CN107064893A - Pareto distribution with wide scope method for parameter estimation based on logarithmic moment - Google Patents
Pareto distribution with wide scope method for parameter estimation based on logarithmic moment Download PDFInfo
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- CN107064893A CN107064893A CN201611245597.1A CN201611245597A CN107064893A CN 107064893 A CN107064893 A CN 107064893A CN 201611245597 A CN201611245597 A CN 201611245597A CN 107064893 A CN107064893 A CN 107064893A
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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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/414—Discriminating targets with respect to background clutter
Abstract
The invention discloses a kind of Pareto distribution with wide scope method for parameter estimation based on logarithmic moment, the problem of mainly solving the estimated accuracy difference and low execution efficiency of existing method for parameter estimation.Its technical scheme is：1 obtains sea clutter data sample by surface monitoring radar；2 are normalized the clutter data sample got by clutter power；3 calculate inspection estimator of the data in log-domain using the clutter data sample after normalization；4 utilizations examine estimator to calculate distributed constant.The present invention improves the estimated accuracy of traditional Pareto estimation of distribution parameters method, and calculating speed is fast, can adapt to the requirement of radar system real time signal processing, the target detection that can be used under sea clutter background.
Description
Technical field
The invention belongs to signal processing technology field, and in particular to a kind of Pareto distribution with wide scope method for parameter estimation, can
For the target detection under sea clutter background.
Background technology
Target detection technique under sea clutter background is a vital research direction in radar application technology, in army
Thing and civil area have been used widely.And the accurate analysis for sea clutter statistical property is target under sea clutter background
Can detection technique obtain the key factor of good result.Therefore, provide suitable model and carried out for its model parameter accurate
Really estimation turns into the major issue that we need to solve.
With the raising of modern radar system range resolution, there is conventional low resolution radar system and not had in radar return
Some statistical properties, the hangover for being usually expressed as its echo envelope is elongated, the characteristics of exceptional value becomes many.And Pareto distribution with wide scope
As one kind of complex Gaussian model, achieved well in the power distribution fitting for the low grazing angle sea clutter of high-resolution
Effect.Therefore critical role is occupied in the research of sea clutter statistical property.And in the target detection under sea clutter background, it is miscellaneous
The estimation quality of wave pattern parameter has a significant impact for target detection effect again, therefore is provided under the clutter data trailed again
The distributed constant of broad sense Pareto has important Research Significance.
In recent years, method for parameter estimation of the Many researchers to Pareto distribution with wide scope, it is proposed that some are based on specific bar
Pareto distribution with wide scope parameter estimation theories under part.
Document " Castillo, E., Hadi, A.S., 1997.Fitting the generalized Pareto
Pareto distribution with wide scope is provided in distribution to data.J.Amer.Statist.Assoc.92,1609-1620. "
Moments estimation and maximum Likelihood, estimated respectively according to sample moment and likelihood function for parameter, still
Because moments estimation is easily influenceed by sample size and abnormal data in itself, its estimated accuracy is difficult to ensure that.And maximum likelihood
Although the estimated accuracy of estimation disclosure satisfy that requirement, but Algorithms T-cbmplexity is high, therefore Project Realization is more difficult.
Document " Arnold, B.C., Press, S.J., 1989.Bayesian estimation and prediction
For Pareto data.J.Amer.Statist.Assoc.84,1079-1084. " give the broad sense handkerchief based on prior information
Tired support estimation of distribution parameters method, but its calculating is relative complex, and estimation effect is by the shadow of prior information order of accuarcy
Ring, using more inconvenient.
The content of the invention
It is an object of the invention to propose a kind of Pareto distribution with wide scope method for parameter estimation based on logarithmic moment, to improve
Estimated accuracy and execution efficiency, and then lift the performance of target detection under follow-up sea clutter background.
Realizing the technical scheme of the object of the invention is：By the way that clutter sample power is normalized, obtain its form parameter and
Determination relation between scale parameter, then carries out the estimation of Pareto distribution with wide scope parameter, in fact using the logarithmic moment of sample
Existing step includes as follows：
(1) launch pulse signal using radar transmitter, returning by surface scattering formation is received using radar receiver
Echo sequence in wave number evidence, each resolution cell of the echo data is
X=[x1,x2,…xi,…xN],
Wherein xiRepresent i-th of echo data, i=1,2 ..., N, N represent umber of pulse；
(2) power information of current clutter data is obtained, and it is normalized by power, is obtained after power normalization
Sea clutter data：
Y=[y1,y2,…yi,…yN],
Wherein yiIt is Y i-th of data,WhereinIt is clutter sample power PXI-th of data,
It is clutter sample power PXAverage value.
(3) the single order logarithmic moment estimation amount κ of the sea clutter data Y after power normalization is calculated1, second order logarithmic moment estimation amount
κ2With average κ3：
(4) the single order logarithmic moment estimation amount κ of sea clutter data Y after power normalization is utilized1, second order logarithmic moment estimation amount κ2
With average κ3Calculate the estimate of form parameterWith the estimate of scale parameter
The present invention realizes the estimation of Pareto distribution with wide scope parameter by using the sample information in log-domain, and existing
Technology, which is compared, has advantages below：
1) compared to moment estimation method, the exponent number of moments estimation is reduced, the precision of parameter Estimation is improved；
2) compared to maximum Likelihood, the present invention has analytical expression, without being obtained by way of search
Its optimal solution, arithmetic speed is fast, can adapt to the requirement of radar system real time signal processing；
Brief description of the drawings
Fig. 1 is implementation process figure of the invention；
Fig. 2 is the estimation effect contrast under different parameters value using two kinds of methods of estimation of the invention and existing；
Fig. 3 is the estimation effect contrast under different sample sizes using two kinds of methods of estimation of the invention and existing.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings：
Reference picture 1, step is as follows for of the invention realizing：
Step 1, launch pulse signal using radar transmitter, received using radar receiver by surface scattering formation
Echo data.
Echo data, which is one, includes pulse dimension, apart from the three-dimensional matrice of peacekeeping ripple position dimension, each apart from peacekeeping ripple position dimension
It is X to constitute the echo sequence in a resolution cell, each resolution cell：
X=[x1,x2,...,xi,...,xN]
Wherein xiI-th of echo data is represented, N represents umber of pulse.
Step 2, the power information of current clutter data is obtained, and it is normalized by power, power normalizing is obtained
Clutter data sample Y after change.
2a) calculate current sample data X power PX：
PX=| X |2=[| x1|2,|x2|2,…|xi|2,…|xn|2]
Wherein xiRepresent i-th of echo data, i=1,2 ..., N, N represent umber of pulse, PXObey Pareto distribution with wide scope,
Pareto distribution with wide scope definition is as follows：
Wherein, σ represents scale parameter, and k represents form parameter；
2b) calculate current clutter data sample power PXMean power
Wherein pXiRepresent PXI-th of data；
2c) according to mean powerWith current clutter sample data X power PX, obtain the clutter number after power normalization
According to sample Y：
Wherein,Represent i-th of data of the clutter data sample Y after power normalization.
Step 3, the single order logarithmic moment estimation amount κ of the sea clutter data Y after power normalization is calculated1, second order logarithmic moment estimates
Measure κ2With average κ3：
Step 4, the single order logarithmic moment estimation amount κ of the sea clutter data Y after power normalization is utilized1, second order logarithmic moment estimates
Measure κ2With average κ3, calculate the estimate of form parameterWith the estimate of scale parameter
The effect of the present invention can be further illustrated by following emulation experiment：
1. simulation parameter
The broad sense Pareto data that emulation experiment is produced using emulation.
2. emulation experiment content
The present invention, moments estimation and maximum Likelihood are respectively adopted in emulation experiment for the handkerchief that emulation is produced to tire out
Ask distributed data to carry out the estimation of parameter, the estimation effect of three kinds of distinct methods is compared by relative error and root-mean-square error.
Experiment 1, the handkerchief under different shape parameter and scale parameter is produced using the gprnd functions in matlab softwares respectively
Tired support distributed data, test sample quantity is 1000, respectively using the present invention, moments estimation and maximal possibility estimation for emulation
The form parameter and scale parameter of the Pareto distributed data of generation estimated, by compare parameter Estimation relative error and
Experiment under the effect of the more different methods of estimation of root-mean-square error RMSE, each parameter value is repeated 2000 times, is finally provided
The average value of 2000 experiment relative errors and root-mean-square error RMSE, as a result such as Fig. 2, wherein,
Fig. 2 (a) is the change curve of three kinds of methods of relative error estimated with to(for) scale parameter with scale parameter value,
Wherein abscissa represents scale parameter value, and ordinate represents relative error
Fig. 2 (b) is the change curve of three kinds of methods of relative error estimated with to(for) form parameter with shape parameter value,
Wherein abscissa represents form parameter value, and ordinate represents relative error.
Fig. 2 (c) is the change of estimated with root-mean-square error RMSE three kinds of methods to(for) scale parameter with scale parameter value
Change curve, wherein abscissa represents scale parameter value, and ordinate represents root-mean-square error RMSE.
Fig. 2 (d) is the change of estimated with root-mean-square error RMSE three kinds of methods to(for) form parameter with shape parameter value
Change curve, wherein abscissa represents form parameter value, and ordinate represents root-mean-square error RMSE.
Experiment 2, the Pareto distribution number under different sample sizes is produced using the gprnd functions in matlab softwares respectively
According to form parameter value is 0.4, and scale parameter value is 0.6, respectively using the present invention, moments estimation and maximal possibility estimation
The form parameter and scale parameter of the Pareto distributed data produced for emulation are estimated, by the phase for comparing parameter Estimation
To error and the effect of the more different methods of estimation of root-mean-square error RMSE, the experiment under each sample size is repeated 2000 times,
It is final to provide 2000 experiment relative errors and root-mean-square error RMSE average value.As a result such as Fig. 3, wherein,
Fig. 3 (a) is the change curve of three kinds of methods of relative error estimated with to(for) scale parameter with sample size, wherein
Abscissa represents sample size, and ordinate represents relative error.
Fig. 3 (b) is the change curve of three kinds of methods of relative error estimated with to(for) form parameter with sample size, wherein
Abscissa represents sample size, and ordinate represents relative error.
Fig. 3 (c) is bent with the change of sample size for the root-mean-square error RMSE estimated with three kinds of methods for scale parameter
Line, wherein abscissa represent sample size, and ordinate represents root-mean-square error RMSE.
Fig. 3 (d) is bent with the change of sample size for the root-mean-square error RMSE estimated with three kinds of methods for form parameter
Line, wherein abscissa represent sample size, and ordinate represents root-mean-square error RMSE.
From Fig. 2 and Fig. 3 as can be seen that the obtained Parameter Estimation Precision of the present invention higher than moments estimation and close to it is maximum seemingly
So estimation.Show the Pareto distribution with wide scope method for parameter estimation proposed by the present invention based on logarithmic moment, can be estimated by reduction
The exponent number of meter, improves the estimated accuracy of Pareto distributed constant, and calculating speed is fast, disclosure satisfy that the real-time place of radar system
Reason is required, is conducive to the raising of target detection performance under follow-up sea clutter background.
Claims (2)
1. a kind of Pareto distribution with wide scope method for parameter estimation based on logarithmic moment, comprises the following steps：
(1) launch pulse signal using radar transmitter, the number of echoes by surface scattering formation is received using radar receiver
According to the echo sequence in each resolution cell of the echo data is
X=[x1,x2,…xi,…xN],
Wherein xiRepresent i-th of echo data, i=1,2 ..., N, N represent umber of pulse；
(2) power information of current clutter data is obtained, and it is normalized by power, the sea after power normalization is obtained
Clutter data：
Y=[y1,y2,…yi,…yN],
Wherein yiIt is Y i-th of data, It is clutter sample power PXI-th of data,It is clutter sample
This power PXAverage value.
(3) the single order logarithmic moment estimation amount κ of the sea clutter data Y after power normalization is calculated1, second order logarithmic moment estimation amount κ2With
Average κ3：
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(4) the single order logarithmic moment estimation amount κ of sea clutter data Y after power normalization is utilized1, second order logarithmic moment estimation amount κ2With it is equal
Value κ3Calculate the estimate of form parameterWith the estimate of scale parameter
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2. the sea clutter data after power normalization the method for claim 1, wherein are obtained in step (2), by following
Step is carried out：
2a) calculate current clutter sample data X power PX：
PX=| X |2=[| x1|2,|x2|2,…|xi|2,…|xn|2],
Wherein xiRepresent i-th of echo data, i=1,2 ..., N, N represent umber of pulse；
2b) calculate current clutter data sample power PXMean power
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2c) according to mean powerWith current clutter sample data X power PX, obtain the clutter data sample after power normalization
This Y：
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| CN107741581A (en) * | 2017-09-22 | 2018-02-27 | 西安电子科技大学 | Based on the Pareto distribution with wide scope method for parameter estimation for blocking square |
| CN109388885A (en) * | 2018-10-09 | 2019-02-26 | 上海理工大学 | A kind of dynamic characteristic coefficients of seals value acquisition method based on moments estimation method |
| CN109541566A (en) * | 2018-12-20 | 2019-03-29 | 西安电子科技大学 | K Distribution Sea Clutter method for parameter estimation based on dual fractional order square |
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| CN109541566A (en) * | 2018-12-20 | 2019-03-29 | 西安电子科技大学 | K Distribution Sea Clutter method for parameter estimation based on dual fractional order square |
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