CN107064893B - Pareto distribution with wide scope method for parameter estimation based on logarithmic moment - Google Patents
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- G—PHYSICS
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- 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
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Abstract
The invention discloses a kind of Pareto distribution with wide scope method for parameter estimation based on logarithmic moment, mainly solves the problems, such as that the estimated accuracy difference of existing method for parameter estimation and execution efficiency are low.Its technical solution is: 1 obtains sea clutter data sample by surface monitoring radar；The 2 clutter data samples that will acquire are normalized by clutter power；3 calculate inspection estimator of the data in log-domain using the clutter data sample after normalization；4 calculate distribution parameter using inspection estimator.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, can be used for the target detection under sea clutter background.
Description
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a generalized pareto distribution parameter estimation method which can be used for target detection under a sea clutter background.
Background
The target detection technology under the background of sea clutter is a crucial research direction in radar application technology, and has been widely applied in military and civil fields. The accurate analysis of the statistical characteristics of the sea clutter is an important factor for determining whether the target detection technology can obtain good effect under the background of the sea clutter. Therefore, it is an important problem that we need to solve to provide a suitable model and accurately estimate the model parameters.
With the improvement of the distance resolution of a modern radar system, radar echoes have statistical characteristics which are not possessed by the traditional low-resolution radar system, and the characteristics that the tailing of the echo envelope is lengthened and abnormal values are increased are generally shown. The generalized pareto distribution is used as one of the composite Gaussian models, and a good effect is achieved on the power distribution fitting of the high-resolution low-friction ground angle sea clutter. Therefore, the method plays an important role in the research of the statistical characteristics of the sea clutter. In the target detection under the background of the sea clutter, the estimation quality of the clutter model parameters has great influence on the target detection effect, so that the distribution parameters of the generalized pareto given under the clutter data with heavy tailing have important research significance.
In recent years, many researchers have proposed some generalized pareto distribution parameter estimation theories based on specific conditions for generalized pareto distribution parameter estimation methods.
The moment estimation and maximum likelihood estimation method of generalized Pareto distribution are given in documents of "Castillo, e., Hadi, a.s.,1997.Fitting the generated Pareto distribution to data.j.am.statest.assoc.92, 1609-1620", and estimates parameters according to sample moments and likelihood functions respectively, but since the moment estimation itself is easily affected by the number of samples and abnormal data, the estimation accuracy is difficult to guarantee. The estimation accuracy of the maximum likelihood estimation can meet the requirement, but the algorithm time complexity is high, so the engineering realization is difficult.
The document "Arnold, B.C., Press, S.J.,1989.Bayesian estimation and prediction for Pareto data.J.Amer. Statist.Assoc.84, 1079-1084" provides a generalized Pareto distribution parameter estimation method based on prior information, but the calculation is relatively complex, the estimation effect is influenced by the accuracy degree of the prior information, and the application is inconvenient.
Disclosure of Invention
The invention aims to provide a generalized pareto distribution parameter estimation method based on logarithm moments, so that estimation accuracy and execution efficiency are improved, and performance of target detection under a subsequent sea clutter background is improved.
The technical scheme for realizing the purpose of the invention is as follows: the clutter sample power is normalized to obtain the definite relation between the shape parameter and the scale parameter, and then the logarithm moment of the sample is used for estimating the generalized pareto distribution parameter, and the method comprises the following implementation steps:
(1) transmitting pulse signals by using a radar transmitter, and receiving echo data formed by sea surface scattering by using a radar receiver, wherein the echo sequence in each resolution unit of the echo data is
X＝[x1,x2,…xi,…xN]，
Wherein xiRepresents the ith echo data, i is 1, 2.., N represents the number of pulses;
(2) acquiring power information of current clutter data, and normalizing the power information according to power to obtain sea clutter data with normalized power:
Y＝[y1,y2,…yi,…yN]，
wherein y isiIs the ith data of the Y, and,whereinIs the clutter sample power PXThe (c) th data of (a),is the clutter sample power PXAverage value of (a).
(3) Calculating a first-order logarithmic moment estimator kappa of the sea clutter data Y after power normalization1Second order logarithmic moment estimator k2And mean value k3：
(4) Sea clutter number normalized by powerFirst order logarithmic moment estimator of data Y kappa1Second order logarithmic moment estimator k2And mean value k3Calculating an estimate of a shape parameterAnd an estimate of a scale parameter
The method realizes the estimation of the generalized pareto distribution parameters by utilizing the sample information in the logarithmic domain, and has the following advantages compared with the prior art:
1) compared with a moment estimation method, the order of moment estimation is reduced, and the precision of parameter estimation is improved;
2) compared with a maximum likelihood estimation method, the method has an analytic expression, does not need to obtain the optimal solution in a searching mode, has high operation speed, and can meet the requirement of real-time signal processing of a radar system;
drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a comparison of the estimation effects of the present invention and the existing two estimation methods under different parameter values;
fig. 3 is a comparison of the estimation effect of the present invention and the estimation effect of the existing two estimation methods under different sample numbers.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
referring to fig. 1, the implementation steps of the invention are as follows:
step 1, transmitting a pulse signal by using a radar transmitter, and receiving echo data formed by scattering through the sea surface by using a radar receiver.
The echo data is a three-dimensional matrix comprising a pulse dimension, a distance dimension and a wave position dimension, each distance dimension and wave position dimension form a resolution unit, and the echo sequence in each resolution unit is X:
X＝[x1,x2,...,xi,...,xN]
wherein xiIndicates the ith echo data and N indicates the number of pulses.
And 2, acquiring power information of the current clutter data, and normalizing the power information according to the power to obtain a clutter data sample Y with normalized power.
2a) Calculating the power P of the current sample data XX：
PX＝|X|2＝[|x1|2,|x2|2,…|xi|2,…|xn|2]
Wherein xiDenotes the ith echo data, i 1, 2., N denotes the number of pulses, PXFollowing the generalized pareto distribution, the generalized pareto distribution is defined as follows:
wherein σ represents a scale parameter and k represents a shape parameter;
2b) calculating the power P of the current clutter data sampleXAverage power of
Wherein p isXiRepresents PXThe ith data of (1);
2c) according to average powerAnd current clutter sample data XPower PXObtaining a clutter data sample Y after power normalization:
wherein,and the ith data of the clutter data sample Y after power normalization is represented.
Step 3, calculating a first-order logarithmic moment estimator kappa of the sea clutter data Y after power normalization1Second order logarithmic moment estimator k2And mean value k3：
Step 4, estimating quantity kappa by using first-order logarithmic moment of sea clutter data Y after power normalization1Second order logarithmic moment estimator k2And mean value k3Calculating an estimated value of the shape parameterAnd an estimate of a scale parameter
The effect of the invention can be further illustrated by the following simulation experiment:
1. simulation parameters
The simulation experiment adopts generalized pareto data generated by simulation.
2. Content of simulation experiment
In a simulation experiment, parameters of pareto distribution data generated by simulation are estimated by respectively adopting the method, the moment estimation method and the maximum likelihood estimation method, and estimation effects of three different methods are compared through relative errors and root mean square errors.
Experiment 1, using the gprnd function in matlab software to respectively generate pareto distribution data under different shape parameters and scale parameters, the number of test samples is 1000, using the method, moment estimation and maximum likelihood estimation to respectively estimate the shape parameters and the scale parameters of the pareto distribution data generated by simulation, comparing the effects of different estimation methods by comparing the relative error of parameter estimation and the root mean square error RMSE, repeating the experiment under each parameter value for 2000 times, finally providing the average value of the relative error and the root mean square error RMSE of the experiment for 2000 times, wherein the result is shown in fig. 2,
FIG. 2(a) is a graph showing the variation of the relative error of the scale parameter estimation with the scale parameter value using three methods, in which the abscissa represents the scale parameter value and the ordinate represents the relative error
Fig. 2(b) is a graph of the change of the relative error of the shape parameter estimation with the shape parameter value using three methods, in which the abscissa represents the shape parameter value and the ordinate represents the relative error.
Fig. 2(c) is a graph of the variation of the root mean square error RMSE estimated for the scale parameters with the scale parameter values using three methods, where the abscissa represents the scale parameter values and the ordinate represents the root mean square error RMSE.
Fig. 2(d) is a graph of the variation of the root mean square error RMSE estimated for the shape parameters with the shape parameters using three methods, where the abscissa represents the shape parameter value and the ordinate represents the root mean square error RMSE.
Experiment 2, the gprnd function in matlab software is used for respectively generating pareto distribution data under different sample numbers, the shape parameter value is 0.4, the scale parameter value is 0.6, the shape parameter and the scale parameter of the pareto distribution data generated by simulation are respectively estimated by using the method, the moment estimation and the maximum likelihood estimation, the effects of different estimation methods are compared by comparing the relative error of the parameter estimation and the root mean square error RMSE, the experiment under each sample number is repeated for 2000 times, and finally the average value of the relative error of the experiment and the root mean square error RMSE is given out for 2000 times. The results are shown in fig. 3, in which,
fig. 3(a) is a graph of relative error versus number of samples for scale parameter estimation using three methods, where the abscissa represents the number of samples and the ordinate represents the relative error.
Fig. 3(b) is a graph of relative error with the number of samples for shape parameter estimation using three methods, where the abscissa represents the number of samples and the ordinate represents the relative error.
FIG. 3(c) is a plot of the estimated root mean square error RMSE versus the number of samples for the scale parameters using three methods, where the abscissa represents the number of samples and the ordinate represents the root mean square error RMSE.
FIG. 3(d) is a plot of the estimated root mean square error RMSE versus the number of samples for the shape parameters using three methods, where the abscissa represents the number of samples and the ordinate represents the root mean square error RMSE.
As can be seen from fig. 2 and 3, the parameter estimation accuracy obtained by the present invention is higher than the moment estimation and close to the maximum likelihood estimation. The generalized pareto distribution parameter estimation method based on the logarithm moment can improve the estimation precision of the pareto distribution parameter by reducing the estimation order, has high calculation speed, can meet the real-time processing requirement of a radar system, and is beneficial to the improvement of target detection performance under the subsequent sea clutter background.
Claims (2)
1. A generalized pareto distribution parameter estimation method based on logarithmic moments comprises the following steps:
(1) transmitting pulse signals by using a radar transmitter, and receiving echo data formed by sea surface scattering by using a radar receiver, wherein the echo sequence in each resolution unit of the echo data is
X＝[x1,x2,…xi,…xN]，
Wherein xiRepresents the ith echo data, i is 1, 2.., N represents the number of pulses;
(2) acquiring power information of current clutter data, and normalizing the power information according to power to obtain sea clutter data with normalized power:
Y＝[y1,y2,…yi,…yN]，
wherein y isiIs the ith data of the Y, and, is the clutter sample power PXThe (c) th data of (a),is the clutter sample power PXAverage value of (d);
(3) calculating a first-order logarithmic moment estimator kappa of the sea clutter data Y after power normalization1Second order logarithmic moment estimator k2And mean value k3：
(4) First-order log-moment estimation of sea clutter data Y after power normalizationQuantity k1Second order logarithmic moment estimator k2And mean value k3Calculating an estimate of a shape parameterAnd an estimate of a scale parameter
2. The method of claim 1, wherein the step (2) of obtaining the power-normalized sea clutter data is performed by:
2a) calculating power P of current clutter sample data XX：
PX＝|X|2＝[|x1|2,|x2|2,…|xi|2,…|xn|2]，
Wherein xiRepresents the ith echo data, i is 1, 2.., N represents the number of pulses;
2b) calculating the power P of the current clutter data sampleXAverage power of
WhereinRepresents PXThe ith data of (1);
2c) according to average powerAnd the power P of the current clutter sample data XXObtaining a clutter data sample Y after power normalization:
wherein,and the ith data of the clutter data sample Y after power normalization is represented.
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| CN107607913B (en) * | 2017-08-25 | 2019-12-24 | 西安电子科技大学 | Sea clutter Pareto distribution parameter estimation method based on logarithm cumulant |
| CN107741581B (en) * | 2017-09-22 | 2020-10-09 | 西安电子科技大学 | Generalized pareto distribution parameter estimation method based on truncation moment |
| 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 |
| CN109541566B (en) * | 2018-12-20 | 2023-02-10 | 西安电子科技大学 | K-distribution sea clutter parameter estimation method based on double fractional order moment |
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