CN113466811B - Three-position point parameter estimation method of generalized pareto sea clutter amplitude model - Google Patents
Three-position point parameter estimation method of generalized pareto sea clutter amplitude model Download PDFInfo
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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
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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
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- G01S7/411—Identification of targets based on measurements of radar reflectivity
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Abstract
The invention discloses a three-point parameter estimation method of a generalized pareto sea clutter amplitude model, which comprises the following steps: acquiring sea clutter pulse echo data and performing modular value incremental sequencing; acquiring a second cumulative probability distribution function of a sea clutter model of generalized pareto distribution; setting a first cumulative probability and a second cumulative probability according to the second cumulative probability distribution function; constructing a function expression of the third cumulative probability and the shape parameter; obtaining estimated values of a first amplitude quantile and a second amplitude quantile by using a modular value incremental sequence of sea clutter echo pulses; obtaining a shape parameter estimated value of a 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, the parameter estimation is carried out by utilizing the split point information, so that the influence of a abnormal constant value with larger power in the original data on the parameter estimation performance can be effectively reduced, and the accuracy of target detection under the sea clutter background is further improved.
Description
Technical Field
The invention belongs to the technical field of radar target detection, and particularly relates to a three-position point parameter estimation method of a generalized pareto sea clutter amplitude model, which can be used for target detection under sea clutter conditions.
Background
In the process of sea clutter target detection development, the matching precision of the sea clutter simulation model and the actual sea clutter distribution characteristic is an important consideration premise of the construction of 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 sea clutter background depends on the parameters of the sea clutter amplitude model. 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, and the complex Gaussian model can be used for describing the amplitude characteristics of the sea clutter, and the amplitude model of the sea clutter is usually Rayleigh distribution. However, with the increasing resolution of radar, the conventional complex gaussian model cannot meet the requirement of accurately describing the characteristics of sea clutter. For low ground wiping angles and high-resolution radars, compared with a Rayleigh distribution model, the amplitude distribution of the sea clutter can appear longer trailing and present stronger non-Gaussian property, and the non-Gaussian model is needed 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 fast varying complex gaussian speckle component. For the complex Gaussian model, the speckle component is approximately constant in the sea clutter detection time period, and the statistical property of the complex Gaussian model is mainly influenced by the texture component. When the texture component accords with the inverse gamma distribution, the sea clutter amplitude model accords with the generalized pareto distribution.
The maximum likelihood estimation can realize parameter estimation of the generalized pareto sea clutter amplitude model, but the estimated parameter characteristics are unstable. The literature "BALLERI A, NEHORAI A, and WANG J.Maximum likelihood estimation for compound-Gaussian clutter with inverse Gamma texture [ J ]. IEEE Transactions on Aerospace and Electronic Systems,2007,43 (2): 775-780." proposes a maximum likelihood estimation method that uses an iterative method to estimate parameters, improving estimation accuracy. However, the method does not consider the influence of the abnormal sample on clutter parameter estimation, and for real sea clutter data, the sample often contains a small amount of high-power abnormal values, so that the maximum likelihood estimation performance is greatly reduced, and the accuracy is greatly reduced.
The document "P-L.Shui and M.Liu," Subband adaptive GLRT-LTD for weak moving targets in sea clutter, "IEEE Trans. Aerosp. Electron. Syst.,52 (1): 423-437, 2016)" proposes a method of bipartite estimation where the sample accumulation probability is 0.5 and 0.75, and the fixed bipartite estimation is not accurate due to the fixed estimation points.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a three-position point parameter estimation method of a generalized pareto sea clutter amplitude model. The technical problems to be solved by the invention are realized by the following technical scheme:
the invention provides a three-point parameter estimation method of a generalized pareto sea clutter amplitude model, which comprises the following steps:
s1: acquiring sea clutter pulse echo data, and performing modular value increment sequencing to generate a modular value increment sequence of sea clutter echo pulses;
s2: acquiring a second cumulative probability distribution function of a sea clutter model of generalized pareto distribution;
s3: setting a first cumulative probability and a second cumulative probability according to the second cumulative probability 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 and a second amplitude quantile by using a modular value increasing sequence of the sea clutter echo pulse;
s6: obtaining a shape parameter estimated value of a generalized pareto distribution amplitude model according to the estimated values of the first amplitude quantile and the second amplitude quantile;
s7: and obtaining a scale parameter estimated value of the generalized pareto sea clutter amplitude model according to the shape parameter estimated value.
In one embodiment of the present invention, the S2 includes:
s21: acquiring an amplitude probability density function f (r; mu, v) of a sea clutter model of generalized pareto distribution:
wherein r represents the sea clutter amplitude of the generalized pareto sea clutter amplitude model, mu 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: 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 probability distribution function F (r; 1, v) of the generalized pareto sea clutter amplitude model according to the first cumulative probability distribution function F (r; mu, v):
in one embodiment of the present invention, the S3 includes:
obtaining an expression of a first cumulative probability alpha and a second cumulative probability beta according to the expression of the second cumulative probability 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 0.1<α+0.1<β<1，r α A first amplitude quantile, r, corresponding to a first cumulative probability, alpha β And a second amplitude quantile corresponding to a second cumulative probability beta.
In one embodiment of the present invention, the S4 includes:
s41: dividing the third amplitude into points r according to an estimation error empirical formula ζ The estimation error of (2) is expressed as:
wherein sigma ζ Representing a third amplitude quantile r ζ μ is a scale parameter, v is a shape parameter, ζ represents a third cumulative probability;
s42: setting a shape parameter v between intervals [1,30], traversing the values at intervals of 0.01, and obtaining a plurality of shape parameters gamma;
s43: setting the third cumulative probability zeta between intervals [0.1,0.99], 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 determined according to the formula in S52 ζ Calculating the estimation errors of the parameters to obtain the optimal third accumulation probability corresponding to the parameters with different shapes;
s45: fitting the optimal third cumulative probability 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 one embodiment of the present invention, the S5 includes:
and (2) obtaining estimated values of the first amplitude quantile and the second amplitude quantile by utilizing the modular value increasing sequence of the sea clutter echo pulse obtained in the step (S1):
wherein,for the first amplitude quantile r α Estimated value of ∈10->For the second amplitude quantile r β Round (N x α) represents an integer nearest to N x α, and round (N x β) represents an integer nearest to N x β.
In one embodiment of the present invention, the S6 includes:
s61: given a positive number q greater than 1, the first cumulative probability α and the second cumulative probability β satisfy:
s62: calculating a second quantile estimateAnd a first quantile estimate +.>Square t of the ratio of (2):
s63: obtaining a generalized pareto distribution shape parameter estimation algorithm expression according to the relation between the second cumulative probability distribution function F (r; 1, v) and the first cumulative probability alpha and the second cumulative probability beta:
s64: setting up an intermediate parameter u to letObtaining shape parameter estimate +.>The relational expression of the intermediate parameter u is:
s65: solving for estimated values of shape parameters by iterationThe expression is as follows:
wherein the initial valueu 0 E (1, + -infinity), k is the number of iterations.
In one embodiment of the present invention, the S7 includes:
s71: a functional expression according to a third cumulative probability and a shape parameter and the shape parameter estimation valueCalculating a third cumulative probability value ζ;
s72: using the cumulative distribution function, the third cumulative probability ζ and the shape parameter estimation valueObtaining an estimate of the scale parameter mu>
In one embodiment of the present invention, the S72 includes:
s721: calculating a third amplitude quantile r corresponding to the third cumulative probability ζ ζ Estimate of (2)
Wherein round (N x ζ) represents an integer closest to N x ζ;
s722: according to a cumulative distribution function F (r) corresponding to the third cumulative probability ζ ζ The method comprises the steps of carrying out a first treatment on the surface of the μ, γ) to obtain scale parameter estimation valuesIs represented by the expression:
another aspect of the present invention provides a storage medium having stored therein a computer program for performing the steps of the three-point parameter estimation method of the generalized pareto sea clutter amplitude model of any of the above embodiments.
In a further aspect, the present invention provides an electronic device, including a memory and a processor, where the memory stores a computer program, and the processor, when invoking the computer program in the memory, implements the steps of the method for estimating three-point position parameters of the generalized pareto sea clutter amplitude model according to any of the embodiments above.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the three-position point parameter estimation method of the generalized pareto sea clutter amplitude model, parameter estimation is carried out by utilizing position point information, so that the influence of a larger abnormal constant value in original data on parameter estimation performance can be effectively reduced, compared with the existing moment estimation method, the three-position point parameter estimation method has higher abnormal data resistance, and further the accuracy of target detection under sea clutter background is improved.
2. According to the three-position point parameter estimation method of the generalized pareto sea clutter amplitude model, a functional expression of a cumulative probability value and a shape parameter of scale parameter estimation is constructed by utilizing a theoretical formula, and the scale parameter estimation can be accurately realized under the condition that the shape parameter is known. Meanwhile, compared with double-quantile estimation, the method introduces a third quantile to have smaller estimation error and better estimation performance on the scale parameters.
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-position point parameter estimation method of a generalized pareto sea clutter amplitude model provided by an embodiment of the invention;
FIG. 2a is a graph of a comparison of the relative root mean square error of shape parameter estimation using an embodiment of the present invention and two prior art methods;
FIG. 2b is a graph of relative root mean square error versus shape parameter estimation for a bipartite and a three-partition estimation method according to an embodiment of the invention;
FIG. 2c is a graph of a comparison of the relative root mean square error for a scale parameter estimation using two methods of the present invention and prior art;
FIG. 2d is a graph of relative root mean square error versus a two-part point and a three-part point estimation method of an embodiment of the invention for scale parameter estimation.
Detailed Description
In order to further explain the technical means and effects adopted by the invention to achieve the preset aim, the invention provides a three-position point parameter estimation method of a generalized pareto sea clutter amplitude model, which is described in detail below with reference to the accompanying drawings and the specific embodiments.
The foregoing and other features, aspects, and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments when taken in conjunction with the accompanying drawings. The technical means and effects adopted by the present invention to achieve the intended 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 intended to limit the technical scheme of the present invention.
It should be noted that in this document relational terms such as first and second, and the like are 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. Moreover, 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 one … …" does not exclude the presence of other like elements in an article or apparatus that comprises the element.
In an actual radar working environment, target detection processing is required to be carried out 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 test 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 backgrounds. 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 parameter is to the sea clutter real characteristic parameter, the higher the target detection accuracy is.
The embodiment of the invention aims to provide a three-point parameter estimation method of a generalized pareto sea clutter amplitude model, which is more accurate in estimating the scale parameters and the shape parameters of the clutter under the sea clutter meeting the generalized pareto distribution, and the detection threshold of a target detector designed by the scale parameters and the shape parameters obtained by the method is better, the control of the target detection false alarm rate is better, and the detection precision is higher.
Referring to fig. 1, fig. 1 is a flowchart of a three-position point parameter estimation method of a generalized pareto sea clutter amplitude model according to an embodiment of the present invention. The method comprises the following steps:
s1: and acquiring the sea clutter pulse echo data, and performing modular value increment sequencing to generate a modular value increment sequence of the sea clutter echo pulse.
Electromagnetic pulse signals transmitted by the radar transmitter are scattered at sea level, echo signals of the electromagnetic pulse signals are subjected to complex Gaussian distribution of inverse Gaussian textures after passing through the radar receiver, and sea clutter pulse echo data are obtained through simulation:
{r 1 ,r 2 ,....,r i ,....,r N }
where i=1, 2, …, N represents the number of sea clutter pulse echo data, r i Representing the amplitude of the ith one of the sea clutter pulse echo data.
And then, performing modular value increment sequencing on the sea clutter pulse echo data to obtain a modular value increment sequence of the sea clutter pulse echo data.
S2: and obtaining a second cumulative probability distribution function of the sea clutter model of the generalized pareto distribution.
In this embodiment, step S2 specifically includes:
s21: acquiring an amplitude probability density function f (r; mu, v) of a sea clutter model of generalized pareto distribution:
wherein r represents the sea clutter amplitude of the generalized pareto sea clutter amplitude model, mu 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; μ, γ) obtained in step S21 is integrated to obtain a first cumulative probability distribution function of the generalized pareto sea clutter amplitude model:
s23: and obtaining a second cumulative probability distribution function F (r; 1, v) of the generalized pareto sea clutter amplitude model according to the first cumulative probability distribution function F (r; mu, v).
Specifically, the scale parameter μ of the first cumulative probability distribution function F (r; μ, v) is fixed to 1, resulting in the second cumulative probability distribution function F (r; 1, v):
s3: and setting a first cumulative probability and a second cumulative probability according to the second cumulative probability distribution function.
According to the expression of the second cumulative probability distribution function F (r; 1, v), the first cumulative probability alpha and the second cumulative probability beta of the second cumulative probability 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)
wherein 0.1<α+0.1<β<1，r α A first amplitude quantile, r, corresponding to a first cumulative probability, alpha β And a second amplitude quantile corresponding to a second cumulative probability beta.
S4: and constructing a functional expression of the third cumulative probability and the shape parameter.
Specifically, the S4 includes:
s41: the third amplitude dividing point r is obtained according to an estimation error empirical formula under the premise that the number of samples (in the embodiment, the number N of sea clutter pulse echo data) is given ζ Estimate of (2)Obeying a progressive normal distribution, a third amplitude quantile r ζ The estimation error of (2) can be expressed as:
wherein sigma ζ Representing a third amplitude quantile r ζ μ is a scale parameter, v is a shape parameter, ζ represents a third cumulative probability.
S42: and setting the shape parameter v between the intervals [1,30], and traversing the values 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, and 30 in this order.
S43: the third cumulative probability ζ is set between intervals [0.1,0.99], values are traversed at intervals of 0.01, and a plurality of values of the third cumulative probability ζ are obtained. That is, the third cumulative probability ζ has values of 0, 0.1, 0.11, 0.12, … …, 0.98, and 0.99 in this order.
S44: for each shape parameter γ obtained in step S42, for a third amplitude quantile r ζ And (3) calculating the estimation errors of the parameters to obtain the optimal third cumulative probability corresponding to the parameters with different shapes.
Specifically, for a given shape parameter γ, all values of the third cumulative probability are traversed, and a third magnitude quantile r is recorded ζ Estimation error sigma of (2) ζ A shape parameter value and a third cumulative probability value under the minimum condition, wherein one shape parameter value can obtain an optimal third cumulative probability; then, another shape parameter is selected, the steps are repeated to obtain the optimal third cumulative probability of the shape parameter, and the like, a group of shape parameter values can obtain a group of optimal third cumulative probability. In the calculation, the scale parameter μ is fixed to 1.
S45: fitting the optimal third cumulative probability corresponding to the different shape parameters according to the result obtained in the step S44 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 (7)
where γ represents a shape parameter and ζ represents a third cumulative probability.
S5: obtaining a first amplitude quantile r by using the modular value increasing sequence of the sea clutter echo pulse α And a second amplitude quantile r β Is used for the estimation of the estimated value of (a).
Specifically, using the modular value increasing sequence of the sea clutter echo pulse obtained in the step S1, an estimated value of the first amplitude quantile and the second amplitude quantile is obtained:
wherein,for dividing the first amplitude into pointsr α Estimated value of ∈10->For the second amplitude quantile r β Round (N x α) represents an integer nearest to N x α, and round (N x β) represents an integer nearest to N x β.
S6: obtaining a shape parameter estimated value of a generalized pareto distribution amplitude model according to the estimated values of the first amplitude quantile and the second amplitude quantile
In this embodiment, the step S6 includes:
s61: given a positive number q greater than 1, the first cumulative probability α and the second cumulative probability β satisfy:
s62: calculating a second quantile estimateAnd a first quantile estimate +.>Square t of the ratio of (2):
s63: according to formulas (3), (4) and (5), (9), (10), the deformation yields:
further, the two formulas are deformed, and the square of the ratio of the first amplitude quantile to the second amplitude quantile is provided, so that a generalized pareto distribution shape parameter estimation algorithm expression is obtained:
s64: setting up an intermediate parameter u to letObtaining a simplified shape parameter estimation algorithm expression:
wherein the intermediate parameter u >1;
deforming the shape according to the expression of u to obtain shape parameter estimated valueAnd the relation expression of the intermediate parameter u:
s65: solving for estimated values of shape parameters by iterationThe expression is as follows:
wherein the initial value u 0 ∈(1,+∞)，u 0 Take any value in the range, here u 0 =2, k is the number of iterations, and k takes 200 in the simulation. At this time, the shape parameter can be estimated according to the formula (15)Metering valueThe relation expression with the intermediate parameter u gives a shape parameter estimate +.>
S7: and obtaining a scale parameter estimated value of the generalized pareto sea clutter amplitude model according to the shape parameter estimated value.
In this embodiment, the step S7 includes:
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 parameterThe value of the third cumulative probability ζ is calculated.
Specifically, the shape parameter estimation value obtained in step S65 isSubstituting the value into the formula (7) to obtain a value of a third cumulative probability ζ.
S72: using the cumulative distribution function, the third cumulative probability ζ and the shape parameter estimation valueObtaining an estimate of the scale parameter mu>
Specifically, the S72 includes:
s721: calculating a third amplitude quantile r corresponding to the third cumulative probability ζ ζ Estimate of (2)
Wherein round (N x ζ) represents an integer closest to N x ζ.
S722: third amplitude quantile r calculated according to equation (17) ζ Estimate of (2)And deforming the functional form to obtain a functional expression of the scale parameter mu.
In the present embodiment, let the third cumulative probability ζ be the corresponding cumulative distribution function F (r ζ The method comprises the steps of carrying out a first treatment on the surface of the μ, γ) has:
and (3) for the deformation, providing a scale parameter mu to obtain an estimated value expression of the scale parameter mu:
wherein ζ is a third cumulative probability value, and v is a shape parameter.
S723: substituting a third cumulative probability ζ according to a functional expression of the scale parameter μ of formula (19), and quantilling the estimated value with a third magnitudeInstead of r in formula (19) ζ Estimated value +.>Instead of v in equation (19), a scale parameter estimate is obtained>Is represented by the expression:
according to the formula (20), the scale parameter estimation value of the complex Gaussian sea clutter model with the inverse Gaussian texture can be obtained
Further, obtaining the scale parameter estimation value of the generalized pareto sea clutter amplitude modelAnd shape parameter estimation value +.>Then, according to the obtained scale parameter estimation value +.>And shape parameter estimation value +.>The detection threshold of the target detector can be more accurately selected, and further a more accurate target detection result is obtained.
The effect of the three-point parameter estimation method of the generalized pareto sea clutter amplitude model is further described below by combining simulation experiments.
(1) Simulation parameter setting
Clutter data compliant with a generalized pareto sea clutter amplitude model is generated using MATLAB software simulation, where the number of samples (the number of sea clutter pulse echo data) n=10000. The shape parameter is set to interval 1.2,20, interval 0.05, and scale parameter μ is set to 1. And randomly adding abnormal samples, wherein the ratio of the abnormal sample power to the clutter power is a random number between 10 and 100, and the ratio 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) Simulation experiment contents
The method, the 2-4 order moment estimation and the double-division point estimation are adopted to estimate the shape parameters and the scale parameters of the data sample 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 parameters estimated by the embodiment of the invention and the two existing methods, wherein the abscissa is linear to represent the shape parameter value, and the ordinate is logarithmic to represent the relative root mean square error of the shape parameters; FIG. 2b is a graph showing the comparison of the relative root mean square error of the shape parameter estimation of the two-part point estimation method and the three-part point estimation method according to the embodiment of the invention, wherein the comparison of the two-part point estimation method is not obvious due to the poor moment estimation precision, and the graph is compared with the three-part point estimation method, wherein the abscissa represents the value of the shape parameter linearly, and the ordinate represents the relative root mean square error of the shape parameter; FIG. 2c is a graph showing a comparison of the relative root mean square error of a scale parameter estimation using two methods according to an embodiment of the present invention and the prior art, wherein the abscissa indicates the shape parameter value linearly and the ordinate indicates the relative root mean square error of the scale parameter; fig. 2d is a comparison of relative root mean square errors of scale parameter estimation of a bipartite point and a three-partition point estimation method according to an embodiment of the present invention, wherein the comparison of the bipartite points is not obvious due to poor moment estimation accuracy, the comparison of the bipartite point estimation method is performed in the present invention, wherein the abscissa line represents the value of a shape parameter, and the ordinate logarithm represents the relative root mean square error of the scale parameter.
As can be seen from fig. 2a and fig. 2b, when the number of samples N is the same and the shape parameter estimation is performed by 3 methods, the performance of the 2-4 order moment estimation and the bipartite point estimation is degraded due to the influence of the outlier, wherein the relative root mean square error of the 2-4 order moment estimation method is the largest, the relative root mean square error of the bipartite point estimation method is slightly larger than that of the method of the present invention, and the relative root mean square error of 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 of samples N is the same and the scale parameter estimation is performed by 3 methods, the performance of the 2-4 moment estimation method is significantly degraded, and the performance of the bipartite estimation method is slightly worse than that of the method of the present invention. From the results, the method of the embodiment of the invention has the advantages of minimum relative root mean square error and best estimation performance.
As can be seen from comparing fig. 2a to fig. 2d, the 2-4 order moment estimation uses the sample to estimate the parameters of the generalized pareto sea clutter amplitude model, so the relative root mean square error is greatly affected by the abnormal sample. The double-quantile 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 quantile for estimating the optimal, so that the method has the best anti-abnormal sample capability and relatively high calculation efficiency. In actual radar target detection, abnormal points are unavoidable, and the method of the embodiment of the invention is advanced under the trend of eliminating the influence caused by the abnormal points as much as possible.
In general, the three-position point parameter estimation method of the generalized pareto sea clutter amplitude model provided by the embodiment of the invention utilizes the position point information to carry out parameter estimation, can effectively reduce the influence of abnormal constant values with larger power in original data on parameter estimation performance, has higher abnormal data resistance compared with the existing moment estimation method, and in addition, the method utilizes a theoretical formula to construct a function expression of a cumulative probability value and shape parameters of scale parameter estimation, and can more accurately realize the estimation of the scale parameters under the condition of known shape parameters. Meanwhile, compared with double-quantile estimation, the method introduces a third quantile to have smaller estimation error and better estimation performance on the scale parameters.
A further embodiment of the present invention provides a storage medium having stored therein a computer program for performing the steps of the method described in the above embodiments. In a further aspect the invention provides an electronic device comprising a memory having a computer program stored therein and a processor implementing the steps of the method according to the above embodiments when the processor invokes the computer program in the memory. In particular, the integrated modules described above, implemented in the form of software functional modules, may be stored in a computer readable storage medium. The software functional module is stored in a storage medium and includes instructions for causing an electronic device (which may be a personal computer, a server, or a network device, etc.) or a processor (processor) to perform part of the steps of the methods described in the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.
Claims (4)
1. The three-position point parameter estimation method of the generalized pareto sea clutter amplitude model is characterized by comprising the following steps of:
s1: acquiring sea clutter pulse echo data, and performing modular value increment sequencing to generate a modular value increment sequence of sea clutter echo pulses;
s2: acquiring a second cumulative probability distribution function of a sea clutter model of generalized pareto distribution;
s3: setting a first cumulative probability and a second cumulative probability according to the second cumulative probability 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 and a second amplitude quantile by using a modular value increasing sequence of the sea clutter echo pulse;
s6: obtaining a shape parameter estimated value of a generalized pareto distribution amplitude model according to the estimated values of the first amplitude quantile and the second amplitude quantile;
s7: obtaining a scale parameter estimated value of the generalized pareto sea clutter amplitude model according to the shape parameter estimated value,
the step S2 comprises the following steps:
s21: acquiring an amplitude probability density function f (r; mu, v) of a sea clutter model of generalized pareto distribution:
wherein r represents the sea clutter amplitude of the generalized pareto sea clutter amplitude model, mu 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: 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 probability distribution function F (r; 1, v) of the generalized pareto sea clutter amplitude model according to the first cumulative probability distribution function F (r; mu, v):
the step S3 comprises the following steps:
obtaining an expression of a first cumulative probability alpha and a second cumulative probability beta according to the expression of the second cumulative probability 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 0.1<α+0.1<β<1，r α A first amplitude quantile, r, corresponding to a first cumulative probability, alpha β For a second magnitude quantile corresponding to a second cumulative probability beta,
the step S4 comprises the following steps:
s41: dividing the third amplitude into points r according to an estimation error empirical formula ζ The estimation error of (2) is expressed as:
wherein sigma ζ Representing a third amplitude quantile r ζ μ is a scale parameter, v is a shape parameter, ζ represents a third cumulative probability;
s42: setting a shape parameter v between intervals [1,30], traversing the values at intervals of 0.01, and obtaining a plurality of shape parameters gamma;
s43: setting the third cumulative probability zeta between intervals [0.1,0.99], 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 determined according to the formula in S52 ζ Calculating the estimation errors of the parameters to obtain the optimal third accumulation probability corresponding to the parameters with different shapes;
s45: fitting the optimal third cumulative probability 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
wherein gamma denotes a shape parameter, ζ denotes a third cumulative probability,
the step S5 comprises the following steps:
and (2) obtaining estimated values of the first amplitude quantile and the second amplitude quantile by utilizing the modular value increasing sequence of the sea clutter echo pulse obtained in the step (S1):
wherein,for the first amplitude quantile r α Estimated value of ∈10->For the second amplitude quantile r β Round (N x a) represents an integer nearest to N x a, round (N x β) represents an integer nearest to N x β,
the step S6 comprises the following steps:
s61: given a positive number q greater than 1, the first cumulative probability α and the second cumulative probability β satisfy:
s62: calculating a second quantile estimateAnd a first quantile estimate +.>Square t of the ratio of (2):
s63: obtaining a generalized pareto distribution shape parameter estimation algorithm expression according to the relation between the second cumulative probability distribution function F (r; 1, v) and the first cumulative probability alpha and the second cumulative probability beta:
s64: setting up an intermediate parameter u to letObtaining shape parameter estimate +.>The relational expression of the intermediate parameter u is:
s65: solving for estimated values of shape parameters by iterationThe expression is as follows:
wherein the initial value u 0 E (1, + -infinity), k is the number of iterations,
the step S7 comprises the following steps:
s71: a functional expression according to a third cumulative probability and a shape parameter and the shape parameter estimation valueCalculating a third cumulative probability value ζ;
s72: using the cumulative distribution function, the third cumulative probability ζ and the shape parameter estimation valueObtaining an estimate of the scale parameter μ
2. The method for three-point parameter estimation of a generalized pareto sea clutter amplitude model according to claim 1, wherein the step S72 comprises:
s721: calculating a third amplitude quantile r corresponding to the third cumulative probability ζ ζ Estimate of (2)
Wherein round (N x ζ) represents an integer closest to N x ζ;
s722: according to a cumulative distribution function F (r) corresponding to the third cumulative probability ζ ζ The method comprises the steps of carrying out a first treatment on the surface of the μ, γ) to obtain scale parameter estimation valuesIs represented by the expression:
3. a storage medium, wherein a computer program is stored in the storage medium, and the computer program is configured to perform the steps of the method for estimating the three-position point parameter of the generalized pareto sea clutter amplitude model according to claim 1 or 2.
4. An electronic device comprising a memory and a processor, the memory having stored therein a computer program, the processor implementing the steps of the three-dimensional point parameter estimation method of the generalized pareto sea clutter amplitude model according to claim 1 or 2 when invoking the computer program in the memory.
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