CN113466811A - Three-point parameter estimation method of generalized pareto sea clutter amplitude model - Google Patents

Three-point parameter estimation method of generalized pareto sea clutter amplitude model Download PDF

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CN113466811A
CN113466811A CN202110511457.9A CN202110511457A CN113466811A CN 113466811 A CN113466811 A CN 113466811A CN 202110511457 A CN202110511457 A CN 202110511457A CN 113466811 A CN113466811 A CN 113466811A
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amplitude
sea clutter
cumulative probability
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generalized pareto
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CN113466811B (en
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水鹏朗
田超
封天
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Xidian University
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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
    • 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
    • G01S7/411—Identification of targets based on measurements of radar reflectivity
    • G01S7/412—Identification of targets based on measurements of radar reflectivity based on a comparison between measured values and known or stored values
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention discloses a three-quantile point parameter estimation method of a generalized pareto sea clutter amplitude model, which comprises the following steps: obtaining sea clutter pulse echo data and performing modulus value increasing sequencing; acquiring a second cumulative probability distribution function of the sea clutter model with generalized pareto distribution; setting a first cumulative probability and a second cumulative probability according to a second cumulative distribution function; constructing a function expression of the third cumulative probability and the shape parameter; obtaining estimated values of a first amplitude quantile point and a second amplitude quantile point by using a module value increasing sequence of the sea clutter echo pulse; obtaining a shape parameter estimation value of the generalized pareto distribution amplitude model; and obtaining a scale parameter estimation value of the generalized pareto sea clutter amplitude model according to the shape parameter estimation value. According to the method, parameter estimation is carried out by utilizing the quantile point information, the influence of abnormal values with high power in original data on parameter estimation performance can be effectively reduced, and the target detection precision under the sea clutter background is further improved.

Description

Three-point parameter estimation method of generalized pareto sea clutter amplitude model
Technical Field
The invention belongs to the technical field of radar target detection, and particularly relates to a three-point parameter estimation method of a generalized pareto sea clutter amplitude model, which can be used for target detection under the sea clutter condition.
Background
In the sea clutter target detection development process, the fit precision of the sea clutter simulation model and the actual sea clutter distribution characteristic is an important consideration premise for building the sea clutter simulation model. The amplitude distribution information of the sea clutter can accurately describe the echo statistical characteristics of the sea clutter, and the design of the optimal detector under the background of the sea clutter depends on the parameters of the amplitude model of the sea clutter. The amplitude model of the sea clutter has close relation with meteorological conditions and radar resolution.
When the radar resolution unit is large, the radar resolution is low, the complex Gaussian model can be used for describing the amplitude characteristic of the sea clutter, and the amplitude model of the sea clutter is usually Rayleigh distribution. However, as the resolution of radar is continuously improved, the conventional complex gaussian model cannot meet the requirement of accurately describing the characteristics of the sea clutter. For the radar with low ground-friction angle and high resolution, compared with a Rayleigh distribution model, the amplitude distribution of the sea clutter has longer trailing and presents stronger non-Gaussian property, and at the moment, the non-Gaussian model is needed to be adopted to describe the amplitude distribution of the sea clutter. The complex gaussian model is a widely used sea clutter model that describes the sea clutter amplitude distribution as the product of a slowly varying positive texture component and a rapidly varying complex gaussian speckle component. For the complex Gaussian model, in the sea clutter detection time period, the speckle component is approximately constant, and the statistical characteristic is mainly influenced by the texture component. When the texture component conforms to the inverse gamma distribution, the sea clutter amplitude model conforms to the generalized pareto distribution.
The maximum likelihood estimation can realize parameter estimation of a generalized pareto sea clutter amplitude model, but the estimated parameter characteristic is unstable. The document "BALLERI A, NEHORAI A, and WANG J. maximum likelihood estimation for compound-Gaussian filter with inverse Gamma texture [ J ]. IEEE Transactions on Aerospace and Electronic Systems,2007,43(2): 775-. However, the method does not consider the influence of the abnormal samples on the clutter parameter estimation, and for real sea clutter data, the samples often contain a small number of high-power abnormal values, which greatly reduces the maximum likelihood estimation performance and the accuracy.
The document "P-L.Shu and M.Liu," Subband adaptive GLRT-LTD for well moving targets in the sea catcher, "IEEE Trans. Aerosp. Electron. Syst.,52(1): 423: 437, 2016" proposes a method for estimating the double-locus when the accumulation probability of the sample is 0.5 and 0.75, and the fixed double-locus estimation has insufficient accuracy of the result due to the fixed estimation point.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a three-quantile parameter estimation method of a generalized pareto sea clutter amplitude model. The technical problem to be solved by the invention is realized by the following technical scheme:
the invention provides a three-quantile point parameter estimation method of a generalized pareto sea clutter amplitude model, which comprises the following steps:
s1: obtaining sea clutter pulse echo data, performing modulus value increasing sequencing, and generating a modulus value increasing sequence of sea clutter echo pulses;
s2: acquiring a second cumulative probability distribution function of the sea clutter model with generalized pareto distribution;
s3: setting a first cumulative probability and a second cumulative probability according to the second cumulative distribution function;
s4: constructing a function expression of the third cumulative probability and the shape parameter;
s5: obtaining estimated values of a first amplitude quantile point and a second amplitude quantile point by using a module value increasing sequence of the sea clutter echo pulse;
s6: obtaining a shape parameter estimation value of the generalized pareto distribution amplitude model according to the estimation values of the first amplitude quantile point and the second amplitude quantile point;
s7: and obtaining a scale parameter estimation value of the generalized pareto sea clutter amplitude model according to the shape parameter estimation value.
In an embodiment of the present invention, the S2 includes:
s21: obtaining an amplitude probability density function f (r; mu, v) of a sea clutter model with generalized pareto distribution:
Figure BDA0003060450380000031
wherein r represents a sea clutter amplitude of the generalized pareto sea clutter amplitude model, μ represents a scale parameter of the generalized pareto sea clutter amplitude model, and v represents a shape parameter of the generalized pareto sea clutter amplitude model;
s22: obtaining a first cumulative probability distribution function F (r; mu, gamma) of the generalized pareto sea clutter amplitude model according to the amplitude probability density function:
Figure BDA0003060450380000032
s23: obtaining a second cumulative distribution function F (r; 1, v) of the generalized pareto sea clutter amplitude model from the first cumulative distribution function F (r; mu, v):
Figure BDA0003060450380000033
in an embodiment of the present invention, the S3 includes:
obtaining expressions of a first cumulative probability a and a second cumulative probability β according to the expression of the second cumulative distribution function F (r; 1, v):
α＝p(r≤rα)＝F(rα；1,v)
β＝p(r≤rβ)＝F(rβ；1,v)
wherein, alpha is more than 0.1 and beta is more than 1, rαIs a first amplitude quantile point, r, corresponding to a first cumulative probability alphaβAnd a second amplitude quantile corresponding to the second cumulative probability beta.
In an embodiment of the present invention, the S4 includes:
s41: according to an empirical formula of estimation errors, a third amplitude quantile point r is obtainedζThe estimation error of (d) is expressed as:
Figure BDA0003060450380000041
wherein σζRepresents a third amplitude quantile point rζμ is a scale parameter, v is a shape parameter, and ζ represents a third cumulative probability;
s42: setting the shape parameter v between the intervals [1,30], and traversing at intervals of 0.01 to obtain a plurality of shape parameters gamma;
s43: setting the third cumulative probability zeta between the intervals [0.1 and 0.99], traversing the values at intervals of 0.01, and obtaining a plurality of values of the third cumulative probability zeta;
s44: for each shape parameter γ obtained in step S42, a third amplitude quantile r is assigned according to the formula in S52ζCalculating the estimation error to obtain the optimal third cumulative probability corresponding to the parameters with different shapes;
s45: fitting the optimal third cumulative probabilities corresponding to the different shape parameters to obtain a function expression of the third cumulative probability and the shape parameters:
ζ＝0.6985exp(0.008101v)-0.4008exp(-0.7256v),v＞0
where γ represents a shape parameter and ζ represents a third cumulative probability.
In an embodiment of the present invention, the S5 includes:
obtaining estimated values of the first amplitude quantile point and the second amplitude quantile point by using the module value increasing sequence of the sea clutter echo pulse obtained in the step S1:
Figure BDA0003060450380000051
wherein,
Figure BDA0003060450380000052
is a first amplitude quantile point rαIs determined by the estimated value of (c),
Figure BDA0003060450380000053
is a second amplitude quantile point rβWhere round (N × α) represents an integer closest to N × α, and round (N × β) represents an integer closest to N × βAn integer number.
In an embodiment of the present invention, the S6 includes:
s61: given a positive number q greater than 1, the first and second cumulative probabilities α, β satisfy:
Figure BDA0003060450380000054
s62: calculating a second split point estimate
Figure BDA0003060450380000055
And a first-point estimate
Figure BDA0003060450380000056
Square of (d):
Figure BDA0003060450380000057
s63: obtaining a generalized pareto distribution shape parameter estimation algorithm expression according to the relation between the second cumulative distribution function F (r; 1, v) and the first cumulative probability alpha and the second cumulative probability beta:
Figure BDA0003060450380000058
s64: setting an intermediate parameter u, order
Figure BDA0003060450380000059
Obtaining shape parameter estimates
Figure BDA00030604503800000510
And the relation expression of the intermediate parameter u is:
Figure BDA00030604503800000511
s65: by iteratively solving shape parametersEstimated value
Figure BDA00030604503800000512
The expression is as follows:
Figure BDA0003060450380000061
wherein the initial value u0E (1, + ∞), k is the number of iterations.
In an embodiment of the present invention, the S7 includes:
s71: according to the third cumulative probability and the function expression of the shape parameter and the estimation value of the shape parameter
Figure BDA0003060450380000062
Calculating a third cumulative probability value ζ;
s72: using cumulative distribution function, third cumulative probability ζ and shape parameter estimate
Figure BDA0003060450380000063
Obtaining an estimate of the scale parameter mu
Figure BDA0003060450380000064
In an embodiment of the present invention, the S72 includes:
s721: calculating a third amplitude quantile point r corresponding to the third cumulative probability zetaζIs estimated value of
Figure BDA0003060450380000065
Figure BDA0003060450380000066
Wherein round (N × ζ) represents an integer closest to N × ζ;
s722: cumulative distribution function F (r) corresponding to third cumulative probability ζζ(ii) a Mu, gamma) to obtain an estimated value of the scale parameter
Figure BDA0003060450380000067
Expression (c):
Figure BDA0003060450380000068
another aspect of the present invention provides a storage medium having a computer program stored therein, where the computer program is configured to execute the steps of the method for estimating parameters of three-way points of the generalized pareto sea clutter amplitude model according to any of the above embodiments.
Yet another aspect of the present invention provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the method for estimating parameters of three-quantile points of the generalized pareto sea clutter amplitude model according to any one of the above embodiments.
Compared with the prior art, the invention has the beneficial effects that:
1. the trisection point parameter estimation method of the generalized pareto sea clutter amplitude model utilizes the trisection point information to carry out parameter estimation, can effectively reduce the influence of abnormal values with larger power in original data on parameter estimation performance, has higher abnormal data resistance compared with the existing moment estimation method, and further improves the target detection precision under the sea clutter background.
2. The invention relates to a trisection point parameter estimation method of a generalized pareto sea clutter amplitude model, which constructs a function expression of an accumulated probability value of scale parameter estimation and a shape parameter by using a theoretical formula, and can accurately realize the estimation of the scale parameter under the condition that the shape parameter is known. Meanwhile, compared with the estimation of the double-quantile, the method of the invention introduces a smaller estimation error of the third quantile and has better estimation performance on the scale parameter.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a flowchart of a three-split-point parameter estimation method of a generalized pareto sea clutter amplitude model according to an embodiment of the present invention;
FIG. 2a is a graph of relative RMS error comparisons for shape parameter estimation using an embodiment of the invention and two prior art methods;
FIG. 2b is a diagram of a comparison of relative root mean square errors of shape parameter estimates for a dual-split-site and a tri-split-site estimation method according to an embodiment of the present invention;
FIG. 2c is a graph of relative root mean square error comparison of scale parameter estimation using an embodiment of the present invention and two methods of the prior art;
FIG. 2d is a diagram of a comparison of relative root mean square errors of scale parameter estimates for a dual-split site and a tri-split site estimation method according to an embodiment of the present invention.
Detailed Description
To further illustrate the technical means and effects of the present invention for achieving the predetermined purpose, the following describes in detail a three-way point parameter estimation method of a generalized pareto sea clutter amplitude model according to the present invention with reference to the accompanying drawings and the detailed description.
The foregoing and other technical matters, features and effects of the present invention will be apparent from the following detailed description of the embodiments, which is to be read in connection with the accompanying drawings. The technical means and effects of the present invention adopted to achieve the predetermined purpose can be more deeply and specifically understood through the description of the specific embodiments, however, the attached drawings are provided for reference and description only and are not used for limiting the technical scheme of the present invention.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of additional identical elements in the article or device comprising the element.
In an actual radar working environment, target detection processing needs to be performed on radar echo data under different sea clutter backgrounds, and the design of a target detector is a key step of a target detection processing link. The detection statistics and the detection threshold of the target detector under different sea clutter backgrounds are closely related to two characteristic parameters of the sea clutter, namely a scale parameter and a shape parameter, and the accuracy and the stability of the two characteristic parameters of the sea clutter are important indexes for evaluating the detection performance of the target detector under the sea background. In other words, the sea clutter characteristic parameters (shape parameters and scale parameters) determine the selection of the detection threshold of the target detector, and the selection of the detection threshold directly affects the false alarm rate and further affects the target detection precision. The closer the sea clutter characteristic parameters are to the sea clutter true characteristic parameters, the higher the target detection precision is.
The embodiment of the invention aims to provide a three-position-point parameter estimation method for a generalized pareto sea clutter amplitude model, under the condition that sea clutter distributed in generalized pareto is met, the estimation on scale parameters and shape parameters of the clutter is more accurate, a target detector designed according to the scale parameters and the shape parameters obtained by the method provided by the embodiment of the invention has a better detection threshold, the control on the target detection false alarm rate is better, and the detection accuracy is higher.
Referring to fig. 1, fig. 1 is a flowchart of a three-split point parameter estimation method for a generalized pareto sea clutter amplitude model according to an embodiment of the present invention. The method comprises the following steps:
s1: and obtaining sea clutter pulse echo data, performing modulus value increasing sequencing, and generating a modulus value increasing sequence of sea clutter echo pulses.
The electromagnetic pulse signal transmitted by the radar transmitter is scattered at the sea level, the echo signal of the electromagnetic pulse signal is subjected to complex Gaussian distribution of inverse Gaussian texture after passing through the radar receiver, and sea clutter pulse echo data are obtained through simulation:
{r1,r2,....,ri,....,rN}
where i 1,2, N represents the number of sea clutter pulse echo data, riAnd the amplitude of the ith sea clutter pulse echo data in the sea clutter pulse echo data is represented.
And then, performing modular value increasing sequencing on the sea clutter pulse echo data to obtain a modular value increasing sequence of the sea clutter pulse echo data.
S2: and acquiring a second cumulative probability distribution function of the sea clutter model of the generalized pareto distribution.
In this embodiment, step S2 specifically includes:
s21: obtaining an amplitude probability density function f (r; mu, v) of a sea clutter model with generalized pareto distribution:
Figure BDA0003060450380000091
wherein r represents the sea clutter amplitude of the generalized pareto sea clutter amplitude model, μ represents the scale parameter of the generalized pareto sea clutter amplitude model, and v represents the shape parameter of the generalized pareto sea clutter amplitude model.
S22: and obtaining a first cumulative probability distribution function F (r; mu, gamma) of the generalized pareto sea clutter amplitude model according to the amplitude probability density function.
Specifically, the amplitude probability density function f (r; mu, gamma) obtained in the step S21 is integrated to obtain a first cumulative distribution function of the generalized pareto sea clutter amplitude model:
Figure BDA0003060450380000101
s23: and obtaining a second cumulative distribution function F (r; 1, v) of the generalized pareto sea clutter amplitude model according to the first cumulative distribution function F (r; mu, v).
Specifically, the scale parameter μ of the first cumulative distribution function F (r; μ, v) is fixed to 1, resulting in the second cumulative distribution function F (r; 1, v):
Figure BDA0003060450380000102
s3: setting a first cumulative probability and a second cumulative probability according to the second cumulative distribution function.
According to the expression of the second cumulative distribution function F (r; 1, v), the first cumulative probability a and the second cumulative probability β of the second cumulative distribution function F (r; 1, v) satisfy:
α＝p(r≤rα)＝F(rα；1,v) (4)
β＝p(r≤rβ)＝F(rβ；1,v) (5)
wherein, alpha is more than 0.1 and beta is more than 1, rαIs a first amplitude quantile point, r, corresponding to a first cumulative probability alphaβAnd a second amplitude quantile corresponding to the second cumulative probability beta.
S4: and constructing a function expression of the third cumulative probability and the shape parameter.
Specifically, the S4 includes:
s41: the third amplitude quantile r can be obtained according to an empirical formula of the estimation error, on the premise that the number of samples (in this embodiment, the number N of the sea clutter pulse echo data) is givenζIs estimated value of
Figure BDA0003060450380000111
Following a progressive normal distribution, the third amplitude quantile rζThe estimation error of (d) can be expressed as:
Figure BDA0003060450380000112
wherein σζRepresents a third amplitude quantile point rζMu is a scale parameter and v is a shape parameterThe number, ζ, represents the third cumulative probability.
S42: and setting the shape parameter v between the intervals [1,30], and traversing at intervals of 0.01 to obtain a plurality of shape parameters gamma. That is, the values of the shape parameter γ are 1, 1.01, 1.02, 1.03 … … 29.99.99, and 30 in this order.
S43: and setting the third cumulative probability zeta between the intervals [0.1 and 0.99], traversing the values at intervals of 0.01, and obtaining a plurality of values of the third cumulative probability zeta. That is, the values of the third cumulative probability ζ are 0, 0.1, 0.11, 0.12 … … 0.98.98, and 0.99 in this order.
S44: for each shape parameter γ obtained in step S42, a point r is assigned to the third amplitude valueζThe estimation error is calculated to obtain the optimal third cumulative probability corresponding to the parameters of different shapes.
Specifically, for a given shape parameter γ, all values of the third cumulative probability are traversed, and a third amplitude quantile point r is recordedζIs estimated error σζThe shape parameter value and the third cumulative probability value under the minimum condition, and one shape parameter value can obtain an optimal third cumulative probability; then, another shape parameter is selected, the steps are repeated, the optimal third cumulative probability of the shape parameter is obtained, and by analogy, a group of shape parameter values can obtain a group of optimal third cumulative probabilities. In the calculation, the scale parameter μ is fixed to 1.
S45: according to the result obtained in step S44, fitting the optimal third cumulative probabilities corresponding to the different shape parameters to obtain a functional expression of the third cumulative probability and the shape parameters:
ζ＝0.6985exp(0.008101v)-0.4008exp(-0.7256v),v＞0 (7)
where γ represents a shape parameter and ζ represents a third cumulative probability.
S5: obtaining a first amplitude quantile point r by utilizing a module value increasing sequence of the sea clutter echo pulseαAnd a second amplitude quantile rβAn estimate of (d).
Specifically, the estimated values of the first amplitude quantile point and the second amplitude quantile point are obtained by using the module value increasing sequence of the sea clutter echo pulse obtained in step S1:
Figure BDA0003060450380000121
wherein,
Figure BDA0003060450380000122
is a first amplitude quantile point rαIs determined by the estimated value of (c),
Figure BDA0003060450380000123
is a second amplitude quantile point rβRound (N × α) represents an integer closest to N × α, and round (N × β) represents an integer closest to N × β.
S6: obtaining shape parameter estimated values of the generalized pareto distribution amplitude model according to the estimated values of the first amplitude quantile point and the second amplitude quantile point
Figure BDA00030604503800001210
In this embodiment, the S6 includes:
s61: given a positive number q greater than 1, the first and second cumulative probabilities α, β satisfy:
Figure BDA0003060450380000124
s62: calculating a second split point estimate
Figure BDA0003060450380000125
And a first-point estimate
Figure BDA0003060450380000126
Square of (d):
Figure BDA0003060450380000127
s63: according to the equations (3), (4) and (5), (9), (10), the modification yields:
Figure BDA0003060450380000128
Figure BDA0003060450380000129
further, the two formulas are deformed, and the square of the ratio of the first amplitude quantile point to the second amplitude quantile point is provided to obtain the generalized pareto distribution shape parameter estimation algorithm expression:
Figure BDA0003060450380000131
s64: setting an intermediate parameter u, order
Figure BDA0003060450380000132
Obtaining a simplified shape parameter estimation calculation expression:
Figure BDA0003060450380000133
wherein the intermediate parameter u is more than 1;
according to the expression of u, the shape parameter estimated value is obtained by deforming the u
Figure BDA0003060450380000134
And intermediate parameter u:
Figure BDA0003060450380000135
s65: solving estimates of shape parameters by iteration
Figure BDA0003060450380000136
The expression is as follows:
Figure BDA0003060450380000137
wherein the initial value u0∈(1,+∞)，u0Take any value within the range, here take u0K is the number of iterations, which is 2, and k is taken to be 200 in the simulation. The shape parameter estimation value in the formula (15) can be used
Figure BDA0003060450380000138
Obtaining shape parameter estimated value by relational expression of intermediate parameter u
Figure BDA0003060450380000139
S7: and obtaining a scale parameter estimation value of the generalized pareto sea clutter amplitude model according to the shape parameter estimation value.
In this embodiment, the S7 includes:
s71: according to the third cumulative probability and the function expression of the shape parameter obtained in step S4 and the shape parameter estimation value
Figure BDA00030604503800001310
The value of the third cumulative probability ζ is calculated.
Specifically, the shape parameter estimation values obtained in step S65 are used
Figure BDA00030604503800001311
Substituting into formula (7) to obtain the value of the third cumulative probability ζ.
S72: using cumulative distribution function, third cumulative probability ζ and shape parameter estimate
Figure BDA0003060450380000141
Obtaining an estimate of the scale parameter mu
Figure BDA0003060450380000142
Specifically, the S72 includes:
s721: calculating a third amplitude quantile point r corresponding to the third cumulative probability zetaζIs estimated value of
Figure BDA0003060450380000143
Figure BDA0003060450380000144
Where round (N × ζ) represents an integer closest to N × ζ.
S722: a third amplitude quantile r calculated according to the formula (17)ζIs estimated value of
Figure BDA0003060450380000145
And (5) deforming the function form to obtain a function expression of the scale parameter mu.
In this embodiment, let the third cumulative probability ζ be the corresponding cumulative distribution function F (r)ζ(ii) a μ, γ) having:
Figure BDA0003060450380000146
and (3) for the deformation, providing a scale parameter mu to obtain an expression of the estimated value of the scale parameter mu:
Figure RE-GDA0003189543670000147
where ζ is the third cumulative probability value and v is the shape parameter.
S723: substituting the third cumulative probability zeta according to the functional expression of the scale parameter mu of formula (19), and estimating the value at the third amplitude quantile
Figure BDA0003060450380000148
Instead of r in the formula (19)ζWith the shape parameter estimation value in step S7
Figure BDA0003060450380000149
Instead of v in equation (19), an estimated value of the scale parameter is obtained
Figure BDA00030604503800001410
Expression (c):
Figure BDA00030604503800001411
the estimated value of the scale parameter of the complex Gaussian sea clutter model of the inverse Gaussian texture can be obtained according to the formula (20)
Figure BDA00030604503800001412
Furthermore, a scale parameter estimation value of the generalized pareto sea clutter amplitude model is obtained
Figure BDA00030604503800001413
And shape parameter estimation
Figure BDA0003060450380000151
Then, based on the obtained scale parameter estimated value
Figure BDA0003060450380000152
And shape parameter estimation
Figure BDA0003060450380000153
The detection threshold of the target detector can be selected more accurately, and a more accurate target detection result is obtained.
The effect of the three-quantile point parameter estimation method of the generalized pareto sea clutter amplitude model of the present invention is further explained by combining with simulation experiments.
(1) Simulation parameter setting
And (3) simulating and generating clutter data which obey a generalized pareto sea clutter amplitude model by using MATLAB software, wherein the number of samples (the number of sea clutter pulse echo data) N is 10000. The shape parameter values are set as interval [1.2,20], interval 0.05 and scale parameter μ as 1. And adding abnormal samples randomly, wherein the ratio of the abnormal sample power to the clutter power is a random number between 10 and 100, and the proportion of the abnormal samples is a random number between 0 and 2 percent. The first and second cumulative probabilities are selected to be 0.37 and 0.80.
(2) Content of simulation experiment
The method of the embodiment of the invention, the 3 methods of 2-4 order moment estimation and double-quantile estimation are respectively adopted to estimate the shape parameters and the scale parameters of the data samples of the generalized pareto sea clutter amplitude model generated by simulation, and the results are shown in fig. 2a to 2d, wherein fig. 2a is a relative root mean square error comparison graph of the shape parameter estimation by using the embodiment of the invention and the two existing methods, wherein the abscissa linearly represents the value of the shape parameter, and the ordinate logarithm represents the relative root mean square error of the shape parameter; FIG. 2b is a diagram of relative root mean square error comparison of shape parameter estimation for a dual-split site and a triple-split site estimation method according to an embodiment of the present invention, where the split site comparison is not obvious due to poor moment estimation accuracy, and the diagram is a comparison of split site estimation methods, where the abscissa represents the shape parameter value linearly and the ordinate represents the relative root mean square error of the shape parameter; FIG. 2c is a diagram of a relative RMS error comparison of scale parameter estimation using two methods according to embodiments of the present invention and the prior art, where the abscissa represents the shape parameter value linearly and the ordinate represents the relative RMS error of the scale parameter; fig. 2d is a comparison of relative root mean square errors of scale parameter estimation of a two-quantile point and a three-quantile point estimation method according to an embodiment of the present invention, where the quantile point comparison is not obvious due to poor moment estimation accuracy.
As can be seen from fig. 2a and 2b, when the number N of samples is the same and shape parameter estimation is performed by using 3 methods, the performance of both 2-4 order moment estimation and dual-site estimation is affected by outliers and becomes worse, wherein the relative root mean square error of the 2-4 order moment estimation method is the largest, the relative root mean square error corresponding to the dual-site estimation method is slightly larger than the method of the present invention, while the relative root mean square error corresponding to the method of the embodiment of the present invention is the smallest, and the estimation performance is the best.
As can be seen from fig. 2c and fig. 2d, when the number N of samples is the same and the scale parameter estimation is performed by using 3 methods, the performance of the 2-4 order moment estimation method is significantly deteriorated, and the performance of the dual-split-point estimation method is slightly inferior to that of the method of the present invention. The result shows that the relative root mean square error corresponding to the method of the embodiment of the invention is the minimum, and the estimation performance is the best.
As can be seen from comparing fig. 2a to fig. 2d, the 2-4 order moment estimation uses the samples to estimate the parameters of the generalized pareto sea clutter amplitude model, so its relative root mean square error is greatly affected by the abnormal samples. The double-branch-point estimation method is similar to the estimation method of the embodiment of the invention, but the method of the embodiment of the invention introduces the third branch point with the optimal estimation, so that the method has the best abnormal sample resistance and relatively high calculation efficiency. In the actual radar target detection, abnormal points are inevitably existed, and the method of the embodiment of the invention has the precedence under the trend of eliminating the influence caused by the abnormal points as much as possible.
In summary, the three-quantile point parameter estimation method of the generalized pareto sea clutter amplitude model according to the embodiment of the present invention performs parameter estimation by using quantile point information, can effectively reduce the influence of abnormal values with large power in original data on parameter estimation performance, has higher capability of resisting abnormal data compared with the existing moment estimation method, and in addition, the method constructs a function expression of an accumulated probability value of scale parameter estimation and a shape parameter by using a theoretical formula, and can more accurately realize the estimation of the scale parameter under the condition that the shape parameter is known. Meanwhile, compared with double-quantile estimation, the method provided by the invention has the advantages that the estimation error of the third quantile introduced is smaller, and the estimation performance of the scale parameter is better.
Yet another embodiment of the present invention provides a storage medium having stored therein a computer program for executing the steps of the method described in the above embodiment. A further aspect of the present invention provides an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method according to the above embodiment when calling the computer program in the memory. Specifically, the integrated module implemented in the form of a software functional module may be stored in a computer readable storage medium. The software functional module is stored in a storage medium and includes several instructions to enable an electronic device (which may be a personal computer, a server, or a network device) or a processor (processor) to execute some steps of the methods according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all should be considered as belonging to the protection scope of the present invention.

Claims (10)

1. A three-point parameter estimation method of a generalized pareto sea clutter amplitude model is characterized by comprising the following steps:
s1: obtaining sea clutter pulse echo data, performing modulus value increasing sequencing, and generating a modulus value increasing sequence of sea clutter echo pulses;
s2: acquiring a second cumulative probability distribution function of the sea clutter model with generalized pareto distribution;
s3: setting a first cumulative probability and a second cumulative probability according to the second cumulative distribution function;
s4: constructing a function expression of the third cumulative probability and the shape parameter;
s5: obtaining estimated values of a first amplitude quantile point and a second amplitude quantile point by using a module value increasing sequence of the sea clutter echo pulse;
s6: obtaining a shape parameter estimation value of the generalized pareto distribution amplitude model according to the estimation values of the first amplitude quantile point and the second amplitude quantile point;
s7: and obtaining a scale parameter estimation value of the generalized pareto sea clutter amplitude model according to the shape parameter estimation value.
2. The method for estimating parameters of three-way points of the generalized pareto sea clutter amplitude model according to claim 1, wherein the S2 includes:
s21: obtaining an amplitude probability density function f (r; mu, v) of a sea clutter model with generalized pareto distribution:
Figure FDA0003060450370000011
wherein r represents a sea clutter amplitude of the generalized pareto sea clutter amplitude model, μ represents a scale parameter of the generalized pareto sea clutter amplitude model, and v represents a shape parameter of the generalized pareto sea clutter amplitude model;
s22: obtaining a first cumulative probability distribution function F (r; mu, gamma) of the generalized pareto sea clutter amplitude model according to the amplitude probability density function:
Figure FDA0003060450370000021
s23: obtaining a second cumulative distribution function F (r; 1, v) of the generalized pareto sea clutter amplitude model from the first cumulative distribution function F (r; mu, v):
Figure FDA0003060450370000022
3. the method for estimating parameters of three-way points of the generalized pareto sea clutter amplitude model according to claim 2, wherein the S3 includes:
obtaining expressions of a first cumulative probability a and a second cumulative probability β according to the expression of the second cumulative distribution function F (r; 1, v):
α＝p(r≤rα)＝F(rα；1,v)
β＝p(r≤rβ)＝F(rβ；1,v)
wherein, alpha is more than 0.1 and beta is more than 1, rαIs a first amplitude quantile point, r, corresponding to a first cumulative probability alphaβAnd a second amplitude quantile corresponding to the second cumulative probability beta.
4. The method for estimating parameters of three-way points of the generalized pareto sea clutter amplitude model according to claim 3, wherein said S4 comprises:
s41: according to an empirical formula of estimation errors, a third amplitude quantile point r is obtainedζThe estimation error of (d) is expressed as:
Figure FDA0003060450370000023
wherein σζRepresents a third amplitude quantile point rζμ is a scale parameter, v is a shape parameter, and ζ represents a third cumulative probability;
s42: setting the shape parameter v between the intervals [1,30], and traversing at intervals of 0.01 to obtain a plurality of shape parameters gamma;
s43: setting the third cumulative probability zeta between the intervals [0.1 and 0.99], traversing the values at intervals of 0.01, and obtaining a plurality of values of the third cumulative probability zeta;
s44: for each shape parameter γ obtained in step S42, a third amplitude quantile r is assigned according to the formula in S52ζCalculating the estimation error to obtain the optimal third cumulative probability corresponding to the parameters with different shapes;
s45: fitting the optimal third cumulative probabilities corresponding to the different shape parameters to obtain a function expression of the third cumulative probabilities and the shape parameters:
ζ＝0.6985exp(0.008101v)-0.4008exp(-0.7256v),v＞0
where γ represents a shape parameter and ζ represents a third cumulative probability.
5. The method for estimating parameters of three-way points of the generalized pareto sea clutter amplitude model according to claim 4, wherein said S5 comprises:
obtaining estimated values of the first amplitude quantile point and the second amplitude quantile point by using the module value increasing sequence of the sea clutter echo pulse obtained in the step S1:
Figure FDA0003060450370000031
wherein,
Figure FDA0003060450370000032
is a first amplitude quantile point rαIs determined by the estimated value of (c),
Figure FDA0003060450370000033
is a second amplitude quantile point rβRound (N × α) represents the integer closest to N × α, and round (N × β) represents the integer closest to N × β.
6. The method for estimating parameters of three-way points of the generalized pareto sea clutter amplitude model according to claim 5, wherein said S6 comprises:
s61: given a positive number q greater than 1, the first and second cumulative probabilities α, β satisfy:
Figure FDA0003060450370000034
s62: calculating a second split point estimate
Figure FDA0003060450370000041
And a first site of attachmentEstimated value
Figure FDA0003060450370000042
Square of (d):
Figure FDA0003060450370000043
s63: obtaining a generalized pareto distribution shape parameter estimation algorithm expression according to the relation between the second cumulative distribution function F (r; 1, v) and the first cumulative probability alpha and the second cumulative probability beta:
Figure FDA0003060450370000044
s64: setting an intermediate parameter u, order
Figure FDA0003060450370000045
Obtaining shape parameter estimates
Figure FDA00030604503700000411
And the intermediate parameter u is expressed as:
Figure FDA0003060450370000046
s65: solving estimates of shape parameters by iteration
Figure FDA0003060450370000047
The expression is as follows:
Figure FDA0003060450370000048
wherein the initial value u0E (1, + ∞), k is the number of iterations.
7. The method for estimating the parameters of the trisection points of the generalized pareto sea clutter amplitude model according to claim 6, wherein said S7 comprises:
s71: according to the third cumulative probability and the function expression of the shape parameter and the estimated value of the shape parameter
Figure FDA00030604503700000412
Calculating a third cumulative probability value ζ;
s72: using cumulative distribution function, third cumulative probability ζ and shape parameter estimate
Figure FDA0003060450370000049
Obtaining an estimate of the scale parameter mu
Figure FDA00030604503700000410
8. The method for estimating the parameters of the trisection points of the generalized pareto sea clutter amplitude model according to claim 7, wherein the S72 includes:
s721: calculating a third amplitude quantile point r corresponding to the third cumulative probability zetaζIs estimated value of
Figure FDA0003060450370000051
Figure FDA0003060450370000052
Wherein round (N × ζ) represents an integer closest to N × ζ;
s722: cumulative distribution function F (r) corresponding to third cumulative probability ζζ(ii) a Mu, gamma) to obtain an estimated value of the scale parameter
Figure FDA0003060450370000053
Expression (c):
Figure FDA0003060450370000054
9. a storage medium having stored thereon a computer program for performing the steps of the method for three-quantile parameter estimation of a generalized pareto sea clutter amplitude model according to any of claims 1 to 8.
10. An electronic device comprising a memory having a computer program stored therein and a processor, the processor implementing the steps of the method for three-quantile parameter estimation of a generalized pareto sea clutter amplitude model according to any of claims 1 to 8 when invoking the computer program in the memory.
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