CN106842240B - Multipath estimator based on minimal error entropy and ε grade differential evolution - Google Patents

Multipath estimator based on minimal error entropy and ε grade differential evolution Download PDF

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CN106842240B
CN106842240B CN201710159265.XA CN201710159265A CN106842240B CN 106842240 B CN106842240 B CN 106842240B CN 201710159265 A CN201710159265 A CN 201710159265A CN 106842240 B CN106842240 B CN 106842240B
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CN106842240A (en
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程兰
任密蜂
谢刚
阎高伟
续欣莹
邢艳君
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Xi'an Sanshi Aerospace Technology Co.,Ltd.
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Taiyuan University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/22—Multipath-related issues

Abstract

Based on minimal error entropy andεThe multipath estimator of grade differential evolution, belong to field of signal processing, it includes auto-correlation computation module, the input of auto-correlation computation module is baseband signal and local pseudo-code signal, the input of the output connection memory module of auto-correlation computation module, the input of output connection constraints degree of the violating computing module of memory module, the input of objective function computing module, the output of the output, objective function computing module that constrain degree of violating computing module are all connected withεThe input of grade comparison module,εThe input of output the connection scale factor and aberration rate computing module of grade comparison module, the input of scale factor and the output connection differential evolution module of aberration rate computing module, the input of the output connection multipath parameter estimation module of differential evolution module, multipath parameter estimation module exports multipath parameter, and initialization module is updated with output result, it prepares for the multipath parameter estimation of subsequent time.Improve the flatness of multipath estimated result under non-Gaussian noise.

Description

Multipath estimator based on minimal error entropy and ε grade differential evolution
Technical field
The present invention relates to a kind of digital signal estimators, more particularly to a kind of digital multipath signal estimator.
Background technique
Signal estimator is to estimate that the transmission is believed as accurately as possible using the transmission signal sequence being disturbed received Number certain parameter values a kind of device.Digital signal estimator is realized in the way of software programming estimates signal parameter Meter has many advantages, such as that achievable complicated algorithm, precision height, low cost, update are easy.Digital signal estimator signal of communication, Voice signal, picture signal and processing of biomedical signals etc. are widely used.
Multipath signal is one of the main error source of high accuracy positioning in GNSS system, and the presence of multipath signal causes to receive Machine can not accurately track direct signal, cause pseudo range measurement deviation occur, and then positioning accuracy is caused to reduce.Multipath signal is brought Tracking error be known as multipath error.Existing multipath error suppressing method can be divided mainly into three classes: the multipath based on front end misses Poor suppressing method, the multipath error suppressing method based on correlator and phase discriminator and the multipath error based on data processing inhibit Method.Wherein the method based on front end mainly antenna end carry out multipath error inhibition, such as choke coil, beam array etc., The shortcoming of such methods is usual cost with higher, and can not usually inhibit the multi-path jamming at the low elevation angle.It is based on Correlator mainly passes through the phase demodulation function or related defeated for improving delay lock loop to the multipath error suppression technology of phase discriminator The shape of function inhibits multipath error out, and this kind of technology is the multipath error suppression technology of a quasi-tradition.And as software connects The house show of receipts machine, the multipath error suppression technology based on Digital Signal Processing attracts wide attention, and achieves in recent years Significant research achievement.
Multipath error suppressing method based on Digital Signal Processing is needed by carrying out data processing to reception signal Parameter, and reconstruct multipath signal according to these parameters, then subtract the influence of multipath signal in signal and obtain directly from receiving Signal realizes the purpose for inhibiting multipath error.The core of such methods is parameter Estimation, and the parameter of especially multipath signal is estimated Meter.Existing multipath signal estimation method is primarily adapted for use in Gaussian noise environment, its multipath estimates performance under non-Gaussian noise It is remarkably decreased.And in practical applications, non-Gaussian noise is generally existing, such as impulsive noise.Therefore, a kind of non-gaussian is designed Multipath signal estimator under noise is with a wide range of applications.
Summary of the invention
The purpose of the present invention is to solve the multipath estimator degradation problems under non-Gaussian noise environment, by non-height Multipath estimation problem under this noise circumstance is converted into the optimization problem of Prescribed Properties, and estimated result can be measured by designing one kind Then the objective function of randomness solves the optimization problem by a kind of improvement ε grade differential evolution algorithm, realizes a kind of base In the multipath estimator of minimal error entropy and ε grade differential evolution.
Technical solution of the present invention: the multipath estimator based on minimal error entropy and ε grade differential evolution, the multipath estimation Device is realized by personal calculator or digital signal processor；Multipath estimator includes auto-correlation computation module, memory module, constraint Degree of violating computing module, objective function computing module, ε grade comparison module, scale factor and aberration rate computing module, difference into Change module, multipath parameter output module and initialization module.Wherein the input of auto-correlation computation module is baseband signal and local Pseudo-code signal, in a storage module, the output of memory module is separately connected constraint and violates for the output storage of auto-correlation computation module The input of computing module, the input of objective function computing module are spent, constrains the output of degree of violating computing module, objective function calculates The output of module is all connected with the input of ε grade comparison module, the output connection scale factor and aberration rate meter of ε grade comparison module The input of module is calculated, the output of scale factor and aberration rate computing module connects the input of differential evolution module, differential evolution mould Block output connection multipath parameter estimation module input, multipath parameter estimation module export multipath parameter, and with export result Initialization module is updated, is prepared for the multipath parameter estimation of subsequent time.
The input of the auto-correlation computation module is baseband signal r (k) and local pseudo-code signalThe output of auto-correlation computation module is the survey of auto-correlation computation MagnitudeThe measured value y of auto-correlation computationkStorage is stored in the relevant parameter of initialization module setting In module, the initial population including k (k is to iterate to calculate number)(i=1,2 ..., Np, Np>=40), individual amount in population Np；Np>=40, differential evolution parameter cp and Tcon, associated branch number S, nuclear parameter δ2, Parzen window width Wmax, aberration rate most Small value CRmin, maximum value CRmax, scale factor minimum value Fmin, maximum value Fmax.While replicating the measured value in memory module, phase Close the output of parameter and initial population as the memory module.The input for constraining degree of violating computing module is to deposit in memory module The measured value of the auto-correlation computation of storage, the relevant parameter set in initialization and initial population.Meanwhile objective function computing module Input be also the measured value of the auto-correlation computation stored in memory module, the relevant parameter set in initialization and initial kind Group.
Constraint degree of violating computing module is violated by calculating the constraint of all individuals of desired output of estimated bias second moment DegreeObjective function computing module then exports the target for not violating the individual of constraint condition by calculating second order Renyi entropy Functional value fi.ε grade comparison module assigns individual grade R according to the constraint degree of violating and target function value of individuali, scale factor With aberration rate computing module according to the scale factor F of each individual of individual rating calculationiWith aberration rate CRi.Differential evolution module root Differential evolution, which is carried out, according to the scale factor and aberration rate of individual obtains new populationMultipath parameter output module is by new populationIn best individualX is exported as multipath parameter estimated resultf, and use new populationUpdate initialization module In initial population, for subsequent time multipath parameter estimation prepare.
The invention has the following beneficial effects:
1) present invention realizes the estimation of the multipath under non-Gaussian noise by Digital Signal Processing, has low cost, is easy to The characteristics of algorithm is transplanted.
2) present invention converts multipath estimation problem to the optimization problem of Prescribed Properties, is realized using intelligent optimization algorithm The global optimizing of the problem, without carrying out derived function.
3) present invention uses minimal error entropy as the performance indicator for measuring estimated result, it is ensured that multipath estimated result tool There is the smallest randomness, solves the problems, such as that the multipath estimated result under existing non-Gaussian noise has larger randomness, mention The flatness of multipath estimated result under high non-Gaussian noise.
4) present invention realizes a kind of improved ε grade differential evolution (ε RDE) algorithm, compared with former algorithm ε RDE, this hair The bright iterative estimate problem that may be directly applied under noise circumstance, and there is lower computation complexity.
Detailed description of the invention
Fig. 1 is multipath estimator structural block diagram.
Fig. 2 is multipath estimator operational flow diagram.
Fig. 3 is the improved ε RDE algorithm flow chart in the present invention.
Shown in Fig. 2, multipath estimator operational process includes the following steps:
(1) cp, S, T are initializedcon, δ2, W, and initial population x is generated according to the prior information of multipath parameteri, i=1, 2,…,Np, NpFor number of particles.
(2) it when k=1, is calculated according to primary condition and constraint degree of violating function and exports the constraint degree of violating of all individualsK is iterative calculation number.
(3) descending arrangement is carried out to all individuals according to constraint degree of violating size, the individual after output descending arrangementAnd Corresponding constraint degree of violating
(4) by the sum of the constraint degree of violating of preceding θ individual, it is denoted as ε (1), and export ε (1).
(5) it is iterated calculating since k+1 times, ε (k) is updated according to ε (1).
(6) the iteration initial population x after iterative calculation is calculatedk。
(7) according to input parameter ε (k), xkWith parameter CRmin, CRmax, Fmin, Fmax, δ2, ε (k), EF=0, EFmaxAnd improvement ε RDE algorithm calculate and export updated population
(8) by updated populationThe best individual of middle performance is as multipath estimated result xfOutput.
(9) meet termination condition, exit.Otherwise, return step (6).
Shown in Fig. 3, improved ε RDE algorithm flow includes the following steps:
(1) CR is initializedmin, CRmax, Fmin, Fmax, ε (1),EF=0, EFmax, give initial populationI=1,2 ..., Np。
(2) the constraint degree of violating of all individuals is calculatedTo the individual calculating target function value for not violating constraint condition fi, target function value of every calculating enables EF=EF+1, exports fiAnd EF.
(3) basisfiDescending arrangement, output descending row are carried out to all individuals with simplified ε grade comparison strategy Individual after column
(4) the best individual of performance is assigned to grade R=1, individual grade second-best is R=2, and so on, performance is most The individual of difference assigns grade R=Np。
(5) according to the scale factor F of each individual of individual rating calculationiWith aberration rate CRi。
(6) experimental subjects of i-th of individual are obtained according to index Crossover Strategy
(7) ε grade comparison strategy defined in root comparesWithThe individual of better performances enters the next generation, is denoted as
(8) new individual is constrained in given range according to prior information.Meanwhile if calculating a target function value Enable EF=EF+1.
(9) if EF < EFmax, then return step (2), otherwise EP (end of program).
Specific embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings.
1) signal structure explanation
Assuming that frequency locking ring has been completed to the carrier frequency tracking for receiving signal, therefore the base band received need to only be believed It number is handled:
Used receipt signal model are as follows:
Wherein, first item (α0c(t-τ0)cos(θ0)) indicate direct signal, Section 2Indicate the road M multipath signal.
C (t) is the C/A code being modulated on carrier wave, and being worth is 1 or -1；
α0,τ0,θ0The respectively amplitude of direct signal, PN code delay time and carrier delay phase；
M is the number of multipath；
αj,τj,θjThe respectively amplitude of jth road multipath signal, the delay time relative to direct signal and delay phase；
τjOnly consider less than 1.5 chips the case where (more than a chip multipath signal to tracking ring influence very It is small)；
N (t) is noise.
Although may theoretically there is multichannel multipath signal at any one time, actually often only has all the way or two-way is main Multipath signal.Therefore the present invention only considers the case where interference signal all the way.So signal model (1) can be write as
R (t)=α0c(t-τ0)cos(θ0)+α1c(t-τ0-τ1)cos(θ0+θ1)+n(t) (2)
The signal received is continuous analog signal, after sampling processing, obtained discrete number can be believed Number indicate are as follows:
R (k)=α0c(k-l0)cos(θ0)+α1c(k-l0-l1)cos(θ0+θ1)+n(k) (3)
Wherein, k indicates the k moment, and a moment iteration is primary；
l0And l1For τ0And τ1Digital representation；
N (k) is Gaussian noise or non-Gaussian noise.
R (k) and local signalObtained after related operation To correlation output vectorWhereinIt is l0Local estimation,It is obtained from capture result.
ds(s=1 ..., S) is the spacing of s-th of associated branch Yu instant branch；
S is the number of correlator；
Work as dsWhen < 0,Indicate local early code；
Work as dsWhen > 0,Indicate local late code；
Work as dsWhen=0,Indicating local is time-code；
Parameter to be estimated is x=[α0,α1,θ0,θ1,l0,l1]T, these parameters pass through measured value ykEstimated.
Wherein, N is positive integer, TpIt is C/A code period, TsIt is the sampling period；
A0,k=α0,kcos(θ0,k) it is complex amplitude of the direct signal at the k moment；
A1,k=α1,kcos(θ1,k) it is complex amplitude of the multipath signal at the k moment；
R (ε) is ideal autocorrelation function；
It is l0,kLocal estimation；
l0,kDelay time of the direct signal at the k moment；
l1,kIt is delay time of the multipath signal at the k moment；
nkFor the correlation output noise at k moment.
From formula (4) as can be seen, the parameter predigesting to be estimated at k moment is xk=[A0,k,A1,k,εk,l1,k]T.Therefore system It is modeled as first-order Markov model.
xk=A (xk-1)+wk (5)
yk=B (xk)+vk (6)
Wherein xk∈RD×1It is state vector.D is the dimension of state to be estimated, for single multipath estimation problem D=4.A () is to rely on state vector xkSytem matrix.wkIt is the Gaussian noise of zero-mean distribution, variance Q.ykBe observation to Amount, It can be obtained according to formula (3), s=1 ..., S.B () is to rely on xkObserving matrix, vkIt is the measurement noise of zero-mean, it is Gaussian noise or non-Gaussian noise.
According to ykEstimate xk.It enables It is xkLocal estimation.
2) optimization problem is converted by multipath estimation problem
In order to make to measure estimated biasThere is the smallest randomness, Jin Erda under the premise of mean value is zero To in a noisy environment with excellent multipath estimation performance purpose, the present invention measured using Renyi entropy estimated bias with Machine using the second moment of estimated bias as constraint condition, while considering the prior information of parameter to be estimated.Therefore, multipath is estimated Meter problem can be converted into the optimization problem of Prescribed Properties.
The design of objective function and constraint condition is completed when solving above-mentioned optimization problem, and is realized a kind of improved ε grade differential evolution algorithm allows to estimate in the multipath under noise circumstance.
The present invention using can measure variable randomness measurement amount --- entropy is as the target to be optimized.The smaller estimation of entropy As a result randomness is smaller.
The present invention measures the randomness of estimated result using Renyi entropy, is expressed as based on minimal error entropy objective function
Wherein
V (e) is the information potential of e；
N is error number of samples；Entropy is smaller, and the randomness of evaluated error is smaller.
In view of the monotone decreasing characteristic of log function, H2(e) minimum is realized by the maximization of V (e).
In order to reduce computation complexity, present invention prompting message gesture Vk(e) V (e) is replaced, i.e.,
In order to further decrease computation complexity, V is calculated using Parzen window setting techniquek(e), therefore formula (9) can be with It is expressed as
Here W is the length of Parzen window.
It can be obtained according to the characteristic of multiple normal distribution
HereIt is gaussian kernel function.It is the smallest in order to have evaluated error Randomness can pass through Vk(e) maximization realizes that the maximization problems can be converted to minimization problem by following formula.
Jk=-Vk(e) (12)
Objective function calculating is realized by objective function computing module.
The constraint condition:
Because entropy has translation invariance, the mean value for guaranteeing estimated result by additional constraint condition is needed to be Zero.By ekSecond order away from be desired for zero as constraint condition, i.e.,
E(eTE)=0 (13)
Meanwhile in order to utilize the prior information of multipath parameter, it is also contemplated that following boundary condition:
0 < A0,k≤1 (14)
0≤Ai,k≤1 (15)
-0.5≤εk≤0.5 (16)
0≤τi,k< 1.5 (17)
Above-mentioned boundary condition is considered based on following: its amplitude can be determined substantially when signal normally receives, with the width Direct signal amplitude and multipath signal amplitude is normalized in degree, it is known that A0,kAnd Ai,kLess than or equal to 1.Since acquisition phase can To guarantee that the estimated bias of direct signal time delay is less than 0.5Tc, so -0.5≤εk≤0.5.According to C/A code auto-correlation letter Several characteristics are it is found that only relative time-delay τi,k1.5T is arrived for 0cMultipath signal direct signal can be had an impact.
In order to reduce computation complexity and make full use of existing error sample information, the present invention utilizes following statistical information To indicate E (eTE):
Here W is the length of the Parzen window in (11).
Equality constraint (18) can be converted to inequality constraints condition by following formula
Here threshold is the positive integer of a very little, and the present invention considers threshold=10-4。
Constraint condition is realized by constraining degree of violating computing module.
3) multipath estimator designs
The present invention constrains grade differential evolution algorithm (ε constrained rank using a kind of improved ε Differential evolution, ε RDE) solve above-mentioned optimization problem.The solution that is proposed to of ε RDE algorithm has equation The optimization problem of constraint condition is currently only used for solving Numerical Optimization, not can be used directly in the iteration for having noise factor Optimization problem.
The present invention is in former algorithm ε RDE (see Takahama T, Sakai S.Efficient Constrained Optimization by theεConstrained Rank-Based Differential Evolution[C]// Evolutionary Computation.IEEE, 2012:1-8.) on the basis of improve, make improved ε RDE algorithm can The optimization problem for having equality constraint in real system is solved with iteration, and then realizes multipath parameter estimation.Multipath estimator Structure is as shown in Figure 1, multipath estimator operational process is as shown in Figure 2.
In the present invention, step is realized based on the multipath estimator for improving ε RDE algorithm are as follows:
Initialize cp, S, Tcon, δ2, W, and initial population x is generated according to the prior information of multipath parameteri, i=1,2 ..., Np, NpFor number of particles.
(1) the k=1 moment calculates the constraint degree of violating of all individuals according to constraint degree of violating function (20).
Hereei,jIndicate i-th of individual in the observation at jth moment Error.
(2) descending arrangements are carried out to all individuals according to constraint degree of violating size, and by first θ individual constraint degree of violating The sum of, it is denoted as ε (1).
(3) it is iterated calculating since the k=k+1 moment, and updates ε (k) according to the following formula at each moment
Cp and TconFor constant, cp=5, T in the designcon=W.
(4) basisCalculate the initial population at k moment, i=1,2 ..., Np。
(5) updated population is calculated according to improved ε RDE algorithmAnd it is performance in updated population is best Individual as multipath estimated result xfOutput.
(6) meet termination condition, exit.Otherwise, (6) are returned to.
Note: in calculating target function value, carrying out canbe used on line according to the following formula
Wherein
Improved ε RDE algorithm flow is as shown in figure 3, specific steps can be described as:
(1) CR is initializedmin, CRmax, Fmin, Fmax, ε (k), EF=0, EFmax=300, give initial populationI=1, 2,….,Np。
(2) the constraint degree of violating of all individuals is calculated according to formula (20)To the individual root for not violating constraint condition According to (12) calculating target function value fi, target function value of every calculating enables EF=EF+1.
(3) descending arrangement is carried out to all individuals according to ε grade comparison strategy.Assuming that f1(f1)、For individual x1 (x2) target function value and constraint degree of violating, ε meets ε >=0, then simplified ε grade compares ε<、ε≤Is defined as:
(4) the best individual of performance is assigned to grade R=1, individual grade second-best is R=2, and so on, performance is most The individual of difference assigns grade R=Np。NpFor the individual amount of initial population.
(5) scale factor F of each individual when carrying out differential evolution is calculatediWith aberration rate CRi
RbFor the grade of base vector individual.
(6) experimental subjects of i-th of individual are obtained according to variation Crossover Strategy
Variation: x '=xp1+Fi·(xp2-xp3) (27)
Wherein p1 ≠ i, p2 ≠ i, p3 ≠ i, p1, p2, p3 are from [1, Np] in generate the random integers being not mutually equal, Np For individual amount.
Intersect:
R is the random integers generated from [1, D], and u is the random decimal generated from [0,1]
J ∈ [1, D], D are xiDimension.
(7) the ε grade comparison strategy defined according to formula (23), (24) comparesWithBetter performances individual into Enter the next generation, is denoted as
(8) according to formula (14)~(17), new individual is constrained in given range, specific practice is, if individualJ Dimension within the specified range, does not then regenerate the numerical value of the dimension, and substitute within the specified rangeThe numerical value of jth dimension.Meanwhile such as Fruit calculates a target function value and then enables EF=EF+1.
(9) if EF < EFmax, then (2) are returned to, otherwise EP (end of program).
Heretofore described index Crossover Strategy and ε grade comparison strategy are in Takahama T, Sakai S.Efficient Constrained Optimization by theεConstrained Rank-Based It is on the books in Differential Evolution [C] //Evolutionary Computation.IEEE, 2012:1-8., this Invention is omitted.
For initial population, i=1,2 ..., Np, NpFor individual amount N in populationp, cp and TconIt is differential evolution ginseng Number, S are associated branch number, δ2For nuclear parameter, WmaxFor Parzen window width, CRminFor aberration rate minimum value, CRmaxFor variation Rate maximum value, FminFor scale factor minimum value, FmaxFor scale factor maximum value, ε (k) is the constraint degree of violating of preceding θ individual The sum of (k=1, θ=0.2Np)。

Claims (4)

1. the multipath estimator based on minimal error entropy and ε grade differential evolution, it is characterized in that including auto-correlation computation module, depositing Module, constraint degree of violating computing module, objective function computing module, ε grade comparison module, scale factor and aberration rate is stored up to calculate Module, differential evolution module, multipath join estimation module；Multipath ginseng estimation module includes multipath parameter output module and initialization mould Block；The input of the auto-correlation computation module is baseband signal and local pseudo-code signal, the output connection of auto-correlation computation module The input of memory module, the input of output connection constraints degree of the violating computing module of memory module, objective function computing module The output of input, the output, objective function computing module that constrain degree of violating computing module is all connected with the defeated of ε grade comparison module Enter, the input of output the connection scale factor and aberration rate computing module of ε grade comparison module, scale factor and aberration rate calculate The input of the output connection differential evolution module of module, the output of differential evolution module connect the defeated of multipath parameter estimation module Enter, multipath parameter estimation module exports multipath parameter, and updates initialization module with output result, is that the multipath of subsequent time is joined Number estimation is prepared.
2. the multipath estimator based on minimal error entropy and ε grade differential evolution according to claim 1, it is characterized in that multipath Estimator operational process includes the following steps:
(1) it initializes and initial population is generated according to the prior information of multipath parameter；
(2) it is calculated according to primary condition and constraint degree of violating function and exports the constraint degree of violating of all individuals；
(3) it calculates the sum of constraint degree of violating of preceding θ individual and exports θ=0.2Np, Np≥40；
(4) descending arrangement is carried out to all individuals according to constraint degree of violating size, it is individual and corresponding after output descending arrangement Constrain degree of violating；
(5) calculating is iterated since calculating for second；
(6) the initial population x calculated for the first time is calculatedk；
(7) it calculates using improved ε RDE algorithm and input parameter and exports updated population
(8) by updated populationThe best individual of middle performance is as multipath estimated result xfOutput.
3. the multipath estimator based on minimal error entropy and ε grade differential evolution according to claim 1, it is characterized in that described Baseband signal model are as follows:
Wherein, first item (α0c(t-τ0)cos(θ0)) indicate direct signal；
Section 2Indicate the road M multipath signal；
C (t) is the C/A code being modulated on carrier wave, and being worth is 1 or -1；
α0For the amplitude of direct signal；
τ0For the PN code delay time
θ0For carrier wave delay phase
M is the number of multipath；
αjFor the amplitude of jth road multipath signal；
τjDelay time for jth road multipath signal relative to direct signal；
θjDelay phase for jth road multipath signal relative to direct signal；
τj1.5 chips of <；
N (t) is noise.
4. the multipath estimator based on minimal error entropy and ε grade differential evolution according to claim 1, it is characterized in that initially The relevant parameter for changing module setting includes the initial population calculated for the first timeIndividual amount in population Np, differential evolution parameter cp and Tcon, associated branch number S, nuclear parameter δ2, Parzen window width Wmax, aberration rate minimum value CRmin, aberration rate maximum value CRmax, scale factor minimum value Fmin, scale factor maximum value Fmax, ε (k) is the pact of preceding θ individual The sum of beam degree of violating, k=1, θ=0.2Np。
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