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 PDFInfo
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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
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:
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:
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:
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:
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(t)=A (θ,ω) S(t)+N(t)
wherein the noise matrixM x K row and I column space-time two-dimensional array flow pattern matrix>
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:
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:
wherein ,for one of the solutions of signal azimuth, +.>One solution in a solution space for signal frequencies;
the maximum likelihood equation for maximum likelihood estimation is:
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 Generating H D=2I dimension quanta individuals->The d dimension of the h quantum unit is +.>At the first generation, the value is [0,1 ]]A uniform random number within, d=1, 2, …, D;
odd dimensions of quantum individualsMapping to a range of signal azimuth solutionsEven dimension->Mapping to a range of signal frequency solutionsObtaining mapped individuals->Constructing a quantum individual fitness function:
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 groupThe fitness of (h=1, 2, …, H), the quantum unit with the greatest fitness is elite quantum unit +.>Re-using analog quantum revolving gate by letting b g Random movementLocal search is carried out again to obtain alternative new generation elite quantum individuals +.>First->In the sub-random movement, b g D < th > dimension->The corresponding quantum rotation angle is +.> Is [ -1,1]Inside uniform random number,/, inside uniform random number,/>Updated to The maximum adaptation in the mapping state of +.> wherein />Is->Mapping state of (1), ifThen reserve->Quantum state->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 theFor the h quantum unit in the quantum substance group +. >Define the concentration of the position of the quantum substance group as +.> wherein αh For distinguishing condition->The number of times that it is established,and->
Sequencing each quantum in the quantum substance group from large to small according to concentration, and ranking the concentration by halfThe individual quantum units are divided into high-concentration quantum units->Concentration ranking of the second halfThe individual quantum units are divided into low-concentration quantum units->
All high-concentration quantum units are ordered according to the adaptability from big to small, and the units are arranged in odd number positionsThe high-concentration quantum unit is high-concentration liposoluble quantum unit->Specifying +.>The high-concentration quantum unit is high-concentration non-fat soluble quantum unit->
The high concentration fat-soluble quantum unit free diffusion comprises:
first, thePersonal->The specific process of the movement is as follows: firstly, using a simulated quantum revolving door to enable +.>To w low concentration quantum individuals->Exercise, generate->Individual quantum->Alternatively new generation of high concentration lipid soluble quantum individuals,>d < th > dimension->To w->D < th > dimension->The quantum rotation angle corresponding to the motion is:
updated to-> Personal->Adaptation in mapping state of (c)The maximum degree is->Select the corresponding quantum state->As a new generation of high concentration lipid-soluble quantum entities, wherein Is->Mapping states of (a) for each +.>Executing the above exercise process to generate new generation high concentration liposoluble quantum individual +.>
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 setWherein round represents a rounding for limiting the high concentration of non-fat soluble quantum individuals +.>The movement (1) of (2) specifies the front ++in order of concentration from large to small>Personal->Obtaining a carrier, moving to a low concentration quantum unit, wherein +.>Personal->The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable the first->Personal->To w low concentration quantum individuals->Sport generation->Individual quantum-> Alternative new generation of high concentration non-fat soluble quantum individuals +.>Personal->D < th > dimension->To w->D < th > dimension->Quantum rotation angle +.> Updated to Personal (S)The maximum adaptation in the mapping state of +.>Selecting the corresponding quantum state individualAs a new generation of high concentration non-fat soluble quantum units, whereinIs->Mapping state of>Personal->Executing the above exercise process to generate new generation of high concentration non-fat soluble quantum individual with carrier->
(2) Specifying the remaining high concentration of non-fat soluble quantum individuals 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 Wherein->Personal->D < th > dimension->Direction b g+1 D < th > dimension->Quantum rotation angle +.> Updated to If->Is superior to->Keep->High concentration non-fat soluble quantum dots as new generation carrier-freeA body; no->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 higherThe low-concentration quantum units are low-concentration high-energy quantum units meeting energy limitation +.>Less fitness +.>The low-concentration quantum units are low-concentration low-energy quantum units which do not meet the energy limitFor each low concentration high energy quantum individual there is +.>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 isAnd a total of O are provided,o random integers, where O +.>The specific process of the movement is as follows: first use the mould Quasi quantum revolving door>To (1)>High concentration quantum individuals->Exercise, get->Individual quantum unitsAlternative new generation low concentration high energy quantum individuals, o +.>D < th > dimension->To (1)>Personal->D < th > dimension->Quantum rotation angle corresponding to motion Updated to-> Personal->The maximum adaptation in the mapping state of +.>Selecting the quantum state->Low concentration high energy quantum individuals as new generation derived carriers, wherein +.>Is->Mapping states of (a) for each +.>Executing the above movement process to generate low-concentration high-energy quantum individual of new generation of obtained carrier->
(2) Marking carrier-free low-concentration high-energy quantum individuals asAnd is in common withPersonal (S)>And q.noteq.o, where q.sub.th->The specific motion process of (a) is as follows: firstly using a simulated quantum revolving door to enable +.>Random exercise is taken->Performing local search; the (q) th->D < th > dimension->The corresponding quantum rotation angle is +.> Is [ -1,1]A uniform random number within the matrix is used,
updated to->If->Is superior to->Then reserve->Low concentration high energy quantum individuals as new generation carrier-free, otherwise let +.>Is a new generation of carrier-free low-concentration high-energy quantum individuals,for each->Executing the above movement process to generate new generation carrier-free low concentration high energy quantum individual +. >
(3) All low concentration low energy quantum individualsTo elite quantum unit b g+1 Motion, using analog quantum turnstile, +.>Individual quantum->D < th > dimension->Direction b g+1 D < th > dimension->The quantum rotation angle of the motion is Updated to-> If->Is superior to->Then reserve->As a new generation of low concentration low energy quantum individuals, otherwise let +.>As a new generation of low concentration low energy quantum individuals.
The generation of a new generation of quantum species population includes:
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 envelopeWhere j is an imaginary unit, u i (t) is the amplitude of the signal, +.>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->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 +.> 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 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 matrixFurther simplified to Y (t) =A (θ,ω) S (t) +N (t), wherein the noise matrixM x K row I column space-time two-dimensional array flow pattern matrixRecord the ith snapshot sampleIs Y (U), u=1, 2, …, U, constructing covariance matrix of the sampled data +.>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 wherein />For a possible solution in the solution space of the signal azimuth,/>For one possible solution in the solution space of the signal frequencies, the maximum likelihood equation for the maximum likelihood estimation is +.>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 asGenerating H D=2I dimension quanta individuals->The d dimension of the h quantum unit is +. >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 individualsMapping to a range of signal azimuth solutionsEven dimension->Mapping to the signal frequency solution is +.>Obtaining mapped individuals->Constructing a quantum individual fitness function>
Step six, selecting elite quantum individuals, and carrying out local search on the elite quantum individuals.
Calculating the h quantum unit in quantum substance groupThe fitness of (h=1, 2, …, H), the quantum unit with the greatest fitness is elite quantum unit +.>Re-using analog quantum revolving gate by letting b g Random exercise->Local search is carried out again to obtain alternative new generation elite quantum individuals +.>First->In the sub-random movement, b g D < th > dimension->The corresponding quantum rotation angle is +.> Is [ -1,1]A uniform random number within. />Updated to-> The maximum adaptation in the mapping state of +.> wherein />Is thatMapping state of->Then reserve->Quantum state->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 theFor the h quantum unit in the quantum substance group +.>Define the concentration of the position of the quantum substance group as +. > wherein αh For distinguishing condition->The number of times that it is established,and->Ordering each quantum in the quantum substance group from big to small according to concentration, and ranking the first half of the concentration>The individual quantum units are divided into high-concentration quantum units-> Concentration rank second half +.>Individual quantum units are divided into low-concentration quantum unitsThen sequencing all high-concentration quantum units according to the adaptability from big to small, and defining the odd-numbered +.>The high-concentration quantum units are high-concentration liposoluble quantum unitsSpecifying +.>The high-concentration quantum unit is high-concentration non-fat soluble quantum unit->
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, thePersonal->The specific process of the movement is as follows: firstly, using a simulated quantum revolving door to enable +.>To w low concentration quantum individuals->Exercise, generate->Individual quantum-> Alternatively new generation of high concentration lipid soluble quantum individuals,>d < th > dimension->To w thD < th > dimension->The quantum rotation angle corresponding to the motion is +.> Updated to-> Personal (S)The maximum adaptation in the mapping state of +.>Selecting the corresponding quantum state As a new generation of high concentration lipid-soluble quantum entities, whereinIs->Is a mapping state of (c). For each->Executing the above exercise process to generate new generation high concentration liposoluble quantum individual +.>
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 carriersround represents rounding to limit individuals with high concentration of non-fat soluble quanta +.>Is a motion of (c).
(1) Specifying the front of the order of concentration from big to smallPersonal->The carrier is obtained and moves to the low-concentration quantum individual. Wherein->Personal->The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable the first->Personal->To w low concentration quantum individuals->Sport generation->Individual quantum-> Alternative new generation of high concentration non-fat soluble quantum individuals +.>Personal->D < th > dimension->To w->D < th > dimension->Quantum rotation angle +.> Updated to Personal (S)The maximum adaptation in the mapping state of +.>Selecting the corresponding quantum state individualAs a new generation of high concentration non-fat soluble quantum units, whereinIs->Is a mapping state of (c). For front->Personal->Executing the above exercise process to generate new generation of high concentration non-fat soluble quantum individual with carrier- >
(2) Specifying the remaining high concentration of non-fat soluble quantum individualsWithout 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 Wherein->Personal->D < th > dimension->Direction b g+1 D < th > dimension->Quantum rotation angle +.> Updated to If->Is superior to->Keep->As a new generation of carrier-free high concentration non-fat soluble quantum individuals; no->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 higherThe low-concentration quantum units are low-concentration high-energy quantum units meeting energy limitation +.>Less fitness +.>The low-concentration quantum units are low-concentration low-energy quantum units which do not meet the energy limitFor each low concentration high energy quantum individual there is +.>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 isAnd a total of O are provided,o random integers, where O +. >The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable +.>To (1)>High concentration quantum individuals->Exercise, get->Individual quantum unitsAlternative new generation low concentration high energy quantum individuals, o +.>D < th > dimension->To (1)>Personal->D < th > dimension->Quantum rotation angle corresponding to motion Updated to-> Personal->Maximum fitness in the mapping state of (a)Selecting the quantum state->Low concentration high energy quantum individuals as new generation derived carriers, wherein +.>Is->Mapping states of (a) for each +.>Executing the above movement process to generate low-concentration high-energy quantum individual of new generation of obtained carrier->
(2) Marking carrier-free low-concentration high-energy quantum individuals asAnd is common with->Personal (S)>And q.noteq.o, where q.sub.th->The specific motion process of (a) is as follows: firstly using a simulated quantum revolving door to enable +.>Random exercise is taken->A local search is performed. The (q) th->D < th > dimension->The corresponding quantum rotation angle is Is [ -1,1]A uniform random number within. />Updated to->If->Is superior to->Then reserve->Low concentration high energy quantum individuals as new generation carrier-free, otherwise let +.>Is a new generation of carrier-free low-concentration high-energy quantum individuals. For each->Executing the above movement process to generate new generation carrier-free low concentration high energy quantum individual +. >
(3) All low concentration low energy quantum individualsTo elite amountChild b g+1 And (5) movement. Use of analog quantum turnstiles>Individual quantum->D < th > dimension->Direction b g+1 D < th > dimension->The quantum rotation angle of the motion is Updated to-> If->Is superior to->Then reserve->As a new generation of low concentration low energy quantum individuals, otherwise let +.>As a new generation of low concentration low energy quantum individuals.
Step eleven, generating a new generation quantum substance group.
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,ζ=0.8,/>U=100,H=80,G=30,M=4,K=4,/>
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 envelopeWhere j is an imaginary unit, u i (t) is the amplitude of the signal, +.>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->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 +.> 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 delayWriting 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 matrixFurther simplified to Y (t) =A (θ,ω) S (t) +N (t), wherein the noise matrixM x K row I column space-time two-dimensional array flow pattern matrixRecording 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 +.>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 wherein />For a possible solution in the solution space of the signal azimuth,/>For one possible solution in the solution space of the signal frequency, the maximum likelihood equation of the maximum likelihood estimation istr 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 asGenerating H D=2I dimension quanta individuals->The d dimension of the h quantum unit is +.>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 individualsMapping to signalsWithin the range of azimuth solutionEven dimension->Mapping to a range of signal frequency solutionsObtaining mapped individuals->Constructing quantum individual fitness functions
Step six, selecting elite quantum individuals, and carrying out local search on the elite quantum individuals.
Calculating the h quantum unit in quantum substance groupThe fitness of (h=1, 2, …, H), the quantum unit with the greatest fitness is elite quantum unit +.>Re-using analog quantum revolving gate by letting b g Random movementLocal search is carried out again to obtain alternative new generation elite quantum individuals +.>First->In the course of the secondary random movement,b g d < th > dimension->The corresponding quantum rotation angle is +.> Is [ -1,1]A uniform random number within. />Updated to-> The maximum adaptation in the mapping state of +.> wherein />Is thatMapping state of->Then reserve->Quantum state->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 theFor the h quantum unit in the quantum substance group +.>Define the concentration of the position of the quantum substance group as +.> wherein αh For distinguishing condition->The number of times that it is established,and->Ordering each quantum in the quantum substance group from big to small according to concentration, and ranking the first half of the concentration >The individual quantum units are divided into high-concentration quantum units-> Concentration rank second half +.>Individual quantum units are divided into low-concentration quantum unitsThen sequencing all high-concentration quantum units according to the adaptability from big to small, and defining the odd-numbered +.>The high-concentration quantum units are high-concentration liposoluble quantum unitsSpecifying +.>The high-concentration quantum unit is high-concentration non-fat soluble quantum unit->
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, thePersonal->The specific process of the movement is as follows: firstly, using a simulated quantum revolving door to enable +.>To w low concentration quantum individuals->Exercise, generate->Individual quantum-> Alternatively new generation of high concentration lipid soluble quantum individuals,>d < th > dimension->To w thD < th > dimension->The quantum rotation angle corresponding to the motion is +.> Updated to Personal (S)The maximum adaptation in the mapping state of +.>Selecting the corresponding quantum stateAs a new generation of high concentration lipid-soluble quantum entities, whereinIs->Is a mapping state of (c). For each->Executing the above exercise process to generate new generation high concentration liposoluble quantum individual +. >
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 carriersround represents rounding to limit individuals with high concentration of non-fat soluble quanta +.>Is a motion of (c).
(1) Specifying the front of the order of concentration from big to smallPersonal->The carrier is obtained and moves to the low-concentration quantum individual. Wherein->Personal->The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable the first->Personal->To w low concentration quantum individuals->Sport generation->Individual quantum->/>Alternative new generation of high concentration non-fat soluble quantum individuals +.>Personal->D < th > dimension->To w->D < th > dimension->Quantum rotation angle +.> Updated to Personal (S)The maximum adaptation in the mapping state of +.>Selection ofTheir corresponding quantum state individualsAs a new generation of high concentration non-fat soluble quantum units, whereinIs->Is a mapping state of (c). For front->Personal->Executing the above exercise process to generate new generation of high concentration non-fat soluble quantum individual with carrier->
(2) Specifying the remaining high concentration of non-fat soluble quantum individualsWithout 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 Wherein->Personal->D < th > dimension->Direction b g+1 D < th > dimension->Quantum rotation angle +.> Updated to If->Is superior to->Keep->As a new generation of carrier-free high concentration non-fat soluble quantum individuals; no->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 higherThe low-concentration quantum units are low-concentration high-energy quantum units meeting energy limitation +.>Less fitness +.>The low-concentration quantum units are low-concentration low-energy quantum units which do not meet the energy limitFor each low concentration high energy quantum individual there is +.>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 isAnd a total of O are provided,o random integers, where O +.>The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable +.>To (1)>High concentration quantum individuals->Exercise, get->Individual quantum->Alternatively, the method may compriseNew generation of low concentration high energy quantum individuals, o +. >D < th > dimension->To (1)>Personal->D < th > dimension->Quantum rotation angle corresponding to motion Updated to-> Personal->Maximum fitness in the mapping state of (a)Selecting the quantum state->Low concentration high energy quantum individuals as new generation derived carriers, wherein +.>Is->Mapping states of (a) for each +.>Executing the above movement process to generate low-concentration high-energy quantum individual of new generation of obtained carrier->
(2) Marking carrier-free low-concentration high-energy quantum individuals asAnd is in common withPersonal (S)>And q.noteq.o, where q.sub.th->The specific motion process of (a) is as follows: firstly using a simulated quantum revolving door to enable +.>Random exercise is taken->A local search is performed. The (q) th->D < th > dimension->The corresponding quantum rotation angle is +.> Is [ -1,1]A uniform random number within. />Updated toIf->Is superior to->Then reserve->Low concentration high energy quantum individuals as new generation carrier-free, otherwise let +.>Is a new generation of carrier-free low-concentration high-energy quantum individuals. For each->Executing the above movement process to generate new generation carrier-free low concentration high energy quantum individual +.>
(3) All low concentration low energy quantum individualsTo elite quantum unit b g+1 And (5) movement. Use of analog quantum turnstiles>Individual quantum->D < th > dimension->Direction b g+1 D < th > dimension- >The quantum rotation angle of the motion is Updated to-> If->Is superior to->Then reserve->As a new generation of low concentration low energy quantum individuals, otherwise let +.>As a new generation of low concentration low energy quantum individuals.
Step eleven, generating a new generation quantum substance group.
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:
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:
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:
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:
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(t)=A (θ,ω) S(t)+N(t)
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:
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:
wherein ,for one of the solutions of signal azimuth, +.>One solution in a solution space for signal frequencies;
the maximum likelihood equation for maximum likelihood estimation is:
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 ash=1, 2, …, H; generating H D=2I dimension quanta individuals->The d dimension of the h quantum unit is +.>At the first generation, the value is [0,1 ]]A uniform random number within, d=1, 2, …, D;
odd dimensions of quantum individualsd=1, 3, …, D-1, mapped to the range of signal azimuth solutionsEven dimension->Mapping to a range of signal frequency solutionsObtaining mapped individuals->Constructing a quantum individual fitness function:
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 groupThe fitness of (h=1, 2, …, H), the quantum unit with the greatest fitness is elite quantum unit +.>Re-using analog quantum revolving gate by letting b g Random exercise->Local search is carried out again to obtain alternative new generation elite quantum individuals +. >First->In the sub-random movement, b g D < th > dimension->The corresponding quantum rotation angle is +.>Is [ -1,1]Inside uniform random number,/, inside uniform random number,/>Updated to-> The maximum adaptation in the mapping state of +.> wherein />Is->Mapping state of->Then reserve->Quantum state->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 theFor the h quantum unit in the quantum substance group +.>Define the concentration of the position of the quantum substance group as +.> wherein αh For distinguishing condition->The number of times that it is established,and->
Sequencing each quantum in the quantum substance group from large to small according to concentration, and ranking the concentration by halfThe individual quantum units are divided into high-concentration quantum units->Concentration rank second half +.>The individual quantum units are divided into low-concentration quantum units->
All high-concentration quantum units are ordered according to the adaptability from big to small, and the units are arranged in odd number positionsThe high-concentration quantum unit is high-concentration liposoluble quantum unit->Specifying +.>The high-concentration quantum unit is high-concentration non-fat soluble quantum unit->
The high concentration fat-soluble quantum unit free diffusion comprises:
first, thePersonal->The specific process of the movement is as follows: an analog quantum turnstile is used first, Make->To w low concentration quantum individuals->Exercise, generate->Individual quantum->Alternatively new generation of high concentration lipid soluble quantum individuals,>d < th > dimension->To w->D < th > dimension->The quantum rotation angle corresponding to the motion is:
updated to->d=1,2,…,D,/>Personal->The maximum adaptation in the mapping state of +.>Select the corresponding quantum state->As a new generation of high concentration lipid-soluble quantum entities, whereinIs->Mapping states of (a) for each +.>Executing the above exercise process to generate new generation high concentration liposoluble quantum individual +.>
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 setWherein round represents a rounding for limiting the high concentration of non-fat soluble quantum individuals +.>Motion of (a)
(1) Specifying the front of the order of concentration from big to smallPersonal->Obtaining a carrier, moving to a low concentration quantum unit, wherein +.>Personal->The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable the first->Personal->To w low concentration quantum individuals->Sport generation->Individual quantum-> Alternative new generation of high concentration non-fat soluble quantum individuals +.>Personal->D < th > dimension->To w- >D < th > dimension->Quantum rotation angle +.> Updated tod=1,2,…,D;Personal->The maximum adaptation in the mapping state of +.>Selecting the corresponding quantum state individual->As a new generation of high concentration non-fat soluble quantum units, whereinIs->Mapping state of>Personal->Executing the above exercise process to generate new generation of high concentration non-fat soluble quantum individual with carrier->
(2) Specifying the remaining high concentration of non-fat soluble quantum individualsWithout 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> Wherein->Personal->D < th > dimension->Direction b g+1 D < th > dimension->Quantum rotation angle +.> Updated to->/>d=1, 2, …, D, if->Is superior to->Keep->As a new generation of carrier-free high concentration non-fat soluble quantum individuals; no->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 higherThe low-concentration quantum units are low-concentration high-energy quantum units meeting energy limitation +. >Less fitness +.>Individual low concentration quanta are not meeting energy limitationsLow concentration low energy quantum unitFor each low concentration high energy quantum individual there is +.>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 isAnd a total of O are provided,o random integers, where O +.>The specific process of the movement is as follows: firstly using a simulated quantum revolving door to enable +.>To (1)>High concentration quantum individuals->Exercise, get->Individual quantum unitsAlternative new generation low concentration high energy quantum individuals, o +.>D < th > dimension->To (1)>Personal->D < th > dimension->Quantum rotation angle corresponding to motion Updated to-> d=1,2,…,D,/>Personal->Maximum fitness in the mapping state of (a)Selecting the quantum state->As a new generation of low-concentration high-energy quantum units of the obtained carrier,wherein->Is->Mapping states of (a) for each +.>Executing the above movement process to generate low-concentration high-energy quantum individual of new generation of obtained carrier->
(2) Marking carrier-free low-concentration high-energy quantum individuals asAnd is common with->The number of the two-dimensional space-saving type,and q.noteq.o, where q.sub.th->The specific motion process of (a) is as follows: firstly using a simulated quantum revolving door to enable +.>Random exercise is taken- >Performing local search; the (q) th->D < th > dimension->The corresponding quantum rotation angle is Is [ -1,1]Inside uniform random number,/, inside uniform random number,/>
Updated to->d=1, 2, …, D, if->Is superior to->Then reserveLow concentration high energy quantum individuals as new generation carrier-free, otherwise let +.>For new generation of carrier-free low concentration high energy quantum individuals, for each +.>Executing the above movement process to generate new generation carrier-free low concentration high energy quantum individual +.>
(3) All low concentration low energy quantum individualsTo elite quantum unit b g+1 Motion, using analog quantum turnstile, +.>Individual quantum->D < th > dimension->Direction b g+1 D < th > dimension->The quantum rotation angle of the motion is Updated to-> d=1, 2, …, D, if->Is superior to->Then reserve->As a new generation of low concentration low energy quantum individuals, otherwise let +.>As a new generation of low concentration low energy quantum individuals;
the generation of a new generation of quantum species population includes:
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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