherein ,
Figure BDA0001786102110000036
for one of the solutions of signal azimuth, +.>
Figure BDA0001786102110000037
One solution in a solution space for signal frequencies;
the maximum likelihood equation for maximum likelihood estimation is:
Figure BDA0001786102110000038
wherein tr represents a matrix tracing operation;
setting total number H of quantum units in quantum substance group, maximum iteration number G, and expressing H quantum units in G iteration as
Figure BDA0001786102110000039
Generating H D=2I dimension quanta individuals->
Figure BDA00017861021100000310
The d dimension of the h quantum unit is +.>
Figure BDA0001786102110000041
At the first generation, the value is [0,1 ]]A uniform random number within, d=1, 2, …, D;
odd dimensions of quantum individuals
Figure BDA0001786102110000042
Mapping to a range of signal azimuth solutions
Figure BDA0001786102110000043
Even dimension->
Figure BDA0001786102110000044
Mapping to a range of signal frequency solutions
Figure BDA0001786102110000045
Obtaining mapped individuals->
Figure BDA0001786102110000046
Constructing a quantum individual fitness function:
Figure BDA0001786102110000047
selecting elite quantum individuals, and carrying out local search on the elite quantum individuals, wherein the method comprises the following steps:
calculating the h quantum unit in quantum substance group
Figure BDA0001786102110000048
The fitness of (h=1, 2, …, H), the quantum unit with the greatest fitness is elite quantum unit +.>
Figure BDA0001786102110000049
Re-using analog quantum revolving gate by letting b g Random movement
Figure BDA00017861021100000410
Local search is carried out again to obtain alternative new generation elite quantum individuals +.>
Figure BDA00017861021100000411
First->
Figure BDA00017861021100000412
In the sub-random movement, b g D < th > dimension->
Figure BDA00017861021100000435
The corresponding quantum rotation angle is +.>
Figure BDA00017861021100000413
Figure BDA00017861021100000414
Is [ -1,1]Inside uniform random number,/, inside uniform random number,
Figure BDA00017861021100000415
Updated to
Figure BDA00017861021100000416
Figure BDA00017861021100000417
The maximum adaptation in the mapping state of +.>
Figure BDA00017861021100000418
wherein
Figure BDA00017861021100000419
Is->
Figure BDA00017861021100000420
Mapping state of (1), if
Figure BDA00017861021100000421
Then reserve->
Figure BDA00017861021100000422
Quantum state->
Figure BDA00017861021100000423
As a new generation elite quantum unit; no make b g+1 ＝b g As a new generation elite quantum unit.
The dividing quantum individual types includes:
order the
Figure BDA00017861021100000424
For the h quantum unit in the quantum substance group +. >
Figure BDA00017861021100000425
Define the concentration of the position of the quantum substance group as +.>
Figure BDA00017861021100000426
wherein αh For distinguishing condition->
Figure BDA00017861021100000427
The number of times that it is established,
Figure BDA00017861021100000428
and->
Figure BDA00017861021100000429
Sequencing each quantum in the quantum substance group from large to small according to concentration, and ranking the concentration by half
Figure BDA00017861021100000430
The individual quantum units are divided into high-concentration quantum units->
Figure BDA00017861021100000431
Concentration ranking of the second half
Figure BDA00017861021100000432
The individual quantum units are divided into low-concentration quantum units->
Figure BDA00017861021100000433
All high-concentration quantum units are ordered according to the adaptability from big to small, and the units are arranged in odd number positions
Figure BDA00017861021100000434
The high-concentration quantum unit is high-concentration liposoluble quantum unit->
Figure BDA0001786102110000051
Specifying +.>
Figure BDA0001786102110000052
The high-concentration quantum unit is high-concentration non-fat soluble quantum unit->
Figure BDA0001786102110000053
The high concentration fat-soluble quantum unit free diffusion comprises:
first, the
Figure BDA0001786102110000054
Personal->
Figure BDA0001786102110000055
The specific process of the movement is as follows: firstly, using a simulated quantum revolving door to enable +.>
Figure BDA0001786102110000056
To w low concentration quantum individuals->
Figure BDA0001786102110000057
Exercise, generate->
Figure BDA0001786102110000058
Individual quantum->
Figure BDA0001786102110000059
Alternatively new generation of high concentration lipid soluble quantum individuals,>
Figure BDA00017861021100000510
d < th > dimension->
Figure BDA00017861021100000511
To w->
Figure BDA00017861021100000547
D < th > dimension->
Figure BDA00017861021100000548
The quantum rotation angle corresponding to the motion is:
Figure BDA00017861021100000514
Figure BDA00017861021100000515
updated to->
Figure BDA00017861021100000516
Figure BDA00017861021100000517
Figure BDA00017861021100000518
Personal->
Figure BDA00017861021100000519
Adaptation in mapping state of (c)The maximum degree is->
Figure BDA00017861021100000520
Select the corresponding quantum state->
Figure BDA00017861021100000521
As a new generation of high concentration lipid-soluble quantum entities, wherein
Figure BDA00017861021100000522
Is->
Figure BDA00017861021100000523
Mapping states of (a) for each +.>
Figure BDA00017861021100000524
Executing the above exercise process to generate new generation high concentration liposoluble quantum individual +.>
Figure BDA00017861021100000525
The high concentration of non-fat soluble quantum individual motion comprises:
the high concentration non-fat soluble quantum individual does not need energy for assisting diffusion, but needs carrier, and the number of carriers is set
Figure BDA00017861021100000526
Wherein round represents a rounding for limiting the high concentration of non-fat soluble quantum individuals +.>
Figure BDA00017861021100000527
The movement (1) of (2) specifies the front ++in order of concentration from large to small>
Figure BDA00017861021100000528
Personal->
Figure BDA00017861021100000529
Obtaining a carrier, moving to a low concentration quantum unit, wherein +.>
Figure BDA00017861021100000530
Personal->
Figure BDA00017861021100000531
The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable the first->
Figure BDA00017861021100000532
Personal->
Figure BDA00017861021100000533
To w low concentration quantum individuals->
Figure BDA00017861021100000534
Sport generation->
Figure BDA00017861021100000535
Individual quantum->
Figure BDA00017861021100000536
Figure BDA00017861021100000537
Alternative new generation of high concentration non-fat soluble quantum individuals +.>
Figure BDA00017861021100000538
Personal->
Figure BDA00017861021100000539
D < th > dimension->
Figure BDA00017861021100000540
To w->
Figure BDA00017861021100000541
D < th > dimension->
Figure BDA00017861021100000542
Quantum rotation angle +.>
Figure BDA00017861021100000543
Figure BDA00017861021100000544
Updated to
Figure BDA00017861021100000545
Figure BDA00017861021100000546
Personal (S)
Figure BDA0001786102110000061
The maximum adaptation in the mapping state of +.>
Figure BDA0001786102110000062
Selecting the corresponding quantum state individual
Figure BDA0001786102110000063
As a new generation of high concentration non-fat soluble quantum units, wherein
Figure BDA0001786102110000064
Is->
Figure BDA0001786102110000065
Mapping state of>
Figure BDA0001786102110000066
Personal->
Figure BDA0001786102110000067
Executing the above exercise process to generate new generation of high concentration non-fat soluble quantum individual with carrier->
Figure BDA0001786102110000068
(2) Specifying the remaining high concentration of non-fat soluble quantum individuals
Figure BDA0001786102110000069
The carrier is not obtained and the carrier is not a solid,use of analog quantum turnstiles to elite individual b g+1 The new generation of carrier-free high-concentration non-fat-soluble quantum individuals are obtained through movement
Figure BDA00017861021100000610
Figure BDA00017861021100000611
Wherein->
Figure BDA00017861021100000612
Personal->
Figure BDA00017861021100000613
D < th > dimension->
Figure BDA00017861021100000614
Direction b g+1 D < th > dimension->
Figure BDA00017861021100000615
Quantum rotation angle +.>
Figure BDA00017861021100000616
Figure BDA00017861021100000617
Updated to
Figure BDA00017861021100000618
Figure BDA00017861021100000619
If->
Figure BDA00017861021100000620
Is superior to->
Figure BDA00017861021100000621
Keep->
Figure BDA00017861021100000622
High concentration non-fat soluble quantum dots as new generation carrier-freeA body; no->
Figure BDA00017861021100000623
Is a new generation of carrier-free high-concentration non-fat-soluble quantum individuals.
The low concentration quantum individual motion comprising:
active transportation is a movement mode which requires a carrier and enough energy, all low-concentration quantum individuals are ordered according to the fitness from large to small, and the fitness is regulated to be higher
Figure BDA00017861021100000624
The low-concentration quantum units are low-concentration high-energy quantum units meeting energy limitation +.>
Figure BDA00017861021100000625
Less fitness +.>
Figure BDA00017861021100000626
The low-concentration quantum units are low-concentration low-energy quantum units which do not meet the energy limit
Figure BDA00017861021100000627
For each low concentration high energy quantum individual there is +.>
Figure BDA00017861021100000644
The probability of (2) obtaining a carrier, and moving towards the direction of a high-concentration quantum individual;
(1) The low-concentration high-energy quantum unit of the carrier obtained by marking is
Figure BDA00017861021100000628
And a total of O are provided,
Figure BDA00017861021100000629
o random integers, where O +.>
Figure BDA00017861021100000630
The specific process of the movement is as follows: first use the mould Quasi quantum revolving door>
Figure BDA00017861021100000631
To (1)>
Figure BDA00017861021100000632
High concentration quantum individuals->
Figure BDA00017861021100000633
Exercise, get->
Figure BDA00017861021100000634
Individual quantum units
Figure BDA00017861021100000635
Alternative new generation low concentration high energy quantum individuals, o +.>
Figure BDA00017861021100000636
D < th > dimension->
Figure BDA00017861021100000637
To (1)>
Figure BDA00017861021100000638
Personal->
Figure BDA00017861021100000639
D < th > dimension->
Figure BDA00017861021100000640
Quantum rotation angle corresponding to motion
Figure BDA00017861021100000641
Figure BDA00017861021100000642
Updated to->
Figure BDA00017861021100000643
Figure BDA0001786102110000071
Figure BDA0001786102110000072
Personal->
Figure BDA0001786102110000073
The maximum adaptation in the mapping state of +.>
Figure BDA0001786102110000074
Selecting the quantum state->
Figure BDA0001786102110000075
Low concentration high energy quantum individuals as new generation derived carriers, wherein +.>
Figure BDA0001786102110000076
Is->
Figure BDA0001786102110000077
Mapping states of (a) for each +.>
Figure BDA0001786102110000078
Executing the above movement process to generate low-concentration high-energy quantum individual of new generation of obtained carrier->
Figure BDA0001786102110000079
(2) Marking carrier-free low-concentration high-energy quantum individuals as
Figure BDA00017861021100000710
And is in common with
Figure BDA00017861021100000711
Personal (S)>
Figure BDA00017861021100000712
And q.noteq.o, where q.sub.th->
Figure BDA00017861021100000713
The specific motion process of (a) is as follows: firstly using a simulated quantum revolving door to enable +.>
Figure BDA00017861021100000714
Random exercise is taken->
Figure BDA00017861021100000715
Performing local search; the (q) th->
Figure BDA00017861021100000716
D < th > dimension->
Figure BDA00017861021100000717
The corresponding quantum rotation angle is +.>
Figure BDA00017861021100000718
Figure BDA00017861021100000719
Is [ -1,1]A uniform random number within the matrix is used,
Figure BDA00017861021100000720
updated to->
Figure BDA00017861021100000721
If->
Figure BDA00017861021100000722
Is superior to->
Figure BDA00017861021100000723
Then reserve->
Figure BDA00017861021100000724
Low concentration high energy quantum individuals as new generation carrier-free, otherwise let +.>
Figure BDA00017861021100000725
Is a new generation of carrier-free low-concentration high-energy quantum individuals,for each->
Figure BDA00017861021100000726
Executing the above movement process to generate new generation carrier-free low concentration high energy quantum individual +. >
Figure BDA00017861021100000727
(3) All low concentration low energy quantum individuals
Figure BDA00017861021100000728
To elite quantum unit b g+1 Motion, using analog quantum turnstile, +.>
Figure BDA00017861021100000729
Individual quantum->
Figure BDA00017861021100000730
D < th > dimension->
Figure BDA00017861021100000731
Direction b g+1 D < th > dimension->
Figure BDA00017861021100000732
The quantum rotation angle of the motion is
Figure BDA00017861021100000733
Figure BDA00017861021100000734
Updated to->
Figure BDA00017861021100000735
Figure BDA00017861021100000745
If->
Figure BDA00017861021100000744
Is superior to->
Figure BDA00017861021100000738
Then reserve->
Figure BDA00017861021100000739
As a new generation of low concentration low energy quantum individuals, otherwise let +.>
Figure BDA00017861021100000740
As a new generation of low concentration low energy quantum individuals.
The generation of a new generation of quantum species population includes:
will be
Figure BDA00017861021100000741
Figure BDA00017861021100000742
Quantum substance group combined into new generation +.>
Figure BDA00017861021100000743
The judging whether the maximum iteration number is reached comprises the following steps:
if G is less than G, let g=g+1, return to step six; otherwise, if the maximum iteration times g=g are reached, the mapping state of the quantum unit with the maximum adaptability is output as an estimation result, and the optimal estimation value of the angle and the frequency is obtained.
The invention has the beneficial effects that:
(1) The space-time direction finding method based on the quantum cell membrane optimization mechanism solves the problem of large calculated amount of the maximum likelihood estimation method, can quickly obtain a relatively accurate joint estimation result of the signal angle and the frequency, and is easy to process in real time in engineering application.
(2) The method can estimate the incoherent source and effectively estimate the coherent source, and can still obtain the combined estimation result of azimuth angle and frequency with higher precision under the conditions of low signal-to-noise ratio and small snapshot number.
Drawings
FIG. 1 is a schematic diagram of a space-time direction finding method based on quantum cell membrane optimization mechanism;
angle estimation of the signal of fig. 2;
the angle and frequency joint estimation of the signal of fig. 3;
FIG. 4 is a graph of root mean square error versus signal to noise ratio for signal estimation angles;
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention designs a novel method for jointly estimating the frequency and azimuth angle of a signal, which is characterized in that a space-time direction finding method based on a quantum cell membrane optimization mechanism is used for quickly obtaining a direction finding result. Belonging to the field of array signal processing.
The direction finding technology is an important branch in the array signal processing technology, most of the direction finding technology is estimation of one-dimensional signal parameters of azimuth angles, but estimation of multidimensional parameters is relatively close to practical application, and one important research direction is space-time direction finding.
Among many direction-finding methods, the direction-finding method using the principle of maximum likelihood estimation is simple in principle, can be used for direction-finding of coherent sources, and is strong in robustness and stability, but in practical application, the calculation amount required by two-dimensional search is large due to complex implementation process, and if the multi-dimensional search method is low in efficiency, the direction-finding result may not be converged, and only one approximate extremum of a likelihood function may be found, so that convergence to a global optimal solution is difficult to ensure, and practical application of the method is limited. The rotation-invariant subspace method has the advantages of small calculation amount, no need of spectral peak search, but high-dimensional singular value decomposition and additional parameter pairing operation.
In the "joint estimation of direction of arrival and frequency by means of state space model" published by "optical precision engineering" (2011, vol.19, no. 4) by search findings of prior art documents, zhang Zhicheng et al, a system matrix is proposed in which state space model is constructed and the estimated value of system matrix is subjected to feature decomposition to obtain the direction of arrival and frequency of signal, but the estimation error is large. Hu Xuelong et al in "double rotation subspace method in Signal frequency and direction Joint estimation" published by university of Yangzhou (2004, vol.7, no. 3) propose a method for jointly estimating frequency and direction of a signal based on subspace two rotation transformation, which has small calculation amount and can identify the number of signals, but is sensitive to the correlation among signal to noise ratio, snapshot number and signal sources. The existing literature shows that for the problem of space-time direction finding, a method which is rapid and accurate, has excellent performance and can perform effective joint estimation on angles and frequencies of coherent sources is lacked.
Aiming at the problems that the existing maximum likelihood direction finding method is large in calculated amount and high in system complexity, and the combined estimation of frequency and azimuth angle is difficult to realize rapidly and accurately, the invention designs a space-time direction finding method based on a quantum cell membrane optimization mechanism. The method uses the principle of maximum likelihood estimation, utilizes the global optimizing capability of a cell membrane optimizing mechanism to be strong, introduces the quantum principle on the basis of the cell membrane optimizing mechanism, and uses a quantum revolving gate to evolve a quantum individual. The method can obtain accurate estimation results of the azimuth angle and the frequency of the signal in a short time.
The invention is realized mainly by the following steps:
step one, obtaining signal time domain data.
From the mathematical model of the signal, consider I azimuth angles as θ= (θ) 1 ,θ 2 ,…,θ I ) Frequency ω= (ω) 1 ,ω 2 ,…,ω I ) Is incident on a uniform linear array containing M array elements with eta spacing, each array element has K stages, each stage has a delay device with sigma time domain delay, wherein theta i Is the included angle between the direction of arrival of the ith signal and the normal line direction of the linear array. the ith signal at time t may be represented as a complex envelope
Figure BDA0001786102110000091
Where j is an imaginary unit, u i (t) is the amplitude of the signal, +.>
Figure BDA0001786102110000092
Is the phase of the signal, the ith signal reaching the mth array element at the moment t is s i (t-τ mi )＝s i (t)exp(-jω i τ mi), wherein ,τmi For the spatial delay relative to the reference element, if the position of the mth element is delta m Then->
Figure BDA0001786102110000093
Where c is the propagation velocity of the signal. Under ideal conditions, if each array element in the array has no influence of inconsistent channels or mutual coupling factors, the data received by the mth array element at the moment t is +.>
Figure BDA0001786102110000094
wherein nm And (t) represents Gaussian white noise at the m-th array element at the t moment.
And step two, acquiring signal snapshot sampling and carrying out time domain delay on sampling data.
The signal is passed through the kth stage delay device of the mth array element to generate the output data after time domain delay
Figure BDA0001786102110000095
Writing the data vector into a matrix form to obtain a data vector Y received by an mth array element at the moment t m (t)＝A m S(t)+N m (t) wherein A m Is an array flow pattern matrix, S (t) is a signal vector, N m And (t) is a noise vector, m=1, 2, …, M. And then Y is added m (t) arranged as a matrix
Figure BDA0001786102110000096
Further simplified to Y (t) =A (θ,ω) S (t) +N (t), wherein the noise matrix
Figure BDA0001786102110000101
M x K row I column space-time two-dimensional array flow pattern matrix
Figure BDA0001786102110000102
Record the ith snapshot sampleIs Y (U), u=1, 2, …, U, constructing covariance matrix of the sampled data +.>
Figure BDA0001786102110000103
Where U is the total number of snapshots. H represents a conjugate transpose operation.
And thirdly, constructing a maximum likelihood estimation equation of the maximum likelihood estimation.
Constructing an orthogonal projection matrix by adopting a space-time two-dimensional maximum likelihood method
Figure BDA0001786102110000104
wherein
Figure BDA0001786102110000105
For a possible solution in the solution space of the signal azimuth,
Figure BDA0001786102110000106
For one possible solution in the solution space of the signal frequencies, the maximum likelihood equation for the maximum likelihood estimation is +.>
Figure BDA0001786102110000107
tr represents a matrix tracing operation.
And step four, initializing a quantum substance group.
Setting total number H of quantum units in quantum substance group, setting maximum iteration number G, and expressing H quantum units in the G iteration as
Figure BDA0001786102110000108
Generating H D=2I dimension quanta individuals->
Figure BDA0001786102110000109
The d dimension of the h quantum unit is +. >
Figure BDA00017861021100001010
At the first generation, the value is [0,1 ]]Inside uniform random number, d=1, 2, …, D.
And fifthly, constructing an adaptability function.
Odd dimensions of quantum individuals
Figure BDA00017861021100001011
Mapping to a range of signal azimuth solutions
Figure BDA00017861021100001012
Even dimension->
Figure BDA00017861021100001013
Mapping to the signal frequency solution is +.>
Figure BDA00017861021100001014
Obtaining mapped individuals->
Figure BDA00017861021100001015
Constructing a quantum individual fitness function>
Figure BDA00017861021100001016
Figure BDA00017861021100001017
Step six, selecting elite quantum individuals, and carrying out local search on the elite quantum individuals.
Calculating the h quantum unit in quantum substance group
Figure BDA00017861021100001018
The fitness of (h=1, 2, …, H), the quantum unit with the greatest fitness is elite quantum unit +.>
Figure BDA0001786102110000111
Re-using analog quantum revolving gate by letting b g Random exercise->
Figure BDA0001786102110000112
Local search is carried out again to obtain alternative new generation elite quantum individuals +.>
Figure BDA0001786102110000113
First->
Figure BDA0001786102110000114
In the sub-random movement, b g D < th > dimension->
Figure BDA0001786102110000115
The corresponding quantum rotation angle is +.>
Figure BDA0001786102110000116
Figure BDA0001786102110000117
Is [ -1,1]A uniform random number within.
Figure BDA0001786102110000118
Updated to->
Figure BDA0001786102110000119
Figure BDA00017861021100001110
The maximum adaptation in the mapping state of +.>
Figure BDA00017861021100001111
wherein
Figure BDA00017861021100001112
Is that
Figure BDA00017861021100001113
Mapping state of->
Figure BDA00017861021100001114
Then reserve->
Figure BDA00017861021100001115
Quantum state->
Figure BDA00017861021100001116
As a new generation elite quantum unit; no make b g+1 ＝b g As a new generation elite quantum unit.
And step seven, dividing quantum individual types.
Order the
Figure BDA00017861021100001117
For the h quantum unit in the quantum substance group +.>
Figure BDA00017861021100001118
Define the concentration of the position of the quantum substance group as +. >
Figure BDA00017861021100001119
wherein αh For distinguishing condition->
Figure BDA00017861021100001120
The number of times that it is established,
Figure BDA00017861021100001121
and->
Figure BDA00017861021100001122
Ordering each quantum in the quantum substance group from big to small according to concentration, and ranking the first half of the concentration>
Figure BDA00017861021100001123
The individual quantum units are divided into high-concentration quantum units->
Figure BDA00017861021100001124
Figure BDA00017861021100001125
Concentration rank second half +.>
Figure BDA00017861021100001126
Individual quantum units are divided into low-concentration quantum units
Figure BDA00017861021100001127
Then sequencing all high-concentration quantum units according to the adaptability from big to small, and defining the odd-numbered +.>
Figure BDA00017861021100001128
The high-concentration quantum units are high-concentration liposoluble quantum units
Figure BDA00017861021100001129
Specifying +.>
Figure BDA00017861021100001130
The high-concentration quantum unit is high-concentration non-fat soluble quantum unit->
Figure BDA00017861021100001131
And step eight, the high-concentration fat-soluble quantum individuals are freely diffused.
Free diffusion is the process by which each high concentration of fat-soluble quantum is moved to a low concentration of quantum, and this process requires no carrier or energy. First, the
Figure BDA00017861021100001132
Personal->
Figure BDA00017861021100001133
The specific process of the movement is as follows: firstly, using a simulated quantum revolving door to enable +.>
Figure BDA00017861021100001134
To w low concentration quantum individuals->
Figure BDA00017861021100001135
Exercise, generate->
Figure BDA00017861021100001136
Individual quantum->
Figure BDA00017861021100001137
Figure BDA00017861021100001138
Alternatively new generation of high concentration lipid soluble quantum individuals,>
Figure BDA00017861021100001139
d < th > dimension->
Figure BDA00017861021100001140
To w th
Figure BDA00017861021100001141
D < th > dimension->
Figure BDA00017861021100001142
The quantum rotation angle corresponding to the motion is +.>
Figure BDA00017861021100001143
Figure BDA00017861021100001144
Updated to->
Figure BDA0001786102110000121
Figure BDA0001786102110000122
Personal (S)
Figure BDA0001786102110000123
The maximum adaptation in the mapping state of +.>
Figure BDA0001786102110000124
Selecting the corresponding quantum state
Figure BDA0001786102110000125
As a new generation of high concentration lipid-soluble quantum entities, wherein
Figure BDA0001786102110000126
Is->
Figure BDA0001786102110000127
Is a mapping state of (c). For each->
Figure BDA0001786102110000128
Executing the above exercise process to generate new generation high concentration liposoluble quantum individual +.>
Figure BDA0001786102110000129
Step nine, high-concentration non-fat-soluble quantum individuals move.
The diffusion assistance of high concentrations of non-fat soluble quantum entities requires no energy, but a carrier. Setting the number of carriers
Figure BDA00017861021100001210
round represents rounding to limit individuals with high concentration of non-fat soluble quanta +.>
Figure BDA00017861021100001211
Is a motion of (c).
(1) Specifying the front of the order of concentration from big to small
Figure BDA00017861021100001212
Personal->
Figure BDA00017861021100001213
The carrier is obtained and moves to the low-concentration quantum individual. Wherein->
Figure BDA00017861021100001214
Personal->
Figure BDA00017861021100001215
The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable the first->
Figure BDA00017861021100001216
Personal->
Figure BDA00017861021100001217
To w low concentration quantum individuals->
Figure BDA00017861021100001218
Sport generation->
Figure BDA00017861021100001219
Individual quantum->
Figure BDA00017861021100001220
Figure BDA00017861021100001221
Alternative new generation of high concentration non-fat soluble quantum individuals +.>
Figure BDA00017861021100001222
Personal->
Figure BDA00017861021100001223
D < th > dimension->
Figure BDA00017861021100001224
To w->
Figure BDA00017861021100001225
D < th > dimension->
Figure BDA00017861021100001226
Quantum rotation angle +.>
Figure BDA00017861021100001227
Figure BDA00017861021100001228
Updated to
Figure BDA00017861021100001229
Figure BDA00017861021100001230
Personal (S)
Figure BDA00017861021100001231
The maximum adaptation in the mapping state of +.>
Figure BDA00017861021100001232
Selecting the corresponding quantum state individual
Figure BDA00017861021100001233
As a new generation of high concentration non-fat soluble quantum units, wherein
Figure BDA00017861021100001234
Is->
Figure BDA00017861021100001235
Is a mapping state of (c). For front->
Figure BDA00017861021100001236
Personal->
Figure BDA00017861021100001237
Executing the above exercise process to generate new generation of high concentration non-fat soluble quantum individual with carrier- >
Figure BDA00017861021100001238
(2) Specifying the remaining high concentration of non-fat soluble quantum individuals
Figure BDA00017861021100001239
Without carrier, using simulated quantum turnstiles to elite individual b g+1 The new generation of carrier-free high-concentration non-fat-soluble quantum individuals are obtained through movement
Figure BDA00017861021100001240
Figure BDA00017861021100001241
Wherein->
Figure BDA00017861021100001242
Personal->
Figure BDA00017861021100001243
D < th > dimension->
Figure BDA00017861021100001244
Direction b g+1 D < th > dimension->
Figure BDA00017861021100001245
Quantum rotation angle +.>
Figure BDA0001786102110000131
Figure BDA0001786102110000132
Updated to
Figure BDA0001786102110000133
Figure BDA00017861021100001348
If->
Figure BDA00017861021100001347
Is superior to->
Figure BDA0001786102110000136
Keep->
Figure BDA0001786102110000137
As a new generation of carrier-free high concentration non-fat soluble quantum individuals; no->
Figure BDA0001786102110000138
Is a new generation of carrier-free high-concentration non-fat-soluble quantum individuals.
Step ten, low-concentration quantum individual movement.
Active transportation is a movement mode which requires a carrier and enough energy, all low-concentration quantum individuals are ordered according to the fitness from large to small, and the fitness is regulated to be higher
Figure BDA0001786102110000139
The low-concentration quantum units are low-concentration high-energy quantum units meeting energy limitation +.>
Figure BDA00017861021100001310
Less fitness +.>
Figure BDA00017861021100001311
The low-concentration quantum units are low-concentration low-energy quantum units which do not meet the energy limit
Figure BDA00017861021100001312
For each low concentration high energy quantum individual there is +.>
Figure BDA00017861021100001346
The probability of (2) obtaining a carrier, and moving towards the direction of the high-concentration quantum individuals.
(1) The low-concentration high-energy quantum unit of the carrier obtained by marking is
Figure BDA00017861021100001313
And a total of O are provided,
Figure BDA00017861021100001314
o random integers, where O +. >
Figure BDA00017861021100001315
The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable +.>
Figure BDA00017861021100001316
To (1)>
Figure BDA00017861021100001317
High concentration quantum individuals->
Figure BDA00017861021100001318
Exercise, get->
Figure BDA00017861021100001319
Individual quantum units
Figure BDA00017861021100001320
Alternative new generation low concentration high energy quantum individuals, o +.>
Figure BDA00017861021100001321
D < th > dimension->
Figure BDA00017861021100001322
To (1)>
Figure BDA00017861021100001323
Personal->
Figure BDA00017861021100001324
D < th > dimension->
Figure BDA00017861021100001325
Quantum rotation angle corresponding to motion
Figure BDA00017861021100001326
Figure BDA00017861021100001327
Updated to->
Figure BDA00017861021100001328
Figure BDA00017861021100001329
Figure BDA00017861021100001330
Personal->
Figure BDA00017861021100001331
Maximum fitness in the mapping state of (a)
Figure BDA00017861021100001332
Selecting the quantum state->
Figure BDA00017861021100001333
Low concentration high energy quantum individuals as new generation derived carriers, wherein +.>
Figure BDA00017861021100001334
Is->
Figure BDA00017861021100001335
Mapping states of (a) for each +.>
Figure BDA00017861021100001336
Executing the above movement process to generate low-concentration high-energy quantum individual of new generation of obtained carrier->
Figure BDA00017861021100001337
(2) Marking carrier-free low-concentration high-energy quantum individuals as
Figure BDA00017861021100001338
And is common with->
Figure BDA00017861021100001339
Personal (S)>
Figure BDA00017861021100001340
And q.noteq.o, where q.sub.th->
Figure BDA00017861021100001341
The specific motion process of (a) is as follows: firstly using a simulated quantum revolving door to enable +.>
Figure BDA00017861021100001342
Random exercise is taken->
Figure BDA00017861021100001343
A local search is performed. The (q) th->
Figure BDA00017861021100001344
D < th > dimension->
Figure BDA00017861021100001345
The corresponding quantum rotation angle is
Figure BDA0001786102110000141
Figure BDA0001786102110000142
Is [ -1,1]A uniform random number within.
Figure BDA0001786102110000143
Updated to->
Figure BDA0001786102110000144
If->
Figure BDA0001786102110000145
Is superior to->
Figure BDA0001786102110000146
Then reserve->
Figure BDA0001786102110000147
Low concentration high energy quantum individuals as new generation carrier-free, otherwise let +.>
Figure BDA0001786102110000148
Is a new generation of carrier-free low-concentration high-energy quantum individuals. For each->
Figure BDA0001786102110000149
Executing the above movement process to generate new generation carrier-free low concentration high energy quantum individual +. >
Figure BDA00017861021100001410
(3) All low concentration low energy quantum individuals
Figure BDA00017861021100001411
To elite amountChild b g+1 And (5) movement. Use of analog quantum turnstiles>
Figure BDA00017861021100001412
Individual quantum->
Figure BDA00017861021100001413
D < th > dimension->
Figure BDA00017861021100001414
Direction b g+1 D < th > dimension->
Figure BDA00017861021100001415
The quantum rotation angle of the motion is
Figure BDA00017861021100001416
Figure BDA00017861021100001417
Updated to->
Figure BDA00017861021100001418
Figure BDA00017861021100001419
If->
Figure BDA00017861021100001420
Is superior to->
Figure BDA00017861021100001421
Then reserve->
Figure BDA00017861021100001422
As a new generation of low concentration low energy quantum individuals, otherwise let +.>
Figure BDA00017861021100001423
As a new generation of low concentration low energy quantum individuals.
Step eleven, generating a new generation quantum substance group.
Will be
Figure BDA00017861021100001424
Figure BDA00017861021100001425
Quantum substance group combined into new generation +.>
Figure BDA00017861021100001426
Step twelve, judging whether the maximum iteration times are reached, if G is smaller than G, enabling G to be equal to g+1, and returning to the step six; otherwise, if the maximum iteration times g=g are reached, the mapping state of the quantum unit with the maximum adaptability is output as an estimation result, and the optimal estimation value of the angle and the frequency is obtained.
(1) The space-time direction finding method based on the quantum cell membrane optimization mechanism solves the problem of large calculated amount of the maximum likelihood estimation method, can quickly obtain a relatively accurate joint estimation result of the signal angle and the frequency, and is easy to process in real time in engineering application.
(2) The method can estimate the incoherent source and effectively estimate the coherent source, and can still obtain the combined estimation result of azimuth angle and frequency with higher precision under the conditions of low signal-to-noise ratio and small snapshot number.
FIG. 1 is a schematic diagram of a space-time direction finding method based on quantum cell membrane optimization mechanism.
Angle estimation of the FIG. 2 signal
Joint estimation of angle and frequency of the signal of fig. 3
FIG. 4 is a graph showing the relation between the root mean square error and the signal to noise ratio of the signal estimation angle
The space-time direction finding method parameters based on the quantum cell membrane optimization mechanism are set as follows: η=0.015 m, σ=0.1 ns,
Figure BDA00017861021100001427
ζ＝0.8，
Figure BDA00017861021100001429
U＝100，H＝80，G＝30，M＝4，K＝4，
Figure BDA00017861021100001428
in fig. 2, the two signal angles are (9 °,18 °), db=10. The simulation diagram shows that the space-time direction finding method based on the quantum cell membrane optimization mechanism has higher estimation accuracy under the condition of low signal-to-noise ratio.
In fig. 3, the two signal angles and frequencies are (9 °,0.3GHz,18 °,0.8 GHz), db=20. The simulation diagram shows that the space-time direction finding method based on the quantum cell membrane optimization mechanism can jointly estimate the angle and the frequency of the signal.
In fig. 4, the angle and frequency of the two signals are (9 degrees, 18 degrees), the Monte Carlo test times are 100 times, and from the simulation result, it can be seen that the accuracy of the angle estimation of the space-time direction finding method based on the quantum cell membrane optimization mechanism designed by the invention is better than that of the particle swarm maximum likelihood direction finding method.
Step one, obtaining signal time domain data.
From the mathematical model of the signal, consider I azimuth angles as θ= (θ) 1 ,θ 2 ,…,θ I ) Frequency ω= (ω) 1 ,ω 2 ,…,ω I ) Is incident on a uniform linear array containing M array elements with eta spacing, each array element has K stages, each stage has a delay device with sigma time domain delay, wherein theta i Is the included angle between the direction of arrival of the ith signal and the normal line direction of the linear array. the ith signal at time t may be represented as a complex envelope
Figure BDA0001786102110000151
Where j is an imaginary unit, u i (t) is the amplitude of the signal, +.>
Figure BDA0001786102110000152
Is the phase of the signal, the ith signal reaching the mth array element at the moment t is s i (t-τ mi )＝s i (t)exp(-jω i τ mi), wherein ,τmi For the ith letterThe spatial delay relative to the reference element generated by the m-th element is determined by the position delta of the m-th element m Then->
Figure BDA0001786102110000153
Where c is the propagation velocity of the signal. Under ideal conditions, if each array element in the array has no influence of inconsistent channels or mutual coupling factors, the data received by the mth array element at the moment t is +.>
Figure BDA0001786102110000154
wherein nm And (t) represents Gaussian white noise at the m-th array element at the t moment.
And step two, acquiring signal snapshot sampling and carrying out time domain delay on sampling data.
The signal is passed through the kth stage delay device of the mth array element to generate the output data after time domain delay
Figure BDA0001786102110000155
Writing the data vector into a matrix form to obtain a data vector Y received by an mth array element at the moment t m (t)＝A m S(t)+N m (t) wherein A m Is an array flow pattern matrix, S (t) is a signal vector, N m And (t) is a noise vector, m=1, 2, …, M. And then Y is added m (t) arranged as a matrix
Figure BDA0001786102110000161
Further simplified to Y (t) =A (θ,ω) S (t) +N (t), wherein the noise matrix
Figure BDA0001786102110000162
M x K row I column space-time two-dimensional array flow pattern matrix
Figure BDA0001786102110000163
Recording the sampling data of the ith snapshot sampling as Y (U), wherein u=1, 2, … and U, and constructing a covariance matrix of the sampling data +.>
Figure BDA0001786102110000164
Where U is the total number of snapshots. H represents a conjugate transpose operation.
And thirdly, constructing a maximum likelihood estimation equation of the maximum likelihood estimation.
Constructing an orthogonal projection matrix by adopting a space-time two-dimensional maximum likelihood method
Figure BDA0001786102110000165
wherein
Figure BDA0001786102110000166
For a possible solution in the solution space of the signal azimuth,
Figure BDA0001786102110000167
For one possible solution in the solution space of the signal frequency, the maximum likelihood equation of the maximum likelihood estimation is
Figure BDA0001786102110000168
tr represents a matrix tracing operation.
And step four, initializing a quantum substance group.
Setting total number H of quantum units in quantum substance group, setting maximum iteration number G, and expressing H quantum units in the G iteration as
Figure BDA0001786102110000169
Generating H D=2I dimension quanta individuals->
Figure BDA00017861021100001610
The d dimension of the h quantum unit is +.>
Figure BDA00017861021100001611
At the first generation, the value is [0,1 ]]Inside uniform random number, d=1, 2, …, D.
And fifthly, constructing an adaptability function.
Odd dimensions of quantum individuals
Figure BDA00017861021100001612
Mapping to signalsWithin the range of azimuth solution
Figure BDA00017861021100001613
Even dimension->
Figure BDA00017861021100001614
Mapping to a range of signal frequency solutions
Figure BDA00017861021100001615
Obtaining mapped individuals->
Figure BDA00017861021100001616
Constructing quantum individual fitness functions
Figure BDA00017861021100001617
Figure BDA00017861021100001618
Step six, selecting elite quantum individuals, and carrying out local search on the elite quantum individuals.
Calculating the h quantum unit in quantum substance group
Figure BDA00017861021100001619
The fitness of (h=1, 2, …, H), the quantum unit with the greatest fitness is elite quantum unit +.>
Figure BDA0001786102110000171
Re-using analog quantum revolving gate by letting b g Random movement
Figure BDA0001786102110000172
Local search is carried out again to obtain alternative new generation elite quantum individuals +.>
Figure BDA0001786102110000173
First->
Figure BDA0001786102110000174
In the course of the secondary random movement,b g d < th > dimension->
Figure BDA0001786102110000175
The corresponding quantum rotation angle is +.>
Figure BDA0001786102110000176
Figure BDA0001786102110000177
Is [ -1,1]A uniform random number within.
Figure BDA0001786102110000178
Updated to->
Figure BDA0001786102110000179
Figure BDA00017861021100001710
The maximum adaptation in the mapping state of +.>
Figure BDA00017861021100001711
wherein
Figure BDA00017861021100001712
Is that
Figure BDA00017861021100001713
Mapping state of->
Figure BDA00017861021100001714
Then reserve->
Figure BDA00017861021100001715
Quantum state->
Figure BDA00017861021100001716
As a new generation elite quantum unit; no make b g+1 ＝b g As a new generation elite quantum unit.
And step seven, dividing quantum individual types.
Order the
Figure BDA00017861021100001717
For the h quantum unit in the quantum substance group +.>
Figure BDA00017861021100001718
Define the concentration of the position of the quantum substance group as +.>
Figure BDA00017861021100001719
wherein αh For distinguishing condition->
Figure BDA00017861021100001720
The number of times that it is established,
Figure BDA00017861021100001721
and->
Figure BDA00017861021100001722
Ordering each quantum in the quantum substance group from big to small according to concentration, and ranking the first half of the concentration >
Figure BDA00017861021100001723
The individual quantum units are divided into high-concentration quantum units->
Figure BDA00017861021100001724
Figure BDA00017861021100001725
Concentration rank second half +.>
Figure BDA00017861021100001726
Individual quantum units are divided into low-concentration quantum units
Figure BDA00017861021100001727
Then sequencing all high-concentration quantum units according to the adaptability from big to small, and defining the odd-numbered +.>
Figure BDA00017861021100001728
The high-concentration quantum units are high-concentration liposoluble quantum units
Figure BDA00017861021100001729
Specifying +.>
Figure BDA00017861021100001730
The high-concentration quantum unit is high-concentration non-fat soluble quantum unit->
Figure BDA00017861021100001731
And step eight, the high-concentration fat-soluble quantum individuals are freely diffused.
Free diffusion is the process by which each high concentration of fat-soluble quantum is moved to a low concentration of quantum, and this process requires no carrier or energy. First, the
Figure BDA00017861021100001732
Personal->
Figure BDA00017861021100001733
The specific process of the movement is as follows: firstly, using a simulated quantum revolving door to enable +.>
Figure BDA00017861021100001734
To w low concentration quantum individuals->
Figure BDA00017861021100001735
Exercise, generate->
Figure BDA00017861021100001736
Individual quantum->
Figure BDA00017861021100001737
Figure BDA00017861021100001738
Alternatively new generation of high concentration lipid soluble quantum individuals,>
Figure BDA00017861021100001739
d < th > dimension->
Figure BDA00017861021100001740
To w th
Figure BDA00017861021100001741
D < th > dimension->
Figure BDA00017861021100001742
The quantum rotation angle corresponding to the motion is +.>
Figure BDA00017861021100001743
Figure BDA00017861021100001744
Updated to
Figure BDA0001786102110000181
Figure BDA0001786102110000182
Personal (S)
Figure BDA0001786102110000183
The maximum adaptation in the mapping state of +.>
Figure BDA0001786102110000184
Selecting the corresponding quantum state
Figure BDA0001786102110000185
As a new generation of high concentration lipid-soluble quantum entities, wherein
Figure BDA0001786102110000186
Is->
Figure BDA0001786102110000187
Is a mapping state of (c). For each->
Figure BDA0001786102110000188
Executing the above exercise process to generate new generation high concentration liposoluble quantum individual +. >
Figure BDA0001786102110000189
Step nine, high-concentration non-fat-soluble quantum individuals move.
The diffusion assistance of high concentrations of non-fat soluble quantum entities requires no energy, but a carrier. Setting the number of carriers
Figure BDA00017861021100001810
round represents rounding to limit individuals with high concentration of non-fat soluble quanta +.>
Figure BDA00017861021100001811
Is a motion of (c).
(1) Specifying the front of the order of concentration from big to small
Figure BDA00017861021100001812
Personal->
Figure BDA00017861021100001813
The carrier is obtained and moves to the low-concentration quantum individual. Wherein->
Figure BDA00017861021100001814
Personal->
Figure BDA00017861021100001815
The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable the first->
Figure BDA00017861021100001816
Personal->
Figure BDA00017861021100001817
To w low concentration quantum individuals->
Figure BDA00017861021100001818
Sport generation->
Figure BDA00017861021100001819
Individual quantum->
Figure BDA00017861021100001820
Figure BDA00017861021100001821
Alternative new generation of high concentration non-fat soluble quantum individuals +.>
Figure BDA00017861021100001822
Personal->
Figure BDA00017861021100001823
D < th > dimension->
Figure BDA00017861021100001824
To w->
Figure BDA00017861021100001825
D < th > dimension->
Figure BDA00017861021100001826
Quantum rotation angle +.>
Figure BDA00017861021100001827
Figure BDA00017861021100001828
Updated to
Figure BDA00017861021100001829
Figure BDA00017861021100001830
Personal (S)
Figure BDA00017861021100001831
The maximum adaptation in the mapping state of +.>
Figure BDA00017861021100001832
Selection ofTheir corresponding quantum state individuals
Figure BDA00017861021100001833
As a new generation of high concentration non-fat soluble quantum units, wherein
Figure BDA00017861021100001834
Is->
Figure BDA00017861021100001835
Is a mapping state of (c). For front->
Figure BDA00017861021100001836
Personal->
Figure BDA00017861021100001837
Executing the above exercise process to generate new generation of high concentration non-fat soluble quantum individual with carrier->
Figure BDA00017861021100001838
(2) Specifying the remaining high concentration of non-fat soluble quantum individuals
Figure BDA00017861021100001839
Without carrier, using simulated quantum turnstiles to elite individual b g+1 The new generation of carrier-free high-concentration non-fat-soluble quantum individuals are obtained through movement
Figure BDA00017861021100001840
Figure BDA00017861021100001841
Wherein->
Figure BDA00017861021100001842
Personal->
Figure BDA00017861021100001843
D < th > dimension->
Figure BDA00017861021100001844
Direction b g+1 D < th > dimension->
Figure BDA00017861021100001845
Quantum rotation angle +.>
Figure BDA0001786102110000191
Figure BDA0001786102110000192
Updated to
Figure BDA0001786102110000193
Figure BDA00017861021100001948
If->
Figure BDA00017861021100001947
Is superior to->
Figure BDA0001786102110000196
Keep->
Figure BDA0001786102110000197
As a new generation of carrier-free high concentration non-fat soluble quantum individuals; no->
Figure BDA0001786102110000198
Is a new generation of carrier-free high-concentration non-fat-soluble quantum individuals.
Step ten, low-concentration quantum individual movement.
Active transportation is a movement mode which requires a carrier and enough energy, all low-concentration quantum individuals are ordered according to the fitness from large to small, and the fitness is regulated to be higher
Figure BDA0001786102110000199
The low-concentration quantum units are low-concentration high-energy quantum units meeting energy limitation +.>
Figure BDA00017861021100001910
Less fitness +.>
Figure BDA00017861021100001911
The low-concentration quantum units are low-concentration low-energy quantum units which do not meet the energy limit
Figure BDA00017861021100001912
For each low concentration high energy quantum individual there is +.>
Figure BDA00017861021100001946
The probability of (2) obtaining a carrier, and moving towards the direction of the high-concentration quantum individuals.
(1) The low-concentration high-energy quantum unit of the carrier obtained by marking is
Figure BDA00017861021100001913
And a total of O are provided,
Figure BDA00017861021100001914
o random integers, where O +.>
Figure BDA00017861021100001915
The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable +.>
Figure BDA00017861021100001916
To (1)>
Figure BDA00017861021100001917
High concentration quantum individuals->
Figure BDA00017861021100001918
Exercise, get->
Figure BDA00017861021100001919
Individual quantum->
Figure BDA00017861021100001920
Alternatively, the method may compriseNew generation of low concentration high energy quantum individuals, o +. >
Figure BDA00017861021100001921
D < th > dimension->
Figure BDA00017861021100001922
To (1)>
Figure BDA00017861021100001923
Personal->
Figure BDA00017861021100001924
D < th > dimension->
Figure BDA00017861021100001925
Quantum rotation angle corresponding to motion
Figure BDA00017861021100001926
Figure BDA00017861021100001927
Updated to->
Figure BDA00017861021100001928
Figure BDA00017861021100001929
Figure BDA00017861021100001930
Personal->
Figure BDA00017861021100001931
Maximum fitness in the mapping state of (a)
Figure BDA00017861021100001932
Selecting the quantum state->
Figure BDA00017861021100001933
Low concentration high energy quantum individuals as new generation derived carriers, wherein +.>
Figure BDA00017861021100001934
Is->
Figure BDA00017861021100001935
Mapping states of (a) for each +.>
Figure BDA00017861021100001936
Executing the above movement process to generate low-concentration high-energy quantum individual of new generation of obtained carrier->
Figure BDA00017861021100001937
(2) Marking carrier-free low-concentration high-energy quantum individuals as
Figure BDA00017861021100001938
And is in common with
Figure BDA00017861021100001939
Personal (S)>
Figure BDA00017861021100001940
And q.noteq.o, where q.sub.th->
Figure BDA00017861021100001941
The specific motion process of (a) is as follows: firstly using a simulated quantum revolving door to enable +.>
Figure BDA00017861021100001942
Random exercise is taken->
Figure BDA00017861021100001943
A local search is performed. The (q) th->
Figure BDA00017861021100001944
D < th > dimension->
Figure BDA00017861021100001945
The corresponding quantum rotation angle is +.>
Figure BDA0001786102110000201
Figure BDA0001786102110000202
Is [ -1,1]A uniform random number within.
Figure BDA0001786102110000203
Updated to
Figure BDA0001786102110000204
If->
Figure BDA0001786102110000205
Is superior to->
Figure BDA0001786102110000206
Then reserve->
Figure BDA0001786102110000207
Low concentration high energy quantum individuals as new generation carrier-free, otherwise let +.>
Figure BDA0001786102110000208
Is a new generation of carrier-free low-concentration high-energy quantum individuals. For each->
Figure BDA0001786102110000209
Executing the above movement process to generate new generation carrier-free low concentration high energy quantum individual +.>
Figure BDA00017861021100002010
(3) All low concentration low energy quantum individuals
Figure BDA00017861021100002011
To elite quantum unit b g+1 And (5) movement. Use of analog quantum turnstiles>
Figure BDA00017861021100002012
Individual quantum->
Figure BDA00017861021100002013
D < th > dimension->
Figure BDA00017861021100002014
Direction b g+1 D < th > dimension- >
Figure BDA00017861021100002015
The quantum rotation angle of the motion is
Figure BDA00017861021100002016
Figure BDA00017861021100002017
Updated to->
Figure BDA00017861021100002018
Figure BDA00017861021100002019
If->
Figure BDA00017861021100002020
Is superior to->
Figure BDA00017861021100002021
Then reserve->
Figure BDA00017861021100002022
As a new generation of low concentration low energy quantum individuals, otherwise let +.>
Figure BDA00017861021100002023
As a new generation of low concentration low energy quantum individuals.
Step eleven, generating a new generation quantum substance group.
Will be
Figure BDA00017861021100002024
Figure BDA00017861021100002025
Quantum substance group combined into new generation +.>
Figure BDA00017861021100002026
Step twelve, judging whether the maximum iteration times are reached, if G is smaller than G, enabling G to be equal to g+1, and returning to the step six; otherwise, if the maximum iteration times g=g are reached, the mapping state of the quantum unit with the maximum adaptability is output as an estimation result, and the optimal estimation value of the angle and the frequency is obtained.
The invention designs a space-time direction finding method based on a quantum cell membrane optimization mechanism, which can carry out joint estimation on the azimuth angle and the frequency of a signal. The specific implementation steps are as follows: (1) acquiring signal time domain data. (2) Acquiring a signal snapshot sample and performing time domain delay on the sampled data. (3) And constructing a maximum likelihood estimation equation of the maximum likelihood estimation. (4) A population of quantum substances initializing a quantum cell membrane optimization method. (5) constructing a fitness function. (6) And selecting elite quantum individuals and carrying out local search on the elite quantum individuals. (7) The quantum units are divided into high-concentration fat-soluble quantum units, high-concentration non-fat-soluble quantum units and low-concentration quantum units. (8) Each quantum unit carries out free diffusion, assisted diffusion, active transportation and other movements according to the updating rule. (9) And after the maximum iteration times are reached, mapping the optimal quantum units into a solution space to obtain a mapping state of the optimal quantum units, and outputting the mapping state as an estimation result. The direction finding method designed by the invention has the advantages of high speed and high precision in joint estimation of the azimuth angle and the frequency of the signal, can effectively perform joint estimation on the angle and the frequency of a coherent source, and has excellent performance under the conditions of low signal-to-noise ratio and small snapshot number.

Claims (2)

1. A space-time direction finding method based on a quantum cell membrane optimization mechanism is characterized by comprising the following steps:
(1) Acquiring signal time domain data;
(2) Acquiring signal snapshot sampling and carrying out time domain delay on sampling data;
(3) Constructing a maximum likelihood estimation equation of the maximum likelihood estimation;
(4) Initializing a quantum substance group;
(5) Constructing a fitness function;
(6) Selecting elite quantum individuals, and carrying out local search on the elite quantum individuals;
(7) Dividing quantum individual types;
(8) High concentration fat-soluble quantum individual free diffusion;
(9) High concentration non-fat soluble quantum individual exercise;
(10) Low concentration quantum individual motion;
(11) Generating a new generation quantum substance group;
(12) Judging whether the maximum iteration times are reached;
the acquiring signal time domain data includes:
there are I azimuth angles θ= (θ) 1 ,θ 2 ,…,θ I ) Frequency ω= (ω) 1 ,ω 2 ,…,ω I ) Is incident on a uniform linear array containing M array elements with a spacing eta, each array element has a delay device with K-level time domain delay of sigma, wherein theta i An included angle between the i-th signal arrival direction and the normal line direction of the linear array;
the ith signal at time t is represented by a complex envelope:
Figure FDA0004020475520000011
where j is an imaginary unit, u i (t) is the amplitude of the signal,
Figure FDA0004020475520000012
is the phase of the signal;
the ith signal reaching the mth array element at the moment t is as follows:
s i (t-τ mi )＝s i (t)exp(-jω i τ mi )
wherein ,τmi The spatial delay relative to the reference element for the ith signal to reach the mth element;
mth mThe position of each array element is delta m The following steps are:
Figure FDA0004020475520000013
wherein c is the propagation speed of the signal;
in an ideal state, each array element in the array is not affected by inconsistent channels or mutual coupling factors, and the data received by the mth array element at the moment t is:
Figure FDA0004020475520000021
wherein nm (t) represents gaussian white noise at the mth element at time t;
the output data of the signals after time domain delay generated by the kth-stage delayer of the mth array element is as follows:
Figure FDA0004020475520000022
writing the data vector into a matrix form to obtain the data vector received by the mth array element at the moment t, wherein the data vector is as follows:
Y m (t)＝A m S(t)+N m (t)
wherein ,Am Is an array flow pattern matrix, S (t) is a signal vector, N m (t) is a noise vector, m=1, 2, …, M
Y is set to m (t) arranged as a matrix
Figure FDA0004020475520000023
And further simplifying to obtain:
Y(t)＝A (θ,ω) S(t)+N(t)
wherein the noise matrix
Figure FDA0004020475520000024
M x K row I column space-time two-dimensional array flow pattern matrix
Figure FDA0004020475520000025
The sampling data of the U-th snapshot sampling is Y (U), u=1, 2, …, U, and a covariance matrix of the sampling data is constructed:
Figure FDA0004020475520000026
wherein U is the total number of snapshots, and H represents conjugate transposition operation;
the constructing a maximum likelihood estimation equation for maximum likelihood estimation, initializing a quantum substance group, and constructing an fitness function, including:
Constructing an orthogonal projection matrix by adopting a space-time two-dimensional maximum likelihood method:
Figure FDA0004020475520000027
wherein ,
Figure FDA0004020475520000028
for one of the solutions of signal azimuth, +.>
Figure FDA0004020475520000029
One solution in a solution space for signal frequencies;
the maximum likelihood equation for maximum likelihood estimation is:
Figure FDA0004020475520000031
wherein tr represents a matrix tracing operation;
setting total number H of quantum units in quantum substance group, maximum iteration number G, and expressing H quantum units in G iteration as
Figure FDA0004020475520000032
h=1, 2, …, H; generating H D=2I dimension quanta individuals->
Figure FDA0004020475520000033
The d dimension of the h quantum unit is +.>
Figure FDA0004020475520000034
At the first generation, the value is [0,1 ]]A uniform random number within, d=1, 2, …, D;
odd dimensions of quantum individuals
Figure FDA0004020475520000035
d=1, 3, …, D-1, mapped to the range of signal azimuth solutions
Figure FDA0004020475520000036
Even dimension->
Figure FDA0004020475520000037
Mapping to a range of signal frequency solutions
Figure FDA0004020475520000038
Obtaining mapped individuals->
Figure FDA0004020475520000039
Constructing a quantum individual fitness function:
Figure FDA00040204755200000310
selecting elite quantum individuals, and carrying out local search on the elite quantum individuals, wherein the method comprises the following steps:
calculating the h quantum unit in quantum substance group
Figure FDA00040204755200000311
The fitness of (h=1, 2, …, H), the quantum unit with the greatest fitness is elite quantum unit +.>
Figure FDA00040204755200000312
Re-using analog quantum revolving gate by letting b g Random exercise->
Figure FDA00040204755200000313
Local search is carried out again to obtain alternative new generation elite quantum individuals +. >
Figure FDA00040204755200000314
First->
Figure FDA00040204755200000315
In the sub-random movement, b g D < th > dimension->
Figure FDA00040204755200000316
The corresponding quantum rotation angle is +.>
Figure FDA00040204755200000317
Is [ -1,1]Inside uniform random number,/, inside uniform random number,
Figure FDA00040204755200000318
Updated to->
Figure FDA00040204755200000319
Figure FDA00040204755200000320
The maximum adaptation in the mapping state of +.>
Figure FDA00040204755200000321
wherein
Figure FDA00040204755200000322
Is->
Figure FDA00040204755200000323
Mapping state of->
Figure FDA00040204755200000324
Then reserve->
Figure FDA00040204755200000325
Quantum state->
Figure FDA00040204755200000326
As a new generation elite quantum unit; no make b g+1 ＝b g As a new generation elite quantum unit;
the dividing quantum individual types includes:
order the
Figure FDA00040204755200000327
For the h quantum unit in the quantum substance group +.>
Figure FDA00040204755200000328
Define the concentration of the position of the quantum substance group as +.>
Figure FDA00040204755200000329
wherein αh For distinguishing condition->
Figure FDA00040204755200000330
The number of times that it is established,
Figure FDA00040204755200000331
and->
Figure FDA00040204755200000332
Sequencing each quantum in the quantum substance group from large to small according to concentration, and ranking the concentration by half
Figure FDA0004020475520000041
The individual quantum units are divided into high-concentration quantum units->
Figure FDA0004020475520000042
Concentration rank second half +.>
Figure FDA0004020475520000043
The individual quantum units are divided into low-concentration quantum units->
Figure FDA0004020475520000044
All high-concentration quantum units are ordered according to the adaptability from big to small, and the units are arranged in odd number positions
Figure FDA0004020475520000045
The high-concentration quantum unit is high-concentration liposoluble quantum unit->
Figure FDA0004020475520000046
Specifying +.>
Figure FDA0004020475520000047
The high-concentration quantum unit is high-concentration non-fat soluble quantum unit->
Figure FDA0004020475520000048
The high concentration fat-soluble quantum unit free diffusion comprises:
first, the
Figure FDA0004020475520000049
Personal->
Figure FDA00040204755200000410
The specific process of the movement is as follows: an analog quantum turnstile is used first, Make->
Figure FDA00040204755200000411
To w low concentration quantum individuals->
Figure FDA00040204755200000412
Exercise, generate->
Figure FDA00040204755200000413
Individual quantum->
Figure FDA00040204755200000414
Alternatively new generation of high concentration lipid soluble quantum individuals,>
Figure FDA00040204755200000415
d < th > dimension->
Figure FDA00040204755200000416
To w->
Figure FDA00040204755200000417
D < th > dimension->
Figure FDA00040204755200000418
The quantum rotation angle corresponding to the motion is:
Figure FDA00040204755200000419
Figure FDA00040204755200000420
updated to->
Figure FDA00040204755200000421
d＝1，2，…，D，
Figure FDA00040204755200000422
Personal->
Figure FDA00040204755200000423
The maximum adaptation in the mapping state of +.>
Figure FDA00040204755200000424
Select the corresponding quantum state->
Figure FDA00040204755200000425
As a new generation of high concentration lipid-soluble quantum entities, wherein
Figure FDA00040204755200000426
Is->
Figure FDA00040204755200000427
Mapping states of (a) for each +.>
Figure FDA00040204755200000428
Executing the above exercise process to generate new generation high concentration liposoluble quantum individual +.>
Figure FDA00040204755200000429
The high concentration of non-fat soluble quantum individual motion comprises:
the high concentration non-fat soluble quantum individual does not need energy for assisting diffusion, but needs carrier, and the number of carriers is set
Figure FDA00040204755200000430
Wherein round represents a rounding for limiting the high concentration of non-fat soluble quantum individuals +.>
Figure FDA00040204755200000431
Motion of (a)
(1) Specifying the front of the order of concentration from big to small
Figure FDA00040204755200000432
Personal->
Figure FDA00040204755200000433
Obtaining a carrier, moving to a low concentration quantum unit, wherein +.>
Figure FDA00040204755200000434
Personal->
Figure FDA00040204755200000435
The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable the first->
Figure FDA00040204755200000440
Personal->
Figure FDA00040204755200000436
To w low concentration quantum individuals->
Figure FDA00040204755200000437
Sport generation->
Figure FDA00040204755200000438
Individual quantum->
Figure FDA00040204755200000439
Figure FDA0004020475520000051
Alternative new generation of high concentration non-fat soluble quantum individuals +.>
Figure FDA00040204755200000546
Personal->
Figure FDA0004020475520000052
D < th > dimension->
Figure FDA0004020475520000053
To w- >
Figure FDA0004020475520000054
D < th > dimension->
Figure FDA0004020475520000055
Quantum rotation angle +.>
Figure FDA0004020475520000056
Figure FDA0004020475520000057
Updated to
Figure FDA0004020475520000058
d＝1,2,…,D；
Figure FDA00040204755200000547
Personal->
Figure FDA00040204755200000510
The maximum adaptation in the mapping state of +.>
Figure FDA00040204755200000511
Selecting the corresponding quantum state individual->
Figure FDA00040204755200000512
As a new generation of high concentration non-fat soluble quantum units, wherein
Figure FDA00040204755200000513
Is->
Figure FDA00040204755200000514
Mapping state of>
Figure FDA00040204755200000515
Personal->
Figure FDA00040204755200000516
Executing the above exercise process to generate new generation of high concentration non-fat soluble quantum individual with carrier->
Figure FDA00040204755200000517
(2) Specifying the remaining high concentration of non-fat soluble quantum individuals
Figure FDA00040204755200000518
Without carrier, using simulated quantum turnstiles to elite individual b g+1 The new generation of carrier-free high-concentration non-fat-soluble quantum individuals are obtained by exercise>
Figure FDA00040204755200000519
Figure FDA00040204755200000520
Wherein->
Figure FDA00040204755200000521
Personal->
Figure FDA00040204755200000522
D < th > dimension->
Figure FDA00040204755200000523
Direction b g+1 D < th > dimension->
Figure FDA00040204755200000524
Quantum rotation angle +.>
Figure FDA00040204755200000525
Figure FDA00040204755200000526
Updated to->
Figure FDA00040204755200000527
Figure FDA00040204755200000528
d=1, 2, …, D, if->
Figure FDA00040204755200000529
Is superior to->
Figure FDA00040204755200000530
Keep->
Figure FDA00040204755200000531
As a new generation of carrier-free high concentration non-fat soluble quantum individuals; no->
Figure FDA00040204755200000532
Is a new generation of carrier-free high-concentration non-fat-soluble quantum individuals;
the low concentration quantum individual motion comprising:
active transportation is a movement mode which requires a carrier and enough energy, all low-concentration quantum individuals are ordered according to the fitness from large to small, and the fitness is regulated to be higher
Figure FDA00040204755200000533
The low-concentration quantum units are low-concentration high-energy quantum units meeting energy limitation +. >
Figure FDA00040204755200000534
Less fitness +.>
Figure FDA00040204755200000535
Individual low concentration quanta are not meeting energy limitationsLow concentration low energy quantum unit
Figure FDA00040204755200000536
For each low concentration high energy quantum individual there is +.>
Figure FDA00040204755200000537
The probability of (2) obtaining a carrier, and moving towards the direction of a high-concentration quantum individual;
(1) The low-concentration high-energy quantum unit of the carrier obtained by marking is
Figure FDA00040204755200000538
And a total of O are provided,
Figure FDA00040204755200000539
o random integers, where O +.>
Figure FDA00040204755200000540
The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable +.>
Figure FDA00040204755200000541
To (1)>
Figure FDA00040204755200000542
High concentration quantum individuals->
Figure FDA00040204755200000543
Exercise, get->
Figure FDA00040204755200000544
Individual quantum units
Figure FDA00040204755200000545
Alternative new generation low concentration high energy quantum individuals, o +.>
Figure FDA0004020475520000061
D < th > dimension->
Figure FDA0004020475520000062
To (1)>
Figure FDA0004020475520000063
Personal->
Figure FDA0004020475520000064
D < th > dimension->
Figure FDA0004020475520000065
Quantum rotation angle corresponding to motion
Figure FDA0004020475520000066
Figure FDA0004020475520000067
Updated to->
Figure FDA0004020475520000068
Figure FDA0004020475520000069
d＝1,2,…,D，
Figure FDA00040204755200000652
Personal->
Figure FDA00040204755200000653
Maximum fitness in the mapping state of (a)
Figure FDA00040204755200000612
Selecting the quantum state->
Figure FDA00040204755200000613
As a new generation of low-concentration high-energy quantum units of the obtained carrier,wherein->
Figure FDA00040204755200000614
Is->
Figure FDA00040204755200000615
Mapping states of (a) for each +.>
Figure FDA00040204755200000616
Executing the above movement process to generate low-concentration high-energy quantum individual of new generation of obtained carrier->
Figure FDA00040204755200000617
(2) Marking carrier-free low-concentration high-energy quantum individuals as
Figure FDA00040204755200000618
And is common with->
Figure FDA00040204755200000619
The number of the two-dimensional space-saving type,
Figure FDA00040204755200000620
and q.noteq.o, where q.sub.th->
Figure FDA00040204755200000621
The specific motion process of (a) is as follows: firstly using a simulated quantum revolving door to enable +.>
Figure FDA00040204755200000622
Random exercise is taken- >
Figure FDA00040204755200000623
Performing local search; the (q) th->
Figure FDA00040204755200000624
D < th > dimension->
Figure FDA00040204755200000625
The corresponding quantum rotation angle is
Figure FDA00040204755200000626
Figure FDA00040204755200000627
Is [ -1,1]Inside uniform random number,/, inside uniform random number,/>
Figure FDA00040204755200000628
Updated to->
Figure FDA00040204755200000629
d=1, 2, …, D, if->
Figure FDA00040204755200000630
Is superior to->
Figure FDA00040204755200000631
Then reserve
Figure FDA00040204755200000632
Low concentration high energy quantum individuals as new generation carrier-free, otherwise let +.>
Figure FDA00040204755200000633
For new generation of carrier-free low concentration high energy quantum individuals, for each +.>
Figure FDA00040204755200000634
Executing the above movement process to generate new generation carrier-free low concentration high energy quantum individual +.>
Figure FDA00040204755200000635
(3) All low concentration low energy quantum individuals
Figure FDA00040204755200000636
To elite quantum unit b g+1 Motion, using analog quantum turnstile, +.>
Figure FDA00040204755200000637
Individual quantum->
Figure FDA00040204755200000638
D < th > dimension->
Figure FDA00040204755200000639
Direction b g+1 D < th > dimension->
Figure FDA00040204755200000640
The quantum rotation angle of the motion is
Figure FDA00040204755200000641
Figure FDA00040204755200000642
Updated to->
Figure FDA00040204755200000643
Figure FDA00040204755200000644
d=1, 2, …, D, if->
Figure FDA00040204755200000645
Is superior to->
Figure FDA00040204755200000646
Then reserve->
Figure FDA00040204755200000647
As a new generation of low concentration low energy quantum individuals, otherwise let +.>
Figure FDA00040204755200000648
As a new generation of low concentration low energy quantum individuals;
the generation of a new generation of quantum species population includes:
will be
Figure FDA00040204755200000649
Figure FDA00040204755200000650
Quantum substance group combined into new generation +.>
Figure FDA00040204755200000651
2. The method of claim 1, wherein said determining whether the maximum number of iterations is reached comprises:
if G is less than G, let g=g+1, return to step six; otherwise, if the maximum iteration times g=g are reached, the mapping state of the quantum unit with the maximum adaptability is output as an estimation result, and the optimal estimation value of the angle and the frequency is obtained.
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