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

Abstract

The invention discloses a method for estimating parameters of three-point points of a generalized Pareto sea clutter amplitude model. The second cumulative probability distribution function of the sea clutter model; the first cumulative probability and the second cumulative probability are set according to the second cumulative distribution function; the functional expression of the third cumulative probability and the shape parameter is constructed; the sea clutter echo pulse is used The modulo value increasing sequence of , obtains the estimated value of the first magnitude quantile and the second magnitude quantile; obtains the estimated value of the shape parameter of the magnitude model of the generalized Pareto distribution; obtains the estimated value of the generalized Pareto according to the estimated value of the shape parameter Scale parameter estimates for the sea clutter amplitude model. This method uses quantile information for parameter estimation, which can effectively reduce the influence of abnormal values with large power in the original data on the performance of parameter estimation, thereby improving the accuracy of target detection in the background of sea clutter.

Description

Tertile parameter estimation method for generalized Pareto clutter amplitude model

technical field

The invention belongs to the technical field of radar target detection, and in particular relates to a method for estimating three-point parameter of a generalized Pareto sea clutter amplitude model, which can be used for target detection under sea clutter conditions.

Background technique

In the development process of sea clutter target detection, the accuracy of the sea clutter simulation model and the actual sea clutter distribution characteristics is an important prerequisite for the construction of the sea clutter simulation model. The amplitude distribution information of sea clutter can accurately describe the statistical characteristics of the echo of sea clutter, and the design of the optimal detector under the background of sea clutter depends on the parameters of the sea clutter amplitude model. The amplitude model of sea clutter is closely related to meteorological conditions and radar resolution.

When the radar resolution unit is large, the radar resolution is low, and the complex Gaussian model can be used to describe the amplitude characteristics of sea clutter. At this time, the amplitude model of sea clutter is usually a Rayleigh distribution. However, with the continuous improvement of radar resolution, the traditional complex Gaussian model cannot meet the needs of accurately describing the characteristics of sea clutter. For radars with low ground angle and high resolution, compared with the Rayleigh distribution model, the amplitude distribution of sea clutter will have a longer tail, showing a strong non-Gaussian property. In this case, a non-Gaussian model needs to be used. to describe the distribution of sea clutter amplitudes. The complex Gaussian model is a widely used sea clutter model, which describes the amplitude distribution of sea clutter as the product of a slow-varying positive texture component and a fast-varying complex Gaussian speckle component. For the complex Gaussian model, in the sea clutter detection period, the speckle component is approximately constant, and its statistical characteristics are mainly affected by the texture component. When the texture component conforms to the inverse gamma distribution, its sea clutter amplitude model conforms to the generalized Pareto distribution.

The maximum likelihood estimation can realize the parameter estimation of the generalized Pareto clutter amplitude model, but the estimated parameter characteristics are unstable. The document "BALLERI A, NEHORAI A, and WANG J. Maximum likelihood estimation for compound-Gaussian clutter with inverse Gamma texture [J]. IEEE Transactionson Aerospace and Electronic Systems, 2007, 43(2): 775-780." proposes a maximum likelihood estimation Likelihood estimation, the maximum likelihood estimation method uses an iterative method to estimate parameters, which improves the estimation accuracy. However, this method does not consider the influence of abnormal samples on clutter parameter estimation. For real sea clutter data, the samples often contain a small number of high-power outliers, which will greatly reduce the performance of maximum likelihood estimation and increase the accuracy. range down.

The document "P-L.Shui and M.Liu,"Subband adaptive GLRT-LTD for weak movingtargets in sea clutter,"IEEE Trans.Aerosp.Electron.Syst.,52(1):423-437,2016."Proposed sample accumulation in The biquantile estimation method when the probability is 0.5 and 0.75, the fixed biquantile estimation The accuracy of the results is insufficient due to the fixed estimated points.

SUMMARY OF THE INVENTION

In order to solve the above-mentioned problems existing in the prior art, the present invention provides a method for estimating the parameters of the tertiles of the generalized Pareto sea clutter amplitude model. The technical problem to be solved by the present invention is realized by the following technical solutions:

The invention provides a tertile parameter estimation method of a generalized Pareto clutter amplitude model, including:

S1: Acquire the sea clutter pulse echo data and sort the modulo value in ascending order to generate the modulo value increasing sequence of the sea clutter echo pulse;

S2: Obtain the second cumulative probability distribution function of the sea clutter model of the generalized Pareto distribution;

S3: Set a first cumulative probability and a second cumulative probability according to the second cumulative distribution function;

S4: Construct the functional expression of the third cumulative probability and the shape parameter;

S5: Obtain the estimated values of the first amplitude quantile and the second amplitude quantile by using the increasing sequence of the modulo value of the sea clutter echo pulse;

S6: obtain the estimated value of the shape parameter of the generalized Pareto distribution amplitude model according to the estimated value of the first amplitude quantile and the second amplitude quantile;

S7: Obtain the estimated value of the scale parameter of the generalized Pareto sea clutter amplitude model according to the estimated value of the shape parameter.

In an embodiment of the present invention, the S2 includes:

S21: Obtain the amplitude probability density function f(r; μ, v) of the sea clutter model of the generalized Pareto distribution:

Among them, r represents the sea clutter amplitude of the generalized Pareto clutter amplitude model, μ represents the scale parameter of the generalized Pareto clutter amplitude model, and v represents the generalized Pareto clutter amplitude model. shape parameter;

S22: Obtain the first cumulative probability distribution function F(r; μ, γ) of the generalized Pareto clutter amplitude model according to the amplitude probability density function:

S23: Obtain the second cumulative distribution function F(r; 1, v) of the generalized Pareto clutter amplitude model according to the first cumulative distribution function F(r; μ, v):

In an embodiment of the present invention, the S3 includes:

According to the expression of the second cumulative distribution function F(r; 1, v), the expressions of the first cumulative probability α and the second cumulative probability β are obtained:

α=p(r≤r _α )=F(r _α ; 1,v)

β=p(r≤r _β )=F(r _β ; 1,v)

0.1<α+0.1<β<1, r _α is the first amplitude quantile corresponding to the first cumulative probability α, and r _β is the second amplitude quantile corresponding to the second cumulative probability β.

In an embodiment of the present invention, the S4 includes:

S41: According to the empirical formula of estimation error, the estimation error of the third amplitude quantile r _ζ is expressed as:

Among them, σ _ζ represents the estimated error of the third amplitude quantile r _ζ , μ is the scale parameter, v is the shape parameter, ζ represents the third cumulative probability;

S42: Set the shape parameter v between the interval [1, 30], and traverse the value at an interval of 0.01 to obtain multiple shape parameters γ;

S43: Set the third cumulative probability ζ between the interval [0.1, 0.99], and traverse the value at an interval of 0.01 to obtain multiple values of the third cumulative probability ζ;

S44: For each shape parameter γ obtained in step S42, calculate the estimated error of the third amplitude quantile r _ζ according to the formula in S52, and obtain the optimal third cumulative probability corresponding to different shape parameters;

S45: Fit the optimal third cumulative probability corresponding to different shape parameters to obtain the 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 the shape parameter and ζ represents the third cumulative probability.

In an embodiment of the present invention, the S5 includes:

Using the increasing sequence of the modulus value of the sea clutter echo pulse obtained in step S1, the estimated values of the first amplitude quantile and the second amplitude quantile are obtained:

为第一幅值分位点r_α的估计值，

为第二幅值分位点r_β的估 计值，round(N*α)表示最接近N*α的整数，round(N*β)表示最接近N*β的 整数。in,

is the estimated value of the first magnitude quantile r _α ,

is the estimated value of the second magnitude quantile r _β , round(N*α) represents the integer closest to N*α, and round(N*β) represents the integer closest to N*β.

In an embodiment of the present invention, the S6 includes:

S61: Given a positive number q greater than 1, make the first cumulative probability α and the second cumulative probability β satisfy:

和第一分位点估计值

的比值平方t：S62: Calculate the second quantile estimate

and the first quantile estimate

The ratio of squared t:

S63: Obtain the generalized Pareto distribution shape parameter estimation algorithm expression according to the relationship between the second cumulative distribution function F(r; 1, v) and the first cumulative probability α and the second cumulative probability β:

获得形状参数估计值

和中 间参数u的关系表达式为：S64: Set up the intermediate parameter u, let

Obtain shape parameter estimates

The relational expression with the intermediate parameter u is:

其表达式为：S65: Solve the estimated value of the shape parameter by iteration

Its expression is:

Among them, the initial value u ₀ ∈(1,+∞), and k is the number of iterations.

In an embodiment of the present invention, the S7 includes:

计算第三累计概率值ζ；S71: According to the third cumulative probability and the function expression of the shape parameter and the estimated value of the shape parameter

Calculate the third cumulative probability value ζ;

获得 尺度参数μ的估计值

S72: Utilize the cumulative distribution function, the third cumulative probability ζ and the estimated value of the shape parameter

obtain an estimate of the scale parameter μ

In an embodiment of the present invention, the S72 includes:

S721: Calculate the estimated value of the third amplitude quantile r _ζ corresponding to the third cumulative probability ζ

Among them, round(N*ζ) represents the integer closest to N*ζ;

的表达式：S722: Obtain the estimated value of the scale parameter according to the cumulative distribution function F(r _ζ ; μ, γ) corresponding to the third cumulative probability ζ

expression:

Another aspect of the present invention provides a storage medium, where a computer program is stored in the storage medium, and the computer program is used to execute the generalized Pareto clutter amplitude model described in any one of the foregoing embodiments The steps of the tertile parameter estimation method.

Yet another aspect of the present invention provides an electronic device, including a memory and a processor, where a computer program is stored in the memory, and when the processor invokes the computer program in the memory, any one of the foregoing embodiments is implemented The steps of the tertile parameter estimation method of the generalized Pareto clutter amplitude model.

Compared with the prior art, the beneficial effects of the present invention are:

1. The tertile parameter estimation method of the generalized Pareto clutter amplitude model of the present invention uses the quantile information for parameter estimation, which can effectively reduce the influence of abnormal values with large power in the original data on the parameter estimation performance Compared with the existing moment estimation methods, it has a relatively high ability to resist abnormal data, thereby improving the accuracy of target detection in the background of sea clutter.

2. The tertile parameter estimation method of the generalized Pareto sea clutter amplitude model of the present invention uses theoretical formulas to construct a functional expression of the cumulative probability value of the scale parameter estimation and the shape parameter, under the condition that the shape parameters are known In this way, the estimation of the scale parameter can be achieved more accurately. At the same time, compared with the biquantile estimation, the method of the present invention introduces a smaller estimation error of the third quantile, and has better performance for estimating scale parameters.

The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

Description of drawings

Fig. 1 is the flow chart of the tertile parameter estimation method of a kind of generalized Pareto sea clutter amplitude model provided in the embodiment of the present invention;

Fig. 2 a is the relative root mean square error comparison diagram that uses the embodiment of the present invention and two existing methods to carry out shape parameter estimation;

Fig. 2 b is the relative root mean square error comparison diagram of biquantile point and the tertile point estimation method shape parameter estimation of the embodiment of the present invention;

Fig. 2 c is the relative root mean square error comparison diagram of using the embodiment of the present invention and two methods of prior art to carry out scale parameter estimation;

Fig. 2d is a comparison diagram of relative root mean square error of the scale parameter estimation of the biquantile point and the tertile point estimation method according to the embodiment of the present invention.

Detailed ways

In order to further illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the following describes the tertiles of a generalized Pareto clutter amplitude model proposed by the present invention with reference to the accompanying drawings and specific embodiments. The parameter estimation method is described in detail.

The foregoing and other technical contents, features and effects of the present invention can be clearly presented in the following detailed description of the specific implementation with the accompanying drawings. Through the description of the specific embodiments, the technical means and effects adopted by the present invention to achieve the predetermined purpose can be more deeply and specifically understood. However, the accompanying drawings are only for reference and description, and are not used for the technical description of the present invention. program is restricted.

It should be noted that, in this document, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any relationship between these entities or operations. any such actual relationship or sequence exists. Moreover, the terms "comprising", "comprising" or any other variation are intended to encompass a non-exclusive inclusion, whereby an article or device comprising a list of elements includes not only those elements, but also other elements not expressly listed. Without further limitation, an element qualified by the phrase "comprising a..." does not preclude the presence of additional identical elements in the article or device comprising said element.

In the actual radar working environment, it is necessary to perform target detection and processing on the radar echo data under different sea clutter backgrounds, and the design of the target detector is a key step in the target detection and processing link. The test statistics and detection thresholds of the target detector under different sea clutter backgrounds are closely related to the two characteristic parameters of sea clutter, namely the scale parameter and the shape parameter. The accuracy and stability of these two characteristic parameters of sea clutter are An important indicator for evaluating the detection performance of object detectors in the ocean 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, thereby affecting the target detection accuracy. The closer the sea clutter characteristic parameters are to the real sea clutter characteristic parameters, the higher the target detection accuracy.

The purpose of the embodiments of the present invention is to propose a method for estimating the parameters of the tertiles of the generalized Pareto sea clutter amplitude model. The parameter estimation is more accurate, the detection threshold of the target detector designed according to the scale parameters and shape parameters obtained by the method of the embodiment of the present invention is better, the false alarm rate of target detection is better controlled, and the detection accuracy is higher.

Please refer to FIG. 1. FIG. 1 is a flowchart of a method for estimating tertile parameters of a generalized Pareto clutter amplitude model according to an embodiment of the present invention. The method includes the following steps:

S1: Acquire sea clutter pulse echo data and perform an ascending sequence of modulo values to generate an ascending sequence of modulo value of sea clutter echo pulses.

The electromagnetic pulse signal emitted by the radar transmitter is scattered at the sea level, and its echo signal obeys the complex Gaussian distribution of the inverse Gaussian texture after passing through the radar receiver. The sea clutter pulse echo data is obtained by simulation:

{r ₁ ,r ₂ ,....,r _i ,....,r _N }

Among them, i=1,2,...,N, N represents the number of sea clutter pulse echo data, ri represents the amplitude of the _i -th sea clutter pulse echo data in the sea clutter pulse echo data value.

Then, the sea clutter pulse echo data is sorted in ascending order of modulo values to obtain an increasing sequence of modulo values of the sea clutter pulse echo data.

S2: Obtain the second cumulative probability distribution function of the generalized Pareto distributed sea clutter model.

In this embodiment, step S2 specifically includes:

S21: Obtain the amplitude probability density function f(r; μ, v) of the sea clutter model of the generalized Pareto distribution:

Among them, r represents the sea clutter amplitude of the generalized Pareto clutter amplitude model, μ represents the scale parameter of the generalized Pareto clutter amplitude model, and v represents the generalized Pareto clutter amplitude model. shape parameter.

S22: Obtain the first cumulative probability distribution function F(r; μ, γ) of the generalized Pareto clutter amplitude model according to the amplitude probability density function.

Specifically, the amplitude probability density function f(r; μ, γ) obtained in step S21 is integrated to obtain the first cumulative distribution function of the generalized Pareto clutter amplitude model:

S23: Obtain a second cumulative distribution function F(r; 1, v) of the generalized Pareto clutter amplitude model according to the first cumulative distribution function F(r; μ, v).

Specifically, the scale parameter μ of the first cumulative distribution function F(r; μ, v) is fixed to 1 to obtain the second cumulative distribution function F(r; 1, v):

S3: Set the first cumulative probability and the 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 α and the second cumulative probability β of the second cumulative distribution function F(r; 1, v) satisfy:

α=p(r≤r _α )=F(r _α ; 1,v) (4)

β=p(r≤r _β )=F(r _β ; 1,v) (5)

0.1<α+0.1<β<1, r _α is the first amplitude quantile corresponding to the first cumulative probability α, and r _β is the second amplitude quantile corresponding to the second cumulative probability β.

S4: Construct a functional expression of the third cumulative probability and the shape parameter.

Specifically, the S4 includes:

服从渐进正态分布，则第三幅值分位点r_ζ的估计误差可以表示为：S41: According to the empirical formula of estimation error, it can be obtained, under the premise that the number of samples (in this embodiment, the number N of sea clutter pulse echo data) is given, the estimated value of the third amplitude quantile r _ζ

Following the asymptotic normal distribution, the estimated error of the third magnitude quantile r _ζ can be expressed as:

Among them, σ _ζ represents the estimation error of the third magnitude quantile r _ζ , μ is the scale parameter, v is the shape parameter, and ζ represents the third cumulative probability.

S42: Set the shape parameter v between the interval [1, 30], and traverse the value at an interval of 0.01 to obtain multiple shape parameters γ. That is, the values of the shape parameter γ are 1, 1.01, 1.02, 1.03... 29.99, 30 in sequence.

S43: Set the third cumulative probability ζ in the interval [0.1, 0.99], and traverse the values at an interval of 0.01 to obtain multiple values of the third cumulative probability ζ. That is, the values of the third cumulative probability ζ are 0, 0.1, 0.11, 0.12... 0.98, 0.99 in sequence.

S44: For each shape parameter γ obtained in step S42, calculate the estimated error of the third amplitude quantile r _ζ to obtain the optimal third cumulative probability corresponding to different shape parameters.

Specifically, for a given shape parameter γ, traverse all the values of the third cumulative probability, and record the shape parameter value and the third cumulative probability when the estimated error σ _ζ of the third amplitude quantile r _ζ is the smallest Probability value, a shape parameter value can obtain an optimal third cumulative probability; then, select another shape parameter, repeat the above steps, obtain the optimal third cumulative probability of the shape parameter, and so on, a set of shape parameters value to obtain a set of optimal third cumulative probabilities. It should be noted that, in the calculation process, the scale parameter μ is fixed to 1.

S45: According to the result obtained in step S44, the optimal third cumulative probability corresponding to different shape parameters is fitted to obtain the function expression of the third cumulative probability and shape parameter:

ζ=0.6985exp(0.008101v)-0.4008exp(-0.7256v), v＞0 (7)

where γ represents the shape parameter and ζ represents the third cumulative probability.

S5: Obtain the estimated values of the first amplitude quantile r _α and the second amplitude quantile r _β by using the increasing sequence of the modulo value of the sea clutter echo pulse.

Specifically, using the increasing sequence of the modulo value of the sea clutter echo pulse obtained in step S1, the estimated values of the first amplitude quantile and the second amplitude quantile are obtained:

为第一幅值分位点r_α的估计值，

为第二幅值分位点r_β的估 计值，round(N*α)表示最接近N*α的整数，round(N*β)表示最接近N*β的 整数。in,

is the estimated value of the first magnitude quantile r _α ,

is the estimated value of the second magnitude quantile r _β , round(N*α) represents the integer closest to N*α, and round(N*β) represents the integer closest to N*β.

S6: Obtain the estimated value of the shape parameter of the generalized Pareto distribution amplitude model according to the estimated value of the first amplitude quantile and the second amplitude quantile

In this embodiment, the S6 includes:

S61: Given a positive number q greater than 1, so that the first cumulative probability α and the second cumulative probability β satisfy:

和第一分位点估计值

的比值平方t：S62: Calculate the second quantile estimate

and the first quantile estimate

The ratio of squared t:

S63: According to formulas (3), (4) and (5), (9), (10), the deformation is obtained:

Further, by transforming the above two equations, the square of the ratio of the first amplitude quantile and the second amplitude quantile is proposed to obtain the generalized Pareto distribution shape parameter estimation algorithm expression:

得到简化的形状参数估计算 法表达式：S64: Set up the intermediate parameter u, let

Get the simplified shape parameter estimation algorithm expression:

Among them, the intermediate parameter u>1;

和中间参数u的关系 表达式：According to the expression of u, the shape parameter estimation value is obtained by its deformation

and the relational expression of the intermediate parameter u:

其表达式为：S65: Solve the estimated value of the shape parameter by iteration

Its expression is:

和中间 参数u的关系表达式得到形状参数估计值

Among them, the initial value u ₀ ∈(1,+∞), u ₀ takes any value within the range, where u ₀ =2 is taken here, k is the number of iterations, and k takes 200 in the simulation. At this time, the estimated value of the shape parameter in formula (15) can be

and the relational expression of the intermediate parameter u to obtain the estimated value of the shape parameter

S7: Obtain the estimated value of the scale parameter of the generalized Pareto sea clutter amplitude model according to the estimated value of the shape parameter.

In this embodiment, the S7 includes:

计算第三累计概率ζ的值。S71: According to the third cumulative probability obtained in step S4 and the function expression of the shape parameter and the estimated value of the shape parameter

The value of the third cumulative probability ζ is calculated.

代入公式(7)中，得到第 三累计概率ζ的值。Specifically, the estimated value of the shape parameter obtained in step S65

Substitute into formula (7) to obtain the value of the third cumulative probability ζ.

获得 尺度参数μ的估计值

S72: Utilize the cumulative distribution function, the third cumulative probability ζ and the estimated value of the shape parameter

obtain an estimate of the scale parameter μ

Specifically, the S72 includes:

S721: Calculate the estimated value of the third amplitude quantile r _ζ corresponding to the third cumulative probability ζ

where round(N*ζ) represents the integer closest to N*ζ.

对其函 数形式变形，得到尺度参数μ的函数表达式。S722: the estimated value of the third amplitude quantile r _ζ calculated according to formula (17)

Transform its functional form to obtain the functional expression of the scale parameter μ.

In this embodiment, let the third cumulative probability ζ, then the corresponding cumulative distribution function F(r _ζ ; μ, γ) has:

For its deformation, the scale parameter μ is proposed, and the estimated value expression of the scale parameter μ is obtained:

Among them, ζ is the third cumulative probability value, and v is the shape parameter.

替代公式(19)中的r_ζ，以步骤S7中的形状 参数估计值

替代公式(19)中的v，得到尺度参数估计值

的表达式：S723: According to the functional expression of the scale parameter μ of formula (19), substitute the third cumulative probability ζ, and estimate the value with the third amplitude quantile

Substitute r _ζ in formula (19) with the estimated value of the shape parameter in step S7

Substitute v in equation (19) to get the scale parameter estimate

expression:

According to formula (20), the estimated value of the scale parameter of the complex Gaussian sea clutter model of the inverse Gaussian texture can be obtained

和形状参数估计值

之后，根据获得的尺度参数估计值

和形状参数估计值

可以更加精确地选取目标检测器的检测门限，进而获得更加精确的目标检 测结果。Further, after obtaining the scale parameter estimates of the generalized Pareto clutter amplitude model

and shape parameter estimates

After that, according to the obtained scale parameter estimates

and shape parameter estimates

The detection threshold of the target detector can be selected more accurately, thereby obtaining more accurate target detection results.

The effect of the three-point parameter estimation method of the generalized Pareto sea clutter amplitude model of the present invention will be further described below in conjunction with simulation experiments.

(1) Simulation parameter setting

The clutter data obeying the generalized Pareto sea clutter amplitude model was generated using MATLAB software simulation, where the number of samples (the number of sea clutter pulse echo data) N=10000. The value of the shape parameter is set to the interval [1.2, 20], the interval is 0.05, and the scale parameter μ is set to 1. Randomly add abnormal samples, wherein the ratio of abnormal sample power to clutter power is a random number between 10-100, and the ratio of abnormal samples is a random number between 0-2%. The first cumulative probability and the second cumulative probability were chosen to be 0.37 and 0.80.

(2) Simulation experiment content

The shape parameters and scale parameters of the data samples of the generalized Pareto sea clutter amplitude model generated by simulation are estimated respectively by using the method of the embodiment of the present invention, the 2-4 order moment estimation and the biquantile estimation. , the results are shown in Figures 2a to 2d, wherein Figure 2a is a comparison diagram of the relative root mean square error of the shape parameter estimation using the embodiment of the present invention and the existing two methods, wherein the abscissa linearly represents the shape parameter. The logarithm of the ordinate represents the relative root mean square error of the shape parameter; Figure 2b is a comparison of the relative root mean square error of the shape parameter estimation between the biquantile point and the tertile point estimation method according to the embodiment of the present invention. The difference causes the quantile comparison to be inconspicuous. This figure compares the quantile estimation methods. The abscissa linearly represents the value of the shape parameter, and the logarithm of the ordinate represents the relative root mean square error of the shape parameter; Figure 2c shows the implementation of the present invention. Example and the relative root mean square error comparison of scale parameter estimation by two methods of the prior art, wherein the abscissa linearly represents the value of the shape parameter, and the logarithm of the ordinate represents the relative root mean square error of the scale parameter; Compared with the relative root mean square error of the scale parameter estimation of the quantile point estimation method according to the embodiment of the present invention, the comparison of the quantile points is not obvious due to the poor moment estimation accuracy. This figure compares the quantile point estimation methods. Among them, the linear axis of the abscissa represents the value of the shape parameter, and the logarithm of the ordinate represents the relative root mean square error of the scale parameter.

It can be seen from Figure 2a and Figure 2b that when the number of samples N is the same and three methods are used to estimate the shape parameters, the performance of the 2-4 order moment estimation and the biquantile estimation are both affected by the outliers and deteriorate, among which 2- The relative root mean square error of the fourth-order moment estimation method is the largest, the relative root mean square error corresponding to the biquantile estimation method is slightly larger than that of the method of the present invention, and the relative root mean square error corresponding to the method of the embodiment of the present invention is the smallest, and the estimation performance most.

It can be seen from Figure 2c and Figure 2d that when the number of samples N is the same and the scale parameters are estimated by three methods, the performance of the 2-4 order moment estimation method is obviously worse, and the performance of the biquantile estimation method is slightly worse than that of the method of the present invention. . It can be seen from the results that 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.

Comparing Fig. 2a to Fig. 2d, it can be seen that the 2-4 order moment estimation uses samples to estimate the parameters of the generalized Pareto sea clutter amplitude model, so its relative root mean square error is greatly affected by abnormal samples. The biquantile estimation method is similar to the estimation method of the embodiment of the present invention, but the method of the embodiment of the present invention introduces the third quantile with the best estimation, so that the method has the best anti-abnormal sample ability and relatively high computational efficiency. In actual radar target detection, it is inevitable that there are abnormal points, and under the trend of eliminating the influence of abnormal points as much as possible, the method of the embodiment of the present invention has its advantages.

In general, the method for estimating the parameters of the tertiles of the generalized Pareto sea clutter amplitude model according to the embodiment of the present invention uses the information of the quantiles to estimate the parameters, which can effectively reduce the parameter estimation of abnormal values with high power in the original data. Compared with the existing moment estimation methods, it has a relatively high ability to resist abnormal data. In addition, this method uses theoretical formulas to construct a functional expression of the cumulative probability value of the scale parameter estimation and the shape parameter. Under the condition that the parameters are known, the estimation of the scale parameters can be achieved relatively accurately. At the same time, compared with biquantile estimation, the method of the present invention introduces a smaller estimation error of the third quantile, and has better performance in estimating scale parameters.

Yet another embodiment of the present invention provides a storage medium, where a computer program is stored in the storage medium, and the computer program is used to execute the steps of the methods described in the above embodiments. Another aspect of the present invention provides an electronic device, including a memory and a processor, where a computer program is stored in the memory, and the processor implements the method described in the above embodiments when the processor invokes the computer program in the memory step. Specifically, the above-mentioned integrated modules implemented in the form of software functional modules can be stored in a computer-readable storage medium. The above-mentioned software function modules are stored in a storage medium, and include several instructions to cause an electronic device (which may be a personal computer, a server, or a network device, etc.) or a processor (processor) to execute the methods described in the various embodiments of the present invention. some steps. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), magnetic disk or optical disk and other media that can store program codes .

The above content is a further detailed description of the present invention in conjunction with the specific preferred embodiments, and it cannot be considered that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, some simple deductions or replacements can also be made, all of which should be regarded 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:

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:

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):

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≤r_α)＝F(r_α；1,v)

β＝p(r≤r_β)＝F(r_β；1,v)

wherein, alpha is more than 0.1 and beta is more than 1, r_αIs a first amplitude quantile point, r, corresponding to a first cumulative probability alpha_βAnd 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 obtained_ζThe estimation error of (d) is expressed as:

wherein σ_ζRepresents a third amplitude quantile point r_ζμ 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 S52_ζCalculating 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:

wherein,

is a first amplitude quantile point r_αIs determined by the estimated value of (c),

is a second amplitude quantile point r_βRound (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:

s62: calculating a second split point estimate

And a first site of attachmentEstimated value

Square of (d):

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:

s64: setting an intermediate parameter u, order

Obtaining shape parameter estimates

And the intermediate parameter u is expressed as:

s65: solving estimates of shape parameters by iteration

The expression is as follows:

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

Calculating a third cumulative probability value ζ;

s72: using cumulative distribution function, third cumulative probability ζ and shape parameter estimate

Obtaining an estimate of the scale parameter mu

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 zeta_ζIs estimated value of

Wherein round (N × ζ) represents an integer closest to N × ζ;

s722: cumulative distribution function F (r) corresponding to third cumulative probability ζ_ζ(ii) a Mu, gamma) to obtain an estimated value of the scale parameter

Expression (c):

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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