CN109270485A - Direction-finding method when a kind of sky based on quantum cells film Optimization Mechanism - Google Patents
Direction-finding method when a kind of sky based on quantum cells film Optimization Mechanism Download PDFInfo
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Abstract
The invention belongs to array signal processing fields, and in particular to direction-finding method when a kind of sky based on quantum cells film Optimization Mechanism, comprising the following steps: obtain signal time domain data, the sampling of signal snap and carry out time domain delay to sampled data；The Maximum-likelihood estimation equation of Maximum-likelihood estimation is constructed, the initialization of quantum substance group is carried out, and constructs fitness function；Elite quantum individual is chosen, local search is carried out to elite quantum individual；Divide quantum individual type；The fat-soluble quantum individual freedom diffusion of high concentration；High concentration non-fat-soluble quantum individual movement；Low concentration quantum individual movement；Generate the quantum substance group of a new generation；Judge whether to reach maximum number of iterations.The direction-finding method when sky based on quantum cells film Optimization Mechanism that the present invention designs, solve the problems, such as that maximum likelihood class estimation method is computationally intensive, the Combined estimator of more accurate signal angle and frequency can quickly be obtained as a result, being easy to handle in real time in engineer 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 of the array signal processing technology, most of the direction-finding technologies are estimation of one-dimensional signal parameters of azimuth angles, but the estimation of the multi-dimensional parameters is relatively closer to practical application, and one important research direction is the space-time direction-finding problem.
Among many direction finding methods, the direction finding method using the maximum likelihood estimation principle is simple in principle, can be used for direction finding of a coherent source, and is high in robustness and stability, but in practical application, due to the fact that the implementation process is complex, the calculation amount needed by two-dimensional search is large, and if the efficiency of the multi-dimensional search method is low, a direction finding result may not be converged, only one approximate extreme value of a likelihood function may be found, convergence to a global optimal solution is difficult to guarantee, 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, high-dimensional singular value decomposition and extra parameter pairing operation.
Through the search of the prior art documents, it is found that in the "joint estimation of the direction of arrival and the frequency by using a state space model" published by the "optical precision engineering" by zhangxie et al, a state space model is constructed, and a system matrix including the direction of arrival and the frequency information of a signal is used to perform characteristic decomposition on an estimated value of the system matrix to obtain the direction of arrival and the frequency of the signal, but the estimation error is large. In the ' double-rotation subspace method in signal frequency direction joint estimation ' published by the university of Yangzhou university ' by Hu scholong et al, a signal frequency and direction joint estimation method based on subspace twice rotation transformation is provided, which has small operation amount and can identify the number of signals, but is sensitive to the signal-to-noise ratio, the fast beat number and the correlation among information sources.
In summary, the existing literature indicates that, for the space-time direction finding problem, a method which is fast and accurate, has excellent performance, and can perform effective joint estimation on angle and frequency of a coherent source is lacking.
Disclosure of Invention
The invention designs a space-time direction finding method based on a quantum cell membrane optimization mechanism aiming at the problems that the existing maximum likelihood direction finding method is large in calculated amount, high in system complexity and difficult to quickly and accurately realize frequency and azimuth joint estimation. The method uses the maximum likelihood estimation principle, utilizes the stronger global optimizing capability of the cell membrane optimization mechanism, introduces the quantum principle on the basis of the cell membrane optimization mechanism, and evolves quantum individuals by using a quantum revolving gate. The method and the device can obtain more accurate estimation results of the azimuth angle and the frequency of the signal in a shorter 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 a fitness function;
(3) selecting an elite quantum individual, and carrying out local search on the elite quantum individual;
(4) dividing the individual types of the quanta;
(5) high-concentration fat-soluble quantum individuals freely diffuse;
(6) high-concentration non-fat-soluble quantum individual exercise;
(7) low-concentration quantum individual exercise;
(8) generating a new generation of quantum substance group;
(9) and judging whether the maximum iteration number is reached.
The acquiring of the signal time domain data, the signal snapshot sampling and the time domain delay of the sampling data comprise:
with I azimuthal angles theta ═ theta1,θ2,…,θI) Frequency of ω ═ ω (ω ═ ω)1,ω2,…,ωI) Is incident on a uniform linear array containing M array elements with the spacing of η, and each array element is provided with a delayer with K stages of time domain delay of sigma, wherein thetaiThe included angle between the ith signal wave arrival direction and the linear array normal direction is set;
the ith signal at time t is represented by the complex envelope as:
wherein j is an imaginary unit, ui(t) is the amplitude of the signal,is the phase of the signal;
the ith signal reaching the mth array element at time t is:
si(t-τmi)＝si(t)exp(-jωiτmi)
wherein ,τmiThe spatial delay for the ith signal to reach the mth array element relative to the reference array element;
the m-th array element position is deltamThen, there are:
wherein c is the propagation speed of the signal;
in an ideal state, each array element in the array does not have the influence of channel inconsistency or mutual coupling factors, and the data received by the mth array element at the time t is as follows:
wherein nm(t) white gaussian noise at the mth array element at time t;
the signal generates output data after time domain delay through the kth stage delayer of the mth array element, and the output data is as follows:
writing the above formula into a matrix form, and obtaining a data vector received by the mth array element at the time t as follows:
Ym(t)＝AmS(t)+Nm(t)
wherein ,AmIs an array flow pattern matrix, S (t) is a signal vector, Nm(t) is a noise vector, M is 1,2, …, M
Will Ym(t) arranged in a matrixFurther simplified to obtain:
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
And (3) the sample data of the U-th snapshot sample is Y (U), U is 1,2, … and U, and a covariance matrix of the sample data is constructed:
wherein, U is the total number of snapshots, and H represents the conjugate transpose operation.
The constructing of the maximum likelihood estimation equation of the maximum likelihood estimation, the initialization of the quantum substance group and the construction of the fitness function comprise:
constructing an orthogonal projection matrix by adopting a space-time two-dimensional maximum likelihood method:
wherein ,is a solution in the solution space of the azimuth of the signal,a solution in a solution space of signal frequencies;
the maximum likelihood equation for the maximum likelihood estimate is:
wherein tr represents a matrix trace-solving operation;
setting the total number H of quantum individuals in the quantum substance group, the maximum iteration number G, and the H quantum individual in the G iteration asGenerating H D-2I dimensional quantum individualsThe dimension d of the h quantum ofAt the initial generation value of [0,1]Inner uniformityRandom number, D ═ 1,2, …, D;
odd dimension of quantum individualsIn the range of the signal azimuth solution mapped toWill have even dimensionIn the range of the signal frequency solution mapped toObtaining the mapping state individualsConstructing a quantum individual fitness function:
the selecting of the elite quantum individuals and the local searching of the elite quantum individuals comprise the following steps:
calculating the h quantum individual in the quantum material groupH1, 2, …, H, the quantum individual with the largest fitness is the elite quantum individualReuse of the analog quantum revolving door by letting bgRandom motionObtaining a new generation of alternative elite quantum individuals by local searchFirst, theIn the second random motion, bgDimension d ofCorresponding quantum rotation angle of Is [ -1,1 [ ]]The number of uniform random numbers in the random number,is updated to Is the most suitable of the mapping states of (1) wherein Is composed ofIf the mapping state ofThen reserveQuantum state ofAs a new generation of elite quantum individuals; otherwise let bg+1＝bgAs a new generation of eliteAnd (5) quantum individuals.
The dividing of the quantum individual types comprises:
order toFor the h quantum body in the quantum substance groupDefining the concentration of the quantum species at the position wherein αhAs a condition for discriminationThe number of times that this is true,and is
Sequencing each quantum individual in the quantum substance group from large to small according to the concentration, wherein the concentration is ranked in the first halfDividing the quantum body into high-concentration quantum bodiesConcentration ranked in the second halfDividing quantum units into low-concentration quantum units
All the high-concentration sub-individuals are ranked from high to low according to the fitness and stipulatedArranged in odd digitsThe high concentration quantum individuals are high concentration fat soluble quantum individualsArranged in even-numbered positionsThe high concentration quantum individuals are high concentration non-fat soluble quantum individuals
The high-concentration fat-soluble quantum individual is free to diffuse, and comprises:
first, theAnThe specific process of the movement is as follows: firstly, use the analog quantum revolving door to makeTo the w low concentration quantum bodyMovement, generationQuantum unitAs an alternative new generation of high concentration fat soluble quantum individuals,dimension d ofTo the w thDimension d ofThe quantum rotation angle for a motion is:
is updated to AnIs the most suitable of the mapping states of (1)Selecting its corresponding quantum stateAs a new generation of high concentration fat soluble quantum individuals, among themIs composed ofFor each of the mapping statesExecuting the above movement process to generate new generation of high concentration fat soluble quantum individual
The high-concentration non-fat-soluble quantum individual movement comprises the following steps:
the high-concentration non-fat-soluble quantum individual assisted diffusion does not need energy, but needs carriers, and the number of the carriers is setWherein round represents rounding for limiting high concentration non-fat soluble quantum individualThe movement (1) of (A) specifies the front of the concentration in the order of magnitudeAnObtaining a carrier which moves to a low concentration quantum entity, whereinAnThe specific process of the movement is as follows: firstly, using an analog quantum revolving door to makeAnTo the w low concentration quantum bodyMotion generationQuantum unit As an alternative, a new generation of high concentration non-fat soluble quantum entitiesAnDimension d ofTo the w thDimension d ofQuantum rotation angle corresponding to movement Is updated to AnIs the most suitable of the mapping states of (1)Selecting the corresponding quantum state individualsAs a new generation of high concentration non-fat soluble quantum individuals, among themIs composed ofMapping state of (2), forwardAnExecuting the above movement process to generate new generation of high-concentration non-fat-soluble quantum individual with obtained carrier
(2) Defining the remaining high concentration of non-fat soluble quantum unitsNo carrier was obtained, and an analog quantum rotating gate was used to transform to an elite individual bg+1Obtaining a new generation of carrier-free high-concentration non-fat-soluble quantum individuals by movement Wherein the first stepAnDimension d ofTo bg+1Dimension d ofQuantum rotation angle corresponding to movement Is updated to If it isIs superior toRetentionAs a new generation of carrier-free high-concentration non-fat-soluble quantum individuals; otherwise makeIs a new generation of carrier-free high-concentration non-fat-soluble quantum individuals.
The low-concentration quantum individual movement comprises:
the active transportation is a movement mode which needs both a carrier and enough energy, all low-concentration quantum individuals are sorted from large to small according to the fitness, and the specified fitness is higherThe low-concentration quantum individuals are low-concentration high-energy quantum individuals meeting energy limitationThe adaptability is lowerThe low-concentration quantum individuals are low-concentration low-energy quantum individuals which do not meet the energy limitFor each low concentration high energy quantum individual, there isThe carrier is obtained according to the probability, and the carrier moves towards the direction of the high-concentration quantum individual;
(1) low concentration high energy quantum individual of the carrier obtained by labelingAnd the total number of the active carbon particles is O,a total of O random integers, of which the O-th oneThe specific process of the movement is as follows: firstly using an analog quantum revolving door to makeTo the firstA high concentration of sub-individualsMove to obtainQuantum unitAs an alternative, the o-th individual of a new generation of low-concentration high-energy quantumDimension d ofTo the firstAnDimension d ofQuantum rotation angle corresponding to movement Is updated to AnIs the most suitable of the mapping states of (1)Selecting its quantum stateLow concentration high energy quantum entities as new generation of carriers, whereinIs composed ofFor each of the mapping statesExecuting the above movement process to generate a new generation of low-concentration high-energy quantum individuals of the obtained carrier
(2) Labeling of carrier-free low-concentration high-energy quantum entitiesAnd have in commonThe number of the main components is one,and q ≠ o, wherein the qth oneThe specific motion process of (A) is as follows: firstly using an analog quantum revolving door to makeRandom motion is obtainedCarrying out local search; the q thDimension d ofCorresponding quantum rotation angle of Is [ -1,1 [ ]]Internal uniform randomThe number of the first and second groups is,
is updated toIf it isIs superior toThen reserveAs a new generation of carrier-free low-concentration high-energy quantum individuals, otherwiseFor a new generation of carrier-free low-concentration high-energy quantum individuals, for eachExecuting the above movement process to generate a new generation of carrier-free low-concentration high-energy quantum individuals
(3) All low-concentration low-energy quantum individualsElite quantum individual bg+1Movement using analog quantum rotary gates, secondQuantum unitDimension d ofTo bg+1Dimension d ofQuantum rotation angle of motion of Is updated to If it isIs superior toThen reserveAs a new generation of low-concentration low-energy quantum individualsAs a new generation of low-concentration low-energy quantum individuals.
The generation of a new generation of quantum populations comprises:
will be provided with Quantum material group combined into new generation
The judging whether the maximum iteration number is reached includes:
if G is less than G, enabling G to be G +1, and returning to the step six; otherwise, if the maximum iteration number G is equal to G, outputting the mapping state of the quantum individual with the maximum fitness as an estimation result to obtain the optimal estimation values of the angle and the frequency.
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 calculation amount of the maximum likelihood estimation method, can quickly obtain a relatively accurate joint estimation result of signal angles and frequencies, and is easy to process in real time in engineering application.
(2) The method can estimate the incoherent source and the coherent source effectively, and can still obtain the joint estimation result of the azimuth angle and the 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 a quantum cell membrane optimization mechanism;
angle estimation of the signal of fig. 2;
FIG. 3 is a joint estimation of angle and frequency of the signal;
FIG. 4 shows a RMS error versus signal-to-noise ratio curve for an estimated angle of a signal;
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 the azimuth angle of a signal, and particularly relates to a space-time direction finding method based on a quantum cell membrane optimization mechanism, which 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 of the array signal processing technology, most of the direction-finding technologies are estimation of one-dimensional signal parameters of azimuth angles, but the estimation of the multi-dimensional parameters is relatively closer to practical application, and one important research direction is the space-time direction-finding problem.
Among many direction finding methods, the direction finding method using the maximum likelihood estimation principle is simple in principle, can be used for direction finding of a coherent source, and is high in robustness and stability, but in practical application, due to the fact that the implementation process is complex, the calculation amount needed by two-dimensional search is large, and if the efficiency of the multi-dimensional search method is low, a direction finding result may not be converged, only one approximate extreme value of a likelihood function may be found, convergence to a global optimal solution is difficult to guarantee, 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, high-dimensional singular value decomposition and extra parameter pairing operation.
As a result of a search of a prior art document, zhangxie et al have proposed a method of obtaining the direction of arrival and frequency of a signal by constructing a state space model and performing feature decomposition on an estimated value of the system matrix using the system matrix including information on the direction of arrival and frequency of the signal, in "joint estimation of the direction of arrival and frequency by using the state space model" published in "optical precision engineering" (2011, vol.19, No.4), but an estimation error is large. In the "dual-rotation subspace method in joint estimation of signal frequency and direction" published by the university of Yangzhou university journal (2004, Vol.7, No.3), Hu Chirong et al proposed a joint estimation method of signal frequency and direction based on two rotation transformations of subspace, which has small computation amount and can identify the number of signals, but is sensitive to the signal-to-noise ratio, fast beat number and correlation between the signal sources. The existing literature shows that a method which is rapid and accurate, has excellent performance and can effectively estimate angles and frequencies jointly for a coherent source is lacked for the space-time direction finding problem.
The invention designs a space-time direction finding method based on a quantum cell membrane optimization mechanism aiming at the problems that the existing maximum likelihood direction finding method is large in calculated amount, high in system complexity and difficult to quickly and accurately realize frequency and azimuth joint estimation. The method uses the maximum likelihood estimation principle, utilizes the stronger global optimizing capability of the cell membrane optimization mechanism, introduces the quantum principle on the basis of the cell membrane optimization mechanism, and evolves quantum individuals by using a quantum revolving gate. The method and the device can obtain more accurate estimation results of the azimuth angle and the frequency of the signal in a shorter time.
The invention is mainly realized by the following steps:
step one, signal time domain data are obtained.
From the mathematical model of the signal, consider the I azimuth angles as (θ)1,θ2,…,θI) Frequency of ω ═ ω (ω ═ ω)1,ω2,…,ωI) The far-field narrow-band signal is incident on a uniform linear array containing M array elements with the spacing of η, each array element has K stages, each stage of time domain delay is a delayer of sigma, wherein thetaiIs the included angle between the ith signal wave arrival direction and the linear array normal direction. the ith signal at time t can be represented as a complex envelopeWherein j is an imaginary unit, ui(t) is the amplitude of the signal,is the phase of the signal, the ith signal arriving at the mth array element at time t is si(t-τmi)＝si(t)exp(-jωiτmi), wherein ,τmiThe spatial delay generated for the ith signal to reach the mth array element relative to the reference array element, if the mth array element is set to be deltamThen, thenWherein c is the transmission of a signalThe playing speed. Assuming that under an ideal state, each array element in the array does not have the influence of channel inconsistency or mutual coupling factors, the data received by the mth array element at the time t is wherein nm(t) represents white gaussian noise at the mth array element at time t.
And step two, acquiring signal snapshot sampling and performing time domain delay on the sampling data.
The signal passes through the kth-stage delayer of the mth array element to generate output data after time domain delayWriting the above formula into a matrix form to obtain a data vector Y received by the mth array element at the time tm(t)＝AmS(t)+Nm(t) wherein AmIs an array flow pattern matrix, S (t) is a signal vector, Nm(t) is the noise vector, M is 1,2, …, M. Then Y is putm(t) arranged in a matrixFurther, the reaction is simplified to obtain Y (t) ═ A(θ,ω)S (t) + N (t), where the noise matrixM x K row and I column space-time two-dimensional array flow pattern matrixThe sample data of the U-th snapshot sample is denoted by Y (U), U is 1,2, … and U, and a covariance matrix of the sample data is constructedWherein U is the total number of snapshots. H represents a conjugate transpose operation.
And step three, constructing a maximum likelihood estimation equation of the maximum likelihood estimation.
Using poles of space-time two dimensionsMethod of constructing orthogonal projection matrix wherein For one possible solution in the solution space of the signal azimuth,for a possible solution in the solution space of the signal frequencies, the maximum likelihood equation of the maximum likelihood estimate istr represents a matrix trace-finding operation.
And step four, initializing the quantum substance group.
Setting the total number H of quantum individuals in the quantum substance group, and setting the maximum iteration number G, wherein the H quantum individual in the G iteration is expressed asGenerating H D-2I dimensional quantum individualsThe dimension d of the h quantum ofAt the initial generation value of [0,1]D is 1,2, …, D.
And step five, constructing a fitness function.
Odd dimension of quantum individualsIn the range of the signal azimuth solution mapped toWill be even numberVitamin CIn the range of the signal frequency solution mapped toObtaining the mapping state individualsConstructing a quantum individual fitness function
And step six, selecting the elite quantum individuals and carrying out local search on the elite quantum individuals.
Calculating the h quantum individual in the quantum material groupH1, 2, …, H, the quantum individual with the largest fitness is the elite quantum individualReuse of the analog quantum revolving door by letting bgRandom motionObtaining a new generation of alternative elite quantum individuals by local searchFirst, theIn the second random motion, bgDimension d ofCorrespond toQuantum rotation angle of Is [ -1,1 [ ]]A uniform random number within.Is updated to Is the most suitable of the mapping states of (1) wherein Is composed ofIf the mapping state ofThen reserveQuantum state ofAs a new generation of elite quantum individuals; otherwise let bg+1＝bgAs a new generation of elite quantum individuals.
And seventhly, dividing the individual quantum types.
Order toFor the h quantum body in the quantum substance groupDefining the concentration of the quantum species at the position wherein αhAs a condition for discriminationThe number of times that this is true,and isSequencing each quantum individual in the quantum substance group from large to small according to the concentration, wherein the concentration is ranked in the first halfDividing the quantum body into high-concentration quantum bodies Concentration ranked in the second halfDividing quantum units into low-concentration quantum unitsThen all the high-concentration sub-individuals are sorted according to the fitness from large to small, and arranged in odd numberThe high concentration quantum individuals are high concentration fat soluble quantum individualsArranged in even-numbered positionsThe high concentration quantum individuals are high concentration non-fat soluble quantum individuals
Step eight, high-concentration fat-soluble quantum individuals are freely diffused.
Free diffusion is the process of moving each high concentration fat soluble quantum individual to a low concentration quantum individual, and the process does not need carriers or energy. First, theAnThe specific process of the movement is as follows: firstly, use the analog quantum revolving door to makeTo the w low concentration quantum bodyMovement, generationQuantum unit As an alternative new generation of high concentration fat soluble quantum individuals,dimension d ofTo the w thDimension d ofThe quantum rotation angle corresponding to the movement is Is updated to AnIs the most suitable of the mapping states of (1)Selecting its corresponding quantum stateAs a new generation of high concentration fat soluble quantum individuals, among themIs composed ofThe mapping state of (2). For each oneExecuting the above movement process to generate new generation of high concentration fat soluble quantum individual
And step nine, carrying out high-concentration non-fat-soluble quantum individual exercise.
The high concentration of non-fat soluble quantum entities does not require energy for diffusion assistance, but does require a carrier. Setting the number of carriersround represents rounding for limiting high-concentration non-fat-soluble quantum individualsThe movement of (2).
(1) Stipulate the top in the order of concentration from large to smallAnObtaining the carrier, and moving to low-concentration quantum individuals. Wherein the first stepAnThe specific process of the movement is as follows: firstly, using an analog quantum revolving door to makeAnTo the w low concentration quantum bodyMotion generationQuantum unit As an alternative, a new generation of high concentration non-fat soluble quantum entitiesAnDimension d ofTo the w thDimension d ofQuantum rotation angle corresponding to movement Is updated to AnIs the most suitable of the mapping states of (1)Selecting the corresponding quantum state individualsAs a new generation of high concentration non-fat soluble quantum individuals, among themIs composed ofThe mapping state of (2). To frontAnExecuting the above movement process to generate new generation of high-concentration non-fat-soluble quantum individual with obtained carrier
(2) Defining the remaining high concentration of non-fat soluble quantum unitsNo carrier was obtained, and an analog quantum rotating gate was used to transform to an elite individual bg+1Obtaining a new generation of carrier-free high-concentration non-fat-soluble quantum individuals by movement Wherein the first stepAnDimension d ofTo bg+1Dimension d ofQuantum rotation angle corresponding to movement Is updated to If it isIs superior toRetentionAs a new generation of carrier-free high-concentration non-fat-soluble quantum individuals; otherwise makeIs a new generation of carrier-free high-concentration non-fat-soluble quantum individuals.
Step ten, the low-concentration quantum individual exercise.
The active transportation is a movement mode which needs both a carrier and enough energy, all low-concentration quantum individuals are sorted from large to small according to the fitness, and the specified fitness is higherThe low-concentration quantum individuals are low-concentration high-energy quantum individuals meeting energy limitationThe adaptability is lowerThe low-concentration quantum individuals are low-concentration low-energy quantum individuals which do not meet the energy limitFor each low concentration high energy quantum individual, there isThe probability of (3) is obtained as a carrier, moving in the direction of the high concentration of the quantum individuals.
(1) Low concentration high energy quantum individual of the carrier obtained by labelingAnd the total number of the active carbon particles is O,a total of O random integers, of which the O-th oneThe specific process of the movement is as follows: firstly using an analog quantum revolving door to makeTo the firstA high concentration of sub-individualsMove to obtainQuantum unitAs an alternative, the o-th individual of a new generation of low-concentration high-energy quantumDimension d ofTo the firstAnDimension d ofQuantum rotation angle corresponding to movement Is updated to AnIs the most suitable of the mapping states of (1)Selecting its quantum stateLow concentration high energy quantum entities as new generation of carriers, whereinIs composed ofFor each of the mapping statesExecuting the above movement process to generate new generation of low concentration high energy content of the obtained carrierSub-individuals
(2) Labeling of carrier-free low-concentration high-energy quantum entitiesAnd have in commonThe number of the main components is one,and q ≠ o, wherein the qth oneThe specific motion process of (A) is as follows: firstly using an analog quantum revolving door to makeRandom motion is obtainedA local search is performed. The q thDimension d ofCorresponding quantum rotation angle of Is [ -1,1 [ ]]A uniform random number within.Is updated toIf it isIs superior toThen reserveAs a new generation of carrier-free low-concentration high-energy quantum individuals, otherwiseIs a new generation of carrier-free low-concentration high-energy quantum individuals. For each oneExecuting the above movement process to generate a new generation of carrier-free low-concentration high-energy quantum individuals
(3) All low-concentration low-energy quantum individualsElite quantum individual bg+1And (6) moving. Using an analogue quantum rotary gate, secondQuantum unitDimension d ofTo bg+1Dimension d ofQuantum rotation angle of motion of Is updated to If it isIs superior toThen reserveAs a new generation of low-concentration low-energy quantum individualsAs a new generation of low-concentration low-energy quantum individuals.
And step eleven, generating a new generation of quantum substance group.
Will be provided with Quantum material group combined into new generation
Step twelve, judging whether the maximum iteration frequency is reached, if G is less than G, making G equal to G +1, and returning to the step six; otherwise, if the maximum iteration number G is equal to G, outputting the mapping state of the quantum individual with the maximum fitness as an estimation result to obtain the optimal estimation values of the angle and the frequency.
(1) The space-time direction finding method based on the quantum cell membrane optimization mechanism solves the problem of large calculation amount of the maximum likelihood estimation method, can quickly obtain a relatively accurate joint estimation result of signal angles and frequencies, and is easy to process in real time in engineering application.
(2) The method can estimate the incoherent source and the coherent source effectively, and can still obtain the joint estimation result of the azimuth angle and the 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 a quantum cell membrane optimization mechanism.
Angle estimation of the signal of fig. 2
Joint angle and frequency estimation of the signal of fig. 3
FIG. 4 shows the RMS error versus SNR curve for an estimated angle of a signal
The parameters of the space-time direction finding method based on the quantum cell membrane optimization mechanism are set as η -0.015 m, sigma-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 °), with dB ═ 10. As can be seen from the simulation diagram, 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 °,0.8GHz), and dB is 20. The simulation chart shows that the space-time direction finding method based on the quantum cell membrane optimization mechanism can carry out joint estimation on the angle and the frequency of the signal.
In fig. 4, the angle and frequency of two signals are (9 °,18 °), and the number of Monte Carlo tests is 100, and it can be seen from the simulation result that the accuracy of the diagonal estimation of the space-time direction finding method based on the quantum cell membrane optimization mechanism designed by the present invention is better than that of the particle swarm maximum likelihood direction finding method.
Step one, signal time domain data are obtained.
From the mathematical model of the signal, consider the I azimuth angles as (θ)1,θ2,…,θI) Frequency of ω ═ ω (ω ═ ω)1,ω2,…,ωI) The far-field narrow-band signal is incident on a uniform linear array containing M array elements with the spacing of η, each array element has K stages, each stage of time domain delay is a delayer of sigma, wherein thetaiIs the included angle between the ith signal wave arrival direction and the linear array normal direction. the ith signal at time t can be represented as a complex envelopeWherein j is an imaginary unit, ui(t) is the amplitude of the signal,is the phase of the signal, the ith signal arriving at the mth array element at time t is si(t-τmi)＝si(t)exp(-jωiτmi), wherein ,τmiThe spatial delay generated for the ith signal to reach the mth array element relative to the reference array element, if the mth array element is set to be deltamThen, thenWhere c is the propagation speed of the signal. Assuming that under an ideal state, each array element in the array does not have the influence of channel inconsistency or mutual coupling factors, the data received by the mth array element at the time t is wherein nm(t) represents white gaussian noise at the mth array element at time t.
And step two, acquiring signal snapshot sampling and performing time domain delay on the sampling data.
The signal passes through the kth-stage delayer of the mth array element to generate output data after time domain delayWriting the above formula into a matrix form to obtain a data vector Y received by the mth array element at the time tm(t)＝AmS(t)+Nm(t) wherein AmIs an array flow pattern matrix, S (t) is a signal vector, Nm(t) is the noise vector, M is 1,2, …, M. Then Y is putm(t) arranged in a matrixFurther, the reaction is simplified to obtain Y (t) ═ A(θ,ω)S (t) + N (t), where the noise matrixM x K row and I column space-time two-dimensional array flow pattern matrixThe sample data of the U-th snapshot sample is denoted by Y (U), U is 1,2, … and U, and a covariance matrix of the sample data is constructedWherein U is the total number of snapshots. H represents a conjugate transpose operation.
And step three, constructing a maximum likelihood estimation equation of the maximum likelihood estimation.
Constructing orthogonal projection matrix by adopting space-time two-dimensional maximum likelihood method wherein For one possible solution in the solution space of the signal azimuth,for a possible solution in the solution space of the signal frequencies, the maximum likelihood equation of the maximum likelihood estimate istr represents a matrix trace-finding operation.
And step four, initializing the quantum substance group.
Setting the total number H of quantum individuals in the quantum substance group, and setting the maximum iteration number G, wherein the H quantum individual in the G iteration is expressed asGenerating H D-2I dimensional quantum individualsThe dimension d of the h quantum ofAt the initial generation value of [0,1]D is 1,2, …, D.
And step five, constructing a fitness function.
Odd dimension of quantum individualsIn the range of the signal azimuth solution mapped toWill have even dimensionIn the range of the signal frequency solution mapped toObtaining the mapping state individualsConstructing a quantum individual fitness function
And step six, selecting the elite quantum individuals and carrying out local search on the elite quantum individuals.
Calculating the h quantum individual in the quantum material groupH1, 2, …, H, the quantum individual with the largest fitness is the elite quantum individualReuse of the analog quantum revolving door by letting bgRandom motionObtaining a new generation of alternative elite quantum individuals by local searchFirst, theIn the second random motion, bgDimension d ofCorresponding quantum rotation angle of Is [ -1,1 [ ]]A uniform random number within.Is updated to Is the most suitable of the mapping states of (1) wherein Is composed ofIf the mapping state ofThen reserveQuantum state ofAs a new generation of elite quantum individuals; otherwise let bg+1＝bgAs a new generation of elite quantum individuals.
And seventhly, dividing the individual quantum types.
Order toFor the h quantum body in the quantum substance groupDefining the concentration of the quantum species at the position wherein αhAs a condition for discriminationThe number of times that this is true,and isSequencing each quantum individual in the quantum substance group from large to small according to the concentration, wherein the concentration is ranked in the first halfDividing the quantum body into high-concentration quantum bodies Concentration ranked in the second halfDividing quantum units into low-concentration quantum unitsThen all the high-concentration sub-individuals are sorted according to the fitness from large to small, and arranged in odd numberThe high concentration quantum individuals are high concentration fat soluble quantum individualsArranged in even-numbered positionsThe high concentration quantum individuals are high concentration non-fat soluble quantum individuals
Step eight, high-concentration fat-soluble quantum individuals are freely diffused.
Free diffusion is the process of moving each high concentration fat soluble quantum individual to a low concentration quantum individual, and the process does not need carriers or energy. First, theAnThe specific process of the movement is as follows: firstly, use the analog quantum revolving door to makeTo the w low concentration quantum bodyMovement, generationQuantum unit As an alternative new generation of high concentration fat soluble quantum individuals,dimension d ofTo the w thDimension d ofSports pairThe quantum rotation angle should be Is updated to AnIs the most suitable of the mapping states of (1)Selecting its corresponding quantum stateAs a new generation of high concentration fat soluble quantum individuals, among themIs composed ofThe mapping state of (2). For each oneExecuting the above movement process to generate new generation of high concentration fat soluble quantum individual
And step nine, carrying out high-concentration non-fat-soluble quantum individual exercise.
The high concentration of non-fat soluble quantum entities does not require energy for diffusion assistance, but does require a carrier. Setting the number of carriersround represents rounding for limiting high-concentration non-fat-soluble quantum individualsThe movement of (2).
(1) Stipulate the top in the order of concentration from large to smallAnObtaining the carrier, and moving to low-concentration quantum individuals. Wherein the first stepAnThe specific process of the movement is as follows: firstly, using an analog quantum revolving door to makeAnTo the w low concentration quantum bodyMotion generationQuantum unit As an alternative, a new generation of high concentration non-fat soluble quantum entitiesAnDimension d ofTo the w thDimension d ofQuantum rotation angle corresponding to movement Is updated to AnIs the most suitable of the mapping states of (1)Selecting the corresponding quantum state individualsAs a new generation of high concentration non-fat soluble quantum individuals, among themIs composed ofThe mapping state of (2). To frontAnExecuting the above movement process to generate new generation of high-concentration non-fat-soluble quantum individual with obtained carrier
(2) Defining the remaining high concentration of non-fat soluble quantum unitsNo carrier was obtained, and an analog quantum rotating gate was used to transform to an elite individual bg+1Obtaining a new generation of carrier-free high-concentration non-fat-soluble quantum individuals by movement Wherein the first stepAnDimension d ofTo bg+1Dimension d ofQuantum rotation angle corresponding to movement Is updated to If it isIs superior toRetentionAs a new generation of carrier-free high-concentration non-fat-soluble quantum individuals; otherwise makeIs a new generation of carrier-free high-concentration non-fat-soluble quantum individuals.
Step ten, the low-concentration quantum individual exercise.
The active transportation is a movement mode which needs both a carrier and enough energy, all low-concentration quantum individuals are sorted from large to small according to the fitness, and the specified fitness is higherThe low-concentration quantum individuals are low-concentration high-energy quantum individuals meeting energy limitationThe adaptability is lowerThe low-concentration quantum individuals are low-concentration low-energy quantum individuals which do not meet the energy limitFor each low concentration high energy quantum individual, there isTo high concentrations of molecular entitiesAnd (4) moving in a direction.
(1) Low concentration high energy quantum individual of the carrier obtained by labelingAnd the total number of the active carbon particles is O,a total of O random integers, of which the O-th oneThe specific process of the movement is as follows: firstly using an analog quantum revolving door to makeTo the firstA high concentration of sub-individualsMove to obtainQuantum unitAs an alternative, the o-th individual of a new generation of low-concentration high-energy quantumDimension d ofTo the firstAnDimension d ofQuantum rotation angle corresponding to movement Is updated to AnIs the most suitable of the mapping states of (1)Selecting its quantum stateLow concentration high energy quantum entities as new generation of carriers, whereinIs composed ofFor each of the mapping statesExecuting the above movement process to generate a new generation of low-concentration high-energy quantum individuals of the obtained carrier
(2) Labeling of carrier-free low-concentration high-energy quantum entitiesAnd have in commonThe number of the main components is one,and q ≠ o, wherein the qth oneThe specific motion process of (A) is as follows: firstly using an analog quantum revolving door to makeRandom motion is obtainedA local search is performed. The q thDimension d ofCorresponding quantum rotation angle of Is [ -1,1 [ ]]A uniform random number within.Is updated toIf it isIs superior toThen reserveAs a new generation of carrier-free low-concentration high-energy quantum individuals, otherwiseIs a new generation of carrier-free low-concentration high-energy quantum individuals. For each oneExecuting the above movement process to generate a new generation of carrier-free low-concentration high-energy quantum individuals
(3) All low-concentration low-energy quantum individualsElite quantum individual bg+1And (6) moving. Using an analogue quantum rotary gate, secondQuantum unitDimension d ofTo bg+1Dimension d ofQuantum rotation angle of motion of Is updated to If it isIs superior toThen reserveAs a new generation of low-concentration low-energy quantum individualsAs a new generation of low-concentration low-energy quantum individuals.
And step eleven, generating a new generation of quantum substance group.
Will be provided with Quantum material group combined into new generation
Step twelve, judging whether the maximum iteration frequency is reached, if G is less than G, making G equal to G +1, and returning to the step six; otherwise, if the maximum iteration number G is equal to G, outputting the mapping state of the quantum individual with the maximum fitness as an estimation result to obtain the optimal estimation values of the angle and the frequency.
The invention designs a space-time direction finding method based on a quantum cell membrane optimization mechanism, which can carry out joint estimation on azimuth angles and frequencies of signals. The specific implementation steps are as follows: (1) signal time domain data is acquired. (2) Acquiring signal snapshot sampling and performing time domain delay on sampling data. (3) And constructing a maximum likelihood estimation equation of the maximum likelihood estimation. (4) Initializing a quantum substance group of a quantum cell membrane optimization method. (5) And constructing a fitness function. (6) Selecting an elite quantum individual and carrying out local search on the elite quantum individual. (7) The quantum individuals are divided into high-concentration fat-soluble quantum individuals, high-concentration non-fat-soluble quantum individuals and low-concentration quantum individuals. (8) And each quantum individual performs free diffusion according to an updating rule, assists in diffusion, actively transports and the like. (9) And after the maximum iteration times are reached, mapping the optimal quantum individual into a solution space to obtain a mapping state of the optimal quantum individual, 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 for the joint estimation of the azimuth angle and the frequency of the signal, can effectively carry out the 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 and fast beat number.
Claims (10)
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, 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 a fitness function;
(3) selecting an elite quantum individual, and carrying out local search on the elite quantum individual;
(4) dividing the individual types of the quanta;
(5) high-concentration fat-soluble quantum individuals freely diffuse;
(6) high-concentration non-fat-soluble quantum individual exercise;
(7) low-concentration quantum individual exercise;
(8) generating a new generation of quantum substance group;
(9) and judging whether the maximum iteration number is reached.
2. The method of claim 1, wherein the acquiring signal time domain data, the signal snapshot sampling, and the time domain delaying the sampled data comprises:
with I azimuthal angles theta ═ theta1,θ2,…,θI) Frequency of ω ═ ω (ω ═ ω)1,ω2,…,ωI) Is incident on a uniform linear array containing M array elements with the spacing of η, and each array element is provided with a delayer with K stages of time domain delay of sigma, wherein thetaiThe included angle between the ith signal wave arrival direction and the linear array normal direction is set;
the ith signal at time t is represented by the complex envelope as:
wherein j is an imaginary unit, ui(t) is the amplitude of the signal,is the phase of the signal;
the ith signal reaching the mth array element at time t is:
si(t-τmi)＝si(t)exp(-jωiτmi)
wherein ,τmiThe spatial delay for the ith signal to reach the mth array element relative to the reference array element;
the m-th array element position is deltamThen, there are:
wherein c is the propagation speed of the signal;
in an ideal state, each array element in the array does not have the influence of channel inconsistency or mutual coupling factors, and the data received by the mth array element at the time t is as follows:
wherein nm(t) white gaussian noise at the mth array element at time t;
the signal generates output data after time domain delay through the kth stage delayer of the mth array element, and the output data is as follows:
writing the above formula into a matrix form, and obtaining a data vector received by the mth array element at the time t as follows:
Ym(t)＝AmS(t)+Nm(t)
wherein ,AmIs an array flow pattern matrix, S (t) is a signal vector, Nm(t) is a noise vector, M is 1,2, …, M
Will Ym(t) arranged in a matrixFurther simplified to obtain:
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
And (3) the sample data of the U-th snapshot sample is Y (U), U is 1,2, … and U, and a covariance matrix of the sample data is constructed:
wherein, U is the total number of snapshots, and H represents the conjugate transpose operation.
3. The method of claim 1, wherein constructing a maximum likelihood estimation equation for maximum likelihood estimation, performing initialization of quantum populations, and constructing a fitness function comprises:
constructing an orthogonal projection matrix by adopting a space-time two-dimensional maximum likelihood method:
wherein ,is a solution in the solution space of the azimuth of the signal,a solution in a solution space of signal frequencies;
the maximum likelihood equation for the maximum likelihood estimate is:
wherein tr represents a matrix trace-solving operation;
setting the total number H of quantum individuals in the quantum substance group, the maximum iteration number G, and the H quantum individual in the G iteration asGenerating H D-2I dimensional quantum individualsThe dimension d of the h quantum ofAt the initial generation value of [0,1]D ═ 1,2, …, D;
odd dimension of quantum individualsIn the range of the signal azimuth solution mapped toWill have even dimensionIn the range of the signal frequency solution mapped toObtaining the mapping state individualsConstructing a quantum individual fitness function:
4. the method of claim 1, wherein the selecting the elite quantum individual and the local search for the elite quantum individual comprises:
calculating the h quantum individual in the quantum material groupH1, 2, …, H, the quantum individual with the largest fitness is the elite quantum individualReuse of the analog quantum revolving door by letting bgRandom motionObtaining a new generation of alternative elite quantum individuals by local searchFirst, theIn the second random motion, bgDimension d ofCorresponding quantum rotation angle of Is [ -1,1 [ ]]The number of uniform random numbers in the random number,is updated to Is the most suitable of the mapping states of (1) wherein Is composed ofIf the mapping state ofThen reserveQuantum state ofAs a new generation of elite quantum individuals; otherwise let bg+1＝bgAs a new generation of elite quantum individuals.
5. The method of claim 1, wherein the partitioning the quantum individual types comprises:
order toFor the h quantum body in the quantum substance groupDefining the concentration of the quantum species at the position wherein αhAs a condition for discriminationThe number of times that this is true,and isd＝1,2,…,D
Sequencing each quantum individual in the quantum substance group from large to small according to the concentration, wherein the concentration is ranked in the first halfDividing the quantum body into high-concentration quantum bodiesConcentration ranked in the second halfDividing quantum units into low-concentration quantum units
All high-concentration sub-individuals are sorted according to the fitness from large to small and arranged in odd numberThe high concentration quantum individuals are high concentration fat soluble quantum individualsArranged in even-numbered positionsThe high concentration quantum individuals are high concentration non-fat soluble quantum individuals
6. The method of claim 1, wherein the high concentration of lipid soluble quantum individuals is free to diffuse, comprising:
first, theAnSpecific course of movementComprises the following steps: firstly, use the analog quantum revolving door to makeTo the w low concentration quantum bodyMovement, generationQuantum unitAs an alternative new generation of high concentration fat soluble quantum individuals,dimension d ofTo the w thDimension d ofThe quantum rotation angle for a motion is:
is updated to AnIs the most suitable of the mapping states of (1)Selecting its corresponding quantum stateAs a new generation of high concentration fat soluble quantum individuals, among themIs composed ofFor each of the mapping statesExecuting the above movement process to generate new generation of high concentration fat soluble quantum individual
7. The method of claim 1, wherein the high concentration of non-fat soluble quantum individual exercise comprises:
the high-concentration non-fat-soluble quantum individual assisted diffusion does not need energy, but needs carriers, and the number of the carriers is setWhere round represents rounding to limit high concentrationsLess-than-liposoluble quantum individualIs moved
(1) Stipulate the top in the order of concentration from large to smallAn Obtaining a carrier which moves to a low concentration quantum entity, whereinAnThe specific process of the movement is as follows: firstly, using an analog quantum revolving door to makeAnTo the w low concentration quantum bodyMotion generationQuantum unit As alternative new generationHigh concentration of non-fat soluble quantum entities, secondAnDimension d ofTo the w thDimension d ofQuantum rotation angle corresponding to movement Is updated to AnIs the most suitable of the mapping states of (1)Selecting the corresponding quantum state individualsAs a new generation of high concentration non-fat soluble quantum individuals, among themIs composed ofMapping state of (2), forwardAnExecuting the above movement process to generate new generation of high-concentration non-fat-soluble quantum individual with obtained carrier
(2) Defining the remaining high concentration of non-fat soluble quantum unitsNo carrier was obtained, and an analog quantum rotating gate was used to transform to an elite individual bg+1Obtaining a new generation of carrier-free high-concentration non-fat-soluble quantum individuals by movement Wherein the first stepAnDimension d ofTo bg+1Dimension d ofQuantum rotation angle corresponding to movement Is updated to If it isIs superior toRetentionAs a new generation of carrier-free high-concentration non-fat-soluble quantum individuals; otherwise makeIs a new generation of carrier-free high-concentration non-fat-soluble quantum individuals.
8. The method of claim 1, wherein the low concentration quantum individual movement comprises:
the active transportation is a movement mode which needs both a carrier and enough energy, all low-concentration quantum individuals are sorted from large to small according to the fitness, and the specified fitness is higherA low concentration amountThe quantum body is low-concentration high-energy quantum body satisfying energy limitationThe adaptability is lowerThe low-concentration quantum individuals are low-concentration low-energy quantum individuals which do not meet the energy limitFor each low concentration high energy quantum individual, there isThe carrier is obtained according to the probability, and the carrier moves towards the direction of the high-concentration quantum individual;
(1) low concentration high energy quantum individual of the carrier obtained by labelingAnd the total number of the active carbon particles is O,a total of O random integers, of which the O-th oneThe specific process of the movement is as follows: firstly using an analog quantum revolving door to makeTo the firstA high concentration of sub-individualsMove to obtainQuantum unitAs an alternative, the o-th individual of a new generation of low-concentration high-energy quantumDimension d ofTo the firstAnDimension d ofQuantum rotation angle corresponding to movement Is updated to AnIs the most suitable of the mapping states of (1)Selecting its quantum stateLow concentration high energy quantum entities as new generation of carriers, whereinIs composed ofFor each of the mapping statesExecuting the above movement process to generate a new generation of low-concentration high-energy quantum individuals of the obtained carrier
(2) Labeling of carrier-free low-concentration high-energy quantum entitiesAnd have in commonThe number of the main components is one,and q ≠ o, wherein the qth oneThe specific motion process of (A) is as follows: firstly using an analog quantum revolving door to makeRandom motion is obtainedCarrying out local search; the q thDimension d ofCorresponding quantum rotation angle of Is [ -1,1 [ ]]The number of uniform random numbers in the random number,
is updated toIf it isIs superior toThen reserveAs a new generation of carrier-free low-concentration high-energy quantum individuals, otherwiseFor a new generation of carrier-free low-concentration high-energy quantum individuals, for eachExecuting the above movement process to generate a new generation of carrier-free low-concentration high-energy quantum individuals
(3) All low-concentration low-energy quantum individualsElite quantum individual bg+1Movement using analog quantum rotary gates, secondQuantum unitDimension d ofTo bg+1Dimension d ofQuantum rotation angle of motion of Is updated to If it isIs superior toThen reserveAs a new generation of low-concentration low-energy quantum individualsAs a new generation of low-concentration low-energy quantum individuals.
9. The method of claim 1, wherein generating the new generation of quantum populations comprises:
will be provided with Quantum material group combined into new generation
10. The method of claim 1, wherein determining whether a maximum number of iterations has been reached comprises:
if G is less than G, enabling G to be G +1, and returning to the step six; otherwise, if the maximum iteration number G is equal to G, outputting the mapping state of the quantum individual with the maximum fitness as an estimation result to obtain the optimal estimation values of the angle and the frequency.
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