CN109557529B - Radar target detection method based on generalized Pareto distribution clutter statistical modeling - Google Patents
Radar target detection method based on generalized Pareto distribution clutter statistical modeling Download PDFInfo
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Abstract
The invention discloses a radar target detection method based on generalized Pareto distribution clutter statistical modeling, and aims to improve radar target detection performance. The technical scheme is that the maximum likelihood estimation of the logarithm is combined with the particle swarm optimization algorithm, a cost function is designed through the maximum likelihood estimation of the logarithm, and the particle swarm optimization algorithm is utilized to minimize the cost function so as to obtain the optimal parameter estimation result; and determining a detection threshold by using the optimal parameter estimation result to complete radar target detection. The invention can ensure the optimality of the solution of the parameter to be estimated in the maximum likelihood sense, improve the precision and the robustness of parameter estimation, improve the accuracy of the detection threshold and ensure the reliability of the radar target detection result.
Description
Technical field
The invention belongs to Radar Targets'Detection field, be related to it is a kind of using particle swarm optimization algorithm to generalized Pareto distribution into
The radar target detection method of the accurate statistical modeling of row.
Background technique
Clutter data statistical modeling (carries out Accurate Curve-fitting to clutter data histogram using suitable distribution or function)
It is a major issue of Radar Targets'Detection field face, chooses (or the fitting of suitable clutter data fitting distributed model
Function) and accurately acquisition model parameter is algorithm of target detection design (such as detection threshold, false-alarm probability, detection probability calculate)
Important foundation.If there are biggish errors for model parameter estimation, you can't get accurate detection thresholdings, so as to cause detection
Probability decline and false-alarm probability rise.
Common clutter data fitting distributed model has Rayleigh distributed model, Weibull distributed model and K points
Cloth model, Gamma distributed model etc..These distributed models have the adaptation range of its own, as Rayleigh distributed model is common
In describing the low uniform clutter data of resolution, K distributed model is then usually used in describing the high-resolution sea clutter under the conditions of low grazing angle
Data.
Generalized Pareto distribution model is a kind of important statistical distribution pattern, is according to Italian economist
The naming of Vilfredo Pareto.The model is initially mainly used in economics, physics, hydrology and seismology
Equal fields are gradually applied to the statistical modeling of high resolution radar clutter data, such as document 1:G.V.Weinberg,
" Assessing Pareto fit to high-resolution high-grazing-angle sea clutter ",
Electronics Letters, 2011,47 (8): (G.V.Weinberg is in 2011 " electronics flash report " volume 47 by 516-517
The paper that 8 phases delivered, Chinese are entitled " Pareto, which is distributed, assesses the capability of fitting of high grazing angle sea clutter ") in research
The result shows that generalized Pareto distribution model have to the high-resolution under the conditions of big grazing angle, big hangover sea clutter data it is good
Good Model Matching and statistical distribution capability of fitting.It can be seen that generalized Pareto distribution model parameter estimation is to solve to enter greatly
Under the conditions of penetrating complementary angle special applications, the important technology that target detection problems are related in sea clutter background.
Generalized Pareto distribution model can be represented by the formula for
In formula, f () indicates that probability density function, z are that independent variable (represents noise signal amplitude, and zero) its value is greater than, k
Indicating form parameter, σ (σ > 0) indicates that scale parameter, exp () are indicated using natural constant e as the exponential function at bottom, f (z | k,
σ) indicate the probability density function of the noise signal amplitude z comprising unknown distribution parameter (k and σ).
Obviously, as k=0, it is exponential distribution model that generalized Pareto distribution, which is just degenerated, and the solution of parameter σ is fairly simple,
Not in discussion range of the invention.
In the case where k < 0, the parameter (i.e. k, σ) of generalized Pareto distribution model usually utilizes noise signal amplitude z
The r rank central moment E (z of (also referred to as clutter data sample)r) (E () expression takes mathematic expectaion, r >=1 and be integer) estimated,
Such as moments estimation method (Method of Moments, MoM) common at present, probability weight Moment Methods (Probability
Weighted Moments Method, PWMM), likelihood Moment Methods (Likelihood Moment Method, LMM) etc..Document
2:P.de Zea Bermudez, Samuel Kotz, " Parameter estimation of the generalized
Pareto distribution Parts I&II ", Stat.Plann.Inference 140,2010:1353-1388 (P.de
For Zea Bermudez et al. in the paper in " statistical rules and reasoning periodical " the 140th curly hair table in 2010, Chinese was entitled " wide
The model parameter estimation of adopted Pareto distribution ") in the method for parameter estimation of several generalized Pareto distribution model is carried out
It summarizes, analyze and compares, and point out that maximal possibility estimation (Maximum Likelihood Estimation, MLE) is most effective
Estimation method.
In fact, actual-structure measurement moment of the orign is miscellaneous with corresponding order when big hangover distribution is presented in radar clutter
It will appear certain deviation, and increase and clutter data sample of the deviation with square order (r) between wave pattern original theoretical point square
The reduction of quantity and increase, this will bring detrimental effect to the estimation method based on statistical moment.Maximal possibility estimation has very
High estimated accuracy, but when radar clutter distributed model (such as generalized Pareto distribution model namely probability density function expression
Formula) it is more complicated when, this method hardly results in the analytical expression of parameter Estimation；It in this case, although can be by such as
Document 3:Tjalling J.Ypma, " Historical development of the Newton-Raphson method ",
SIAM Review, 1995,37 (4): (Tjalling J.Ypma is in nineteen ninety-five in " American industry and applied mathematics by 531-551
Can comment on " paper delivered of periodical the 4th phase of volume 37, the historical development of the entitled newton-Newton Raphson method of Chinese) in
Newton-Raphson numerical algorithm is solved, but this numerical method is easily trapped into local extremum and is unable to get optimal ginseng
Number estimation.
Particle group optimizing (Particle Swarm Optimization, PSO) is a kind of important intelligent optimization algorithm,
Have the characteristics that calculating is simple, fast convergence rate, stability are good, and there is global optimizing ability.Pass through PSO algorithm, it is expected to solve
The certainly parameter high-precision estimation problem of complex model to improve Radar Targets'Detection performance, but has had not yet to see disclosure
Document relates to how to carry out the estimation of Pareto Clutter Model parameter high-precision and high performance objectives detection with PSO algorithm.
Summary of the invention
The technical problem to be solved by the present invention is providing a kind of radar based on generalized Pareto distribution clutter statistical modeling
Object detection method improves Radar Targets'Detection performance.
Technical solution is, by logarithm maximum likelihood (Logarithmic Maximum Likelihood, LML) estimation and grain
Subgroup optimization (PSO) algorithm combines, and cost function is designed by logarithm maximal possibility estimation criterion, and utilize population
Optimization algorithm is come the parameter estimation result that minimizes cost function to obtain optimal；Inspection is determined using optimal parameter estimation result
Thresholding is surveyed, Radar Targets'Detection is completed.
Specific step is as follows:
The first step defines and initializes population.Method is:
1.1 define population G:
Population is by the molecular set of a group grain, and particle herein is parameter to be estimated, and population may be defined as
G={ pi=(σi,ki),vi=(δ σi,δki)；I=1,2 ..., I } (2)
In formula, I is the particle number in G, piFor the position feature of i-th of particle in G, σiFor the ruler of i-th of particle in G
Spend parameter, kiIndicate the form parameter of i-th of particle in G；viFor the velocity characteristic of i-th of particle in G, δ σiFor i-th in G
The scale parameter σ of soniVariable quantity, δ kiFor the form parameter k of i-th of particle in GiVariable quantity.
1.2 initialization particle position features:
The N number of clutter data sample observed from clutter area is denoted as z1,...,zn,...,zN(1≤n≤N, n are whole
Number), then the mean value and variance of N number of clutter data sample are respectivelyWithDo not having
Under conditions of prior information, it can useWithRespectively indicate the thick of parameter σ and k
Thus i-th of 0 moment of particle position feature is initialized as by estimated value
In formula, I is positive integer, and the size of I generally takes 200~500 to be advisable by empirical value；0 expression parameter of subscript
Original state (i.e. 0 moment),For the position feature at i-th of 0 moment of particle in G,For the ruler at i-th of 0 moment of particle in G
Parameter is spent,For the form parameter at i-th of 0 moment of particle in G；Expression uniformly distributed function, interval limit a, on
It is limited to b；It indicates from uniformly distributed functionMiddle direct access takes one between section [a, b] at random
Number.It indicatesIt is from uniformly distributed functionMiddle direct access (the area Ji
BetweenBetween take a number at random),For lower limit,For the upper limit；
It indicatesIt is from uniformly distributed functionMiddle direct access,For lower limit,For the upper limit.
1.3 initialization particle rapidity features:
For the velocity characteristic at i-th of 0 moment of particle in G,For the scale parameter variation at i-th of 0 moment of particle in G
Amount,For the form parameter variable quantity at i-th of 0 moment of particle in G.It indicatesIt is from uniform
Distribution functionIn the number that takes,It indicatesIt is from uniformly distributed functionIn the number that takes.
Second step enables the number of iterations variable t=0.
Third step seeks the cost function of particle when the t times iteration.Method is:
3.1 convert the complex exponent distribution (situation when k < 0) of generalized Pareto distribution model to shown in formula (9)
Logarithmic form likelihood function, i.e.,
In formula, ln () is indicated using natural constant e as the logarithmic function at bottom, and L (z | k, σ) indicate to include unknown distribution parameter
The likelihood function of the noise signal amplitude z of (k and σ).
It can be seen that the maximal possibility estimation of parameter k and σ can be obtained by the partial derivative of solution formula (9), have at this time
It is obvious that the explicit expression about parameter k and σ can not be acquired by formula (10) and (11) two formula of formula,
That is the solution of parameter k and σ can not be found out by the partial derivative result zero setting for obtaining formula (10) and (11) two formula of formula,
The present invention transfers to seek numerical solution by particle swarm optimization algorithm, need to construct cost function.
3.2 cost functions according to shown in formula (10) and (11) building formula (12)
In formula, | | for the symbol that takes absolute value, T (σ, k) can be made constantly to approach to 0 by the minimum of the cost function,
This process, which is equivalent to, is optimal formula (10) and the solution of formula (11).
3.3, which seek the corresponding fitness value of I particle, method in G by formula (12), is
Successively by the position feature of I particle substitutes into formula (12) in G in the t times iteration, obtains I particle the t times and change
The cost function value in generation, the fitness value as the t times iteration of I particle.For i-th of particle in G, specific practice is by it
Position feature in the t times iteration(i.e.Parameter to) substitute into formula (12), calculateAnd enable i-th
The particle fitness value of sub the t times iteration
The I particle t group fitness value that I particle is obtained through the t times iteration, is expressed as
4th step calculates the individual extreme value pbest of population in the t times iterationtWith global extremum gbestt.Method is:
4.1 according toParticle corresponding with smallest particles fitness value in the t times iteration is found,
I.e.
In formula,Expression is first foundIn the smallest value,
And find the corresponding particle of this minimum value (being expressed as parameter to (σ ', k ')).(assuming that the serial number i of the minimum value, then find
Particle beI.e.
4.2 according toIt finds out
Make the smallest particle of adaptive value in 0~t times all iterative process, as preceding t iteration global extremum gbestt, i.e.,
In formula, (σ*,k*) indicate the corresponding particle of preceding t iteration minimum adaptive value.
5th step, enables t=t+1.
6th step, according to the individual extreme value pbest of acquisitiontWith global extremum gbestt, update the position spy of I particle in G
Sign and velocity characteristic, method are:
6.1 enable i=1.
The position feature and velocity characteristic of 6.2 i-th particle are updated by formula (15) and formula (16):
Wherein, wt-1=0.9-0.5 (t-1)/tmax, be t-1 times when Inertia weight factor, tmaxFor maximum number of iterations
(for positive integer, usually taking 100~200)；Rand indicates the uniform random number between [0,1]；c1With c2For Studying factors
(or aceleration pulse) is positive real number, is usually taken as 2.
6.3 enable i=i+1.
6.4 determine whether i≤I is true, if so, turn 6.2；Otherwise, indicate that the position for having updated I particle in G is special
It seeks peace velocity characteristic, executes the 7th step.
7th step, judges whether t is equal to maximum number of iterations tmax, if satisfied, then by global extremum gbestt, namely (σ*,
k*) be used as parameter to the final estimated result of (σ, k), execute the 8th step；Otherwise, turn third step.
8th step utilizes (σ*,k*) Radar Targets'Detection is carried out, method is:
8.1 utilize (σ*,k*) reconstruct probability density function corresponding with generalized Pareto distribution model
I.e.
In formula,It indicates by (σ*,k*) reconstruct the obtained approximate function about independent variable z.
8.2 given target detection false alarm rate Pf(PfUsually take 10-4~10-2), detection threshold th is asked according to formula (18)
In formula, integral formula can be resolved by newton-Ke Ci (Newton-Cotes) Numerical Integral Formulas, specific solution
It can refer to document 3: Ye Qixiao, Shen Yong is joyous etc., " practical mathematics handbook (second edition) ", Science Press, 2006,719~720.
8.3 target detections, method are:
8.3.1 it is observed in real time by radar, obtains J observation data, J >=1 enables j=1；
8.3.2 judge practical j-th of the observation data y obtained of radarjWhether target is had, and method is:
If yj>=th, the conclusion of output " j-th of observation data has target "；If yj< th, output " j-th of observation data without
The conclusion of target "；
8.3.3 determine whether j is less than J, if satisfied, enabling j=j+1, turn 8.3.2；Otherwise, radar real-time observed data is indicated
Processing terminate, completes target detection.
Beneficial effects of the present invention:
1. estimator (the formula that third step of the present invention constructs Pareto distributed model parameter by logarithm maximum likelihood function
(9)), it is ensured that the optimality that parameter to be estimated solves under maximum likelihood meaning；
2. the 4th step of the invention has the ability of global optimizing using particle swarm optimization algorithm, conventional numeric method is overcome
(such as Newton-Raphson) when solving the problems, such as model parameter estimation it is existing it is sensitive to initial value, be easy to converge on local pole
The precision and robustness of parameter Estimation can be improved, it is ensured that the reliability of Radar Targets'Detection result in the defect of value.
3. the present invention plays PSO algorithm in conjunction with the maximum likelihood method for parameter estimation of generalized Pareto distribution model parameter
Come, improves the accuracy of detection threshold th, and then improve the detection performance of radar target.
Detailed description of the invention
Fig. 1 is overview flow chart of the present invention.
Specific embodiment
Embodiments of the present invention will be described with experiment with reference to the accompanying drawing.
Fig. 1 gives overview flow chart of the present invention, illustrates by taking clutter sample number N=100 as an example first below specific
Experimentation.On this basis, by different experiment condition settings (as changed clutter sample number N and mould shapes parameter k
Deng), to investigate detection performance of the present invention under different experimental conditions.
The first step defines and initializes population.N=100 clutter data sample is obtained from clutter area, sets population
Size I=500, population are defined as G={ pi=(σi,ki),vi=(δ σi,δki)；I=1,2 ..., I population initial bit
Set componentExist respectivelyWithSection grab sample, initial velocity componentsIt is unified inBetween grab sample, wherein i=1,2 ..., I；Maximum number of iterations is
tmax=200.
Second step enables t=0.
Third step calculates the particle fitness value in t (t >=0) secondary iteration.According to the cost function T in formula (12)
(σ, k) seeks the corresponding fitness value of I particle in G, obtains the adaptability of all I particles in the t times iteration of I particle
Value, wherein the fitness value of i-th of particleThe I that I particle is obtained through the t times iteration
A particle t group fitness value, is expressed as
4th step, is utilized respectively formula (13) and formula (14) finds the individual extreme value of population in t iterative process
pbesttWith global extremum gbestt, gbestt=(σ*,k*)；
5th step, enables t=t+1.
6th step updates the speed and location components of I particle according to formula (15) and formula (16).
7th step, judges whether t reaches maximum number of iterations tmax.If satisfied, by (σ*,k*) defeated as parameter estimation result
Out, and turn the 8th step；Otherwise third step is returned.
8th step, Radar Targets'Detection.Probability density function is constructed according to formula (17) firstIn this base
On plinth, detection threshold th is determined using formula (18), is observed in real time finally by radar, obtain J observation data (J in experiment
=500) aimless judgement, has been carried out to complete target detection by step 8.3.2~8.3.3 to J observation data.
To illustrate the invention to generalized Pareto distribution model under the conditions of different shape parameter, different clutter sample sizes
The estimation performance of parameter has chosen three canonical parameters in embodiment and is emulated to (σ, k) (corresponding three groups of different experiments)
Verifying.Parameter Estimation Precision mean error (Mean Error, ME) and root-mean-square error (Root of Mean Square
Error, RMSE) two indices assess, and expression formula is respectively as follows:
In formula,Indicate the estimation of parameter υ (υ represents scale parameter or form parameter) obtained in the m times emulation, M table
Show Monte Carlo simulation times.
Influence in view of scale parameter σ to estimated result is little, and form parameter k on generalized Pareto distribution influence compared with
Greatly, and k value is smaller, and generalized Pareto distribution hangover is bigger.Selective analysis of the present invention is assessed the method and is estimated to form parameter
Effect is counted, thus setting σ=1, k=-0.3, -0.2, -0.1 (value of k is taken as -0.3 respectively, -0.2, -0.1, carry out three
The different experiment of group), M=500, to the present invention is based on the broad sense Pareto Clutter Model object detection methods of particle group optimizing
(LML-PSO) it is tested, and compares its performance difference between conventional method (such as MoM, PWMM, LMM).Experiment is logical
It is carried out on computer platform, using Matlab software realization, parameters obtained (σ, k) is in different clutter data sample number (N=
25,50,100,500), simulation result such as 1~table of table 3 under the conditions of different estimation methods (MoM, PWMM, LMM and LML-PSO)
It is shown.Wherein, 1~table of table 3 respectively corresponds mean error (ME) He Junfang under the conditions of k=-0.3, k=-0.2 and k=-0.1
Root error (RMSE).
It can be seen that from 1~table of table 3, the mean error and root-mean-square error of LML-PSO of the present invention is significantly less than another three kinds
Method.
Table 1
Table 2
Table 3
Influence in order to further illustrate form parameter k estimated result to target detection, by taking k=-0.3 as an example, in false-alarm
Probability PfUnder=0.01 application conditions, parameter estimating error, can calculate true target by formula (18) if it does not exist
Detection threshold is th=9.898.When there are different degrees of form parameter evaluated error (i.e. ME and RMSE are not 0), obtain
As shown in table 4 to corresponding target detection thresholding, error size range is -0.12~0.12 (error interval 0.002) in table,
Correspond to the error range of actual parameter ± 40% (- 0.3 × 40%~0.3 × 40%).When evaluated error is -0.12, mesh
Mark detection threshold is th=14.023；When evaluated error is 0.12, target detection thresholding is th=7.149.
| Evaluated error | -0.120 | -0.118 | -0.116 | -0.114 | -0.112 | -0.110 | -0.108 | -0.106 | -0.104 | -0.102 | -0.100 | -0.098 |
| Detection threshold | 14.023 | 13.939 | 13.856 | 13.774 | 13.692 | 13.61 | 13.529 | 13.449 | 13.369 | 13.29 | 13.212 | 13.134 |
| Evaluated error | -0.096 | -0.094 | -0.092 | -0.090 | -0.088 | -0.086 | -0.084 | -0.082 | -0.080 | -0.078 | -0.076 | -0.074 |
| Detection threshold | 13.056 | 12.979 | 12.903 | 12.827 | 12.751 | 12.676 | 12.602 | 12.528 | 12.455 | 12.382 | 12.31 | 12.238 |
| Evaluated error | -0.072 | -0.070 | -0.068 | -0.066 | -0.064 | -0.062 | -0.060 | -0.058 | -0.056 | -0.054 | -0.052 | -0.050 |
| Detection threshold | 12.166 | 12.096 | 12.025 | 11.955 | 11.886 | 11.817 | 11.749 | 11.681 | 11.613 | 11.546 | 11.479 | 11.413 |
| Evaluated error | -0.048 | -0.046 | -0.044 | -0.042 | -0.040 | -0.038 | -0.036 | -0.034 | -0.032 | -0.030 | -0.028 | -0.026 |
| Detection threshold | 11.347 | 11.282 | 11.217 | 11.153 | 11.089 | 11.026 | 10.963 | 10.900 | 10.838 | 10.776 | 10.715 | 10.654 |
| Evaluated error | -0.024 | -0.022 | -0.020 | -0.018 | -0.016 | -0.014 | -0.012 | -0.010 | -0.008 | -0.006 | -0.004 | -0.002 |
| Detection threshold | 10.593 | 10.533 | 10.473 | 10.414 | 10.355 | 10.296 | 10.238 | 10.181 | 10.123 | 10.066 | 10.01 | 9.954 |
| Evaluated error | 0.002 | 0.004 | 0.006 | 0.008 | 0.010 | 0.012 | 0.014 | 0.016 | 0.018 | 0.020 | 0.022 | 0.024 |
| Detection threshold | 9.842 | 9.787 | 9.733 | 9.678 | 9.624 | 9.571 | 9.518 | 9.465 | 9.412 | 9.360 | 9.308 | 9.257 |
| Evaluated error | 0.026 | 0.028 | 0.030 | 0.032 | 0.034 | 0.036 | 0.038 | 0.040 | 0.042 | 0.044 | 0.046 | 0.048 |
| Detection threshold | 9.206 | 9.155 | 9.104 | 9.054 | 9.005 | 8.955 | 8.906 | 8.857 | 8.809 | 8.761 | 8.713 | 8.665 |
| Evaluated error | 0.050 | 0.052 | 0.054 | 0.056 | 0.058 | 0.060 | 0.062 | 0.064 | 0.066 | 0.068 | 0.070 | 0.072 |
| Detection threshold | 8.618 | 8.571 | 8.525 | 8.478 | 8.433 | 8.387 | 8.342 | 8.297 | 8.252 | 8.207 | 8.163 | 8.119 |
| Evaluated error | 0.074 | 0.076 | 0.078 | 0.080 | 0.082 | 0.084 | 0.086 | 0.088 | 0.090 | 0.092 | 0.094 | 0.096 |
| Detection threshold | 8.076 | 8.033 | 7.990 | 7.947 | 7.904 | 7.862 | 7.820 | 7.779 | 7.738 | 7.696 | 7.656 | 7.615 |
| Evaluated error | 0.098 | 0.100 | 0.102 | 0.104 | 0.106 | 0.108 | 0.110 | 0.112 | 0.114 | 0.116 | 0.118 | 0.120 |
| Detection threshold | 7.575 | 7.535 | 7.495 | 7.456 | 7.417 | 7.378 | 7.339 | 7.300 | 7.262 | 7.224 | 7.187 | 7.149 |
Table 4
As can be seen from the table:
1) generally, the evaluated error (or Error Absolute Value) of various methods with clutter data sample size (N) increase
And reduce, illustrate that clutter data sample size is bigger, the precision of parameter Estimation is higher, and estimation performance is also better；
2) in three groups of different experiments, clutter data sample number under the same conditions, the method for the invention with it is other
Three kinds of estimation methods are compared, and all have the smallest mean error and root-mean-square error, illustrate that there is consistent higher parameter to estimate for it
Count precision；
Even if 3) by comparison it is found that in the case where clutter data number of samples smaller (such as N=50), the side LML-PSO
Method estimated accuracy still with higher, illustrates to small sample also well adapting to property.
4) in contrast, LML-PSO method has the smallest parameter estimating error, illustrates that the target being thus calculated is examined
The theoretical value for surveying thresholding and detection threshold is closest, and correspondingly detection performance is also best.
To sum up, it is compared with the traditional method, the method for the invention has generalized Pareto distribution model parameter estimation bright
Aobvious precision property advantage, and it can be well adapted for the variation of model parameter, it can effectively improve in long streaking Distribution Clutter background
Radar Targets'Detection performance.
Although the present invention is described in detail referring to above-described embodiment, it should be appreciated that the present invention is not limited to disclosed
Embodiment.For the technical staff of this professional domain, various changes can be carried out to its form and details.The present invention covers
Various modifications in the spirit and scope of the appended claims.
Claims (7)
1. a kind of radar target detection method based on generalized Pareto distribution clutter statistical modeling, it is characterised in that including following
Step:
The first step defines and initializes population, and method is:
1.1 define population G:
Population is the set being made of a group particle, that is, parameter to be estimated, and population is defined as
G={ pi=(σi,ki),vi=(δ σi,δki)；I=1,2 ..., I } (2)
In formula, I is the particle number in G, piFor the position feature of i-th of particle in G, σiFor the scale ginseng of i-th of particle in G
Number, kiIndicate the form parameter of i-th of particle in G；viFor the velocity characteristic of i-th of particle in G, δ σiFor i-th particle in G
Scale parameter σiVariable quantity, δ kiFor the form parameter k of i-th of particle in GiVariable quantity；
1.2 initialization particle position features:
The N number of clutter data sample observed from clutter area is denoted as z1,...,zn,...,zN, 1≤n≤N, n are integer, then
The mean value and variance of N number of clutter data sample be respectivelyWithBelieve in no priori
Under conditions of breath, useWithRespectively indicate the rough estimate evaluation of parameter σ and k, k
Indicate form parameter, σ indicates that i-th of 0 moment of particle position feature is initialized as by scale parameter, σ > 0
In formula, I is positive integer；The original state of 0 expression parameter of subscript i.e. 0 moment,For the position at i-th of 0 moment of particle in G
Feature,For the scale parameter at i-th of 0 moment of particle in G,For the form parameter at i-th of 0 moment of particle in G；Table
Show uniformly distributed function, interval limit a, upper limit b；"" indicate from uniformly distributed functionIn take at random
Number, i.e., take a number at random between section [a, b]；It indicatesIt is from uniformly distributed functionMiddle direct access, i.e., in sectionBetween take a number at random,For lower limit,For the upper limit；It indicatesIt is from uniformly distributed functionIn take at random
Number,For lower limit,For the upper limit；
1.3 initialization particle rapidity features:
For the velocity characteristic at i-th of 0 moment of particle in G,For the scale parameter variable quantity at i-th of 0 moment of particle in G,For the form parameter variable quantity at i-th of 0 moment of particle in G,It indicatesIt is from uniform point
Cloth functionIn the number that takes,It indicatesIt is from uniformly distributed functionIn the number that takes；
Second step enables the number of iterations variable t=0；
Third step seeks the cost function of particle when the t times iteration, and method is:
3.1 by the complex exponent distribution shifts of generalized Pareto distribution model be formula (9) shown in logarithmic form likelihood letter
Number, k ≠ 0, i.e.,
In formula, ln () is indicated using natural constant e as the logarithmic function at bottom, and L (z | k, σ) indicate to include unknown distribution parameter k and σ
Noise signal amplitude z likelihood function；
The maximal possibility estimation of parameter k and σ are obtained by the partial derivative of solution formula (9), are had at this time
3.2 cost functions according to shown in formula (10) and (11) building formula (12):
In formula, | | for the symbol that takes absolute value, approach T (σ, k) constantly to 0 by the minimum of the cost function, this mistake
Journey, which is equivalent to, is optimal formula (10) and the solution of formula (11)；
3.3 seek the corresponding fitness value of I particle in G, the I grain that I particle is obtained through the t times iteration by formula (12)
Son t group fitness value, is expressed as
4th step calculates the individual extreme value pbest of population in the t times iterationtWith global extremum gbestt, method is:
4.1 according toParticle corresponding with smallest particles fitness value in the t times iteration is found, i.e.,
In formula,Expression is first foundIn the smallest value, and find
The corresponding particle of this minimum value is expressed as parameter to (σ ', k ')；
4.2 according toFind out 0~t
Make the smallest particle of adaptive value in secondary all iterative process, as preceding t iteration global extremum gbestt, i.e.,
(σ*,k*) it is the corresponding particle of preceding t minimum adaptive value；
5th step, enables t=t+1；
6th step, according to the individual extreme value pbest of acquisitiontWith global extremum gbestt, update G in I particle position feature and
Velocity characteristic；
7th step, judges whether t is equal to maximum number of iterations tmax, if satisfied, by global extremum gbestt, namely (σ*,k*) make
It is parameter to the final estimated result of (σ, k), executes the 8th step；Otherwise, turn third step；
8th step utilizes (σ*,k*) Radar Targets'Detection is carried out, method is:
8.1 utilize (σ*,k*) reconstruct probability density function corresponding with generalized Pareto distribution modelI.e.
In formula,It indicates by (σ*,k*) reconstruct the obtained approximate function about independent variable z；
8.2 given target detection false alarm rate Pf, detection threshold th is asked according to formula (18)
8.3 target detections, method are:
8.3.1 it is observed in real time by radar, obtains J observation data, J >=1 enables j=1；
8.3.2 judge practical j-th of the observation data y obtained of radarjWhether target is had, and method is:
If yj>=th, the conclusion of output " j-th of observation data has target "；If yj< th, " j-th of observation data is without mesh for output
The conclusion of mark "；
8.3.3 determine whether j is less than J, if satisfied, enabling j=j+1, turn 8.3.2；Otherwise, the processing of radar real-time observed data is indicated
Terminate, completes target detection.
2. the radar target detection method as described in claim 1 based on generalized Pareto distribution clutter statistical modeling, special
Sign is that the I takes 200~500.
3. the radar target detection method as described in claim 1 based on generalized Pareto distribution clutter statistical modeling, special
Sign is that the method that the corresponding fitness value of I particle in G is sought described in 3.3 steps is: successively by I grain in G in the t times iteration
Son position feature substitute into formula (12), obtain the cost function value of the t times iteration of I particle, as I particle the t times change
The fitness value in generation；For i-th of particle in G, specific practice is by the position feature in its t times iterationI.e.Ginseng
Several pairs of substitution formula (12) calculateAnd enable the particle fitness value of i-th of particle, the t times iteration
4. the radar target detection method as described in claim 1 based on generalized Pareto distribution clutter statistical modeling, special
Sign is described in the 6th step in update G the position feature of I particle and the method for velocity characteristic is:
6.1 enable i=1；
The position feature and velocity characteristic of 6.2 i-th particle are updated by formula (15) and formula (16):
Wherein, wt-1=0.9-0.5 (t-1)/tmax, be t-1 times when Inertia weight factor, tmaxFor maximum number of iterations, it is positive
Integer；Rand indicates the uniform random number between [0,1]；c1With c2It is positive integer for Studying factors；
6.3 enable i=i+1；
6.4 determine whether i≤I is true, if so, turn 6.2；Otherwise, indicate to have updated in G the position feature of I particle with
Velocity characteristic terminates.
5. the radar target detection method as claimed in claim 4 based on generalized Pareto distribution clutter statistical modeling, special
Sign is the tmaxTake 100~200；c1With c2It is taken as 2.
6. the radar target detection method as described in claim 1 based on generalized Pareto distribution clutter statistical modeling, special
Sign is the PfTake 10-4~10-2。
7. the radar target detection method as described in claim 1 based on generalized Pareto distribution clutter statistical modeling, special
Sign is described to ask detection threshold th to pass through newton-Ke Ci i.e. Newton-Cotes Numerical Integral Formulas formula (18) to solve
It calculates.
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