A method for modeling a radar sea clutter amplitude tail distribution

Abstract

The present application belongs to the technical field of radar sea clutter modeling, and discloses a radar sea clutter amplitude tail distribution modeling method, comprising: obtaining clutter amplitude value data; deriving an amplitude tail probability density function based on the clutter amplitude value data, constructing a two-parameter exponential distribution model for describing clutter amplitude tail based on the probability density function; performing parameter estimation on the two-parameter exponential distribution model to obtain model estimation parameters; obtaining measured amplitude tail data, fitting the measured amplitude tail data based on the model estimation parameters to obtain fitting data, adjusting and optimizing the two-parameter exponential distribution model based on the fitting data to obtain an optimized two-parameter exponential distribution model. The technical solution disclosed by the present application can improve the accuracy of radar system target detection and lay a foundation for sea surface target detection under complex sea conditions.

Description

Technical Field

[0001] This invention belongs to the field of radar sea clutter modeling technology, and in particular relates to a method for modeling the amplitude tail distribution of radar sea clutter. Background Technology

[0002] When detecting maritime targets, radar is often interfered with by sea clutter. When radar resolution is high or sea state is high, breaking waves and whitecaps can generate strong scattered echoes, creating false alarms and adversely affecting radar target detection. The amplitude distribution of sea clutter is an important aspect describing its characteristics and is a crucial basis for setting radar detection thresholds and conducting statistical verification.

[0003] Currently, research on sea clutter amplitude distribution mainly focuses on the analysis of the overall amplitude distribution. However, the amplitude distribution characteristics of sea clutter in different radar systems under different scenarios are usually inconsistent, which poses challenges to the setting of radar detection thresholds and the design of detectors. Traditional sea clutter amplitude distribution models, such as log-normal distribution, Weibull distribution, and K distribution, can describe the amplitude distribution of sea clutter to a certain extent, but their fitting effect on the amplitude tail is not ideal. Composite distribution models improve the fitting effect to some extent by introducing different texture component models (such as inverse Gamma distribution, inverse Gaussian distribution, etc.) to model sea clutter, but they still have the problem of limited applicability in certain scenarios.

[0004] Considering that the false alarm probability of radar is usually controlled at a low level, the radar detection threshold only needs to be obtained based on the clutter amplitude tail distribution. Therefore, modeling the radar sea clutter amplitude tail distribution is more instructive for radar target detection. However, there are few studies on dedicated modeling of amplitude tail distribution, especially lacking a universally applicable model for modeling sea clutter amplitude tails under different scenarios. Summary of the Invention

[0005] The purpose of this invention is to provide a radar sea clutter amplitude tail distribution modeling method to solve the problems existing in the prior art.

[0006] To achieve the above objectives, this invention provides a method for modeling the amplitude tail distribution of radar sea clutter, comprising:

[0007] Obtain clutter amplitude data;

[0008] Based on the clutter amplitude data, the probability density function of amplitude tail is derived, and a two-parameter exponential distribution model for describing clutter amplitude tail is constructed based on the probability density function.

[0009] The parameters of the two-parameter exponential distribution model are estimated to obtain the model estimated parameters.

[0010] Obtain measured amplitude trailing data, fit the measured amplitude trailing data based on the model estimation parameters to obtain fitted data, and adjust and optimize the two-parameter exponential distribution model based on the fitted data to obtain the optimized two-parameter exponential distribution model.

[0011] Optionally, deriving the probability density function of the amplitude tail based on the clutter amplitude value data specifically includes:

[0012] Each clutter amplitude measurement process is treated as an independent experiment, and a binomial distribution is used to describe the probability of amplitude data falling into the tailing interval. The binomial distribution is transformed into a Poisson distribution. After the transformation, an event and its corresponding probability are set. The event is that a number of data points in the amplitude data fall into a preset interval.

[0013] After the event is defined, the absence of data points in the preset interval is taken as the initial condition, and the probability corresponding to the initial condition is solved. Based on the probability corresponding to the initial condition, the distribution function of amplitude tailing is derived, and the probability density function is obtained by differentiating the distribution function.

[0014] Optionally, the distribution function of the amplitude tail is specifically:

[0015] F(y)=P(η<Y≤y)=1-P(Y≤η)=1-e -λ(y-η) ,y∈(η,∞)

[0016] In the formula, F(y) represents the distribution function of amplitude tailing, η represents the lower limit of amplitude tailing, i.e., the position parameter, y represents the tailing amplitude value, with a value range of y∈(η,∞), P(Y≤η) is the probability that the data without tailing falls into the interval (η,∞), Y is the amplitude tailing, e represents the natural logarithm, and λ represents the shape parameter.

[0017] Optionally, the probability density function is specifically:

[0018] p(y)=λe -λ(y-η) ,y∈(η,∞)

[0019] In the formula, p(y) is the probability density function of the amplitude tail, y represents the amplitude value of the tail, the range of y∈(η,∞), η represents the lower limit of the amplitude tail, e represents the natural logarithm, and λ represents the shape parameter.

[0020] Optionally, the parameter estimation of the two-parameter exponential distribution model specifically includes:

[0021] Obtain the trailing data located at the end of the distribution in the clutter amplitude value data;

[0022] Calculate the first and second moments of the trailing data to obtain statistical data;

[0023] The parameters of the two-parameter exponential distribution model are estimated based on the statistical data.

[0024] Optionally, the calculation process of the statistical data specifically includes:

[0025]

[0026] In the formula, m1 is the first moment of the trailing data, m2 is the second moment of the trailing data, N1 is the amount of trailing amplitude data, and y i This represents the value for each trailing amplitude.

[0027] Optionally, the parameters of the two-parameter exponential distribution model are estimated based on the statistical data, and the specific calculation formula is as follows:

[0028]

[0029] In the formula, m1 is the first moment of the trailing data, and m2 is the second moment of the trailing data. For parameter estimation of shape parameter λ, This is a parameter estimate for the position parameter η.

[0030] Optionally, the adjustment and optimization process of the two-parameter exponential distribution model specifically includes:

[0031] The goodness of fit of the two-parameter exponential distribution model is evaluated based on the fitted data, and the two-parameter exponential distribution model is adjusted and optimized based on the goodness of fit to obtain the optimized two-parameter exponential distribution model.

[0032] The technical effects of this invention are as follows:

[0033] This invention, by more accurately modeling the amplitude tail distribution of sea clutter, can more effectively distinguish target signals from background noise, effectively reduce the fitting error of clutter amplitude tail, improve the accuracy of radar system target detection, and lay the foundation for sea surface target detection under complex sea conditions. Through parameter estimation and fitting of measured data, this method can adapt to different radar systems and operating conditions, enhancing the universality and applicability of the model. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0036] Figure 1 This is a flowchart illustrating the implementation of the radar sea clutter amplitude tail distribution modeling method in this embodiment of the invention.

[0037] Figure 2 This is a fitting effect diagram of the tail distribution of the SDRDSP measured data in an embodiment of the present invention;

[0038] Figure 3 This is a fitting diagram of the tail distribution of the IPIX measured data in an embodiment of the present invention. Detailed Implementation

[0039] Various exemplary embodiments of the present invention will now be described in detail. This detailed description should not be considered as a limitation of the present invention, but rather as a more detailed description of certain aspects, features, and embodiments of the present invention.

[0040] It should be understood that the terminology used in this invention is merely for describing particular embodiments and is not intended to limit the invention. Furthermore, with respect to numerical ranges in this invention, it should be understood that each intermediate value between the upper and lower limits of the range is also specifically disclosed. Every smaller range between any stated value or intermediate value within a stated range, and any other stated value or intermediate value within said range, is also included in this invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0041] Unless otherwise stated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. While only preferred methods have been described herein, any methods similar or equivalent to those described herein may be used in the implementation or testing of this invention. All references to this specification are incorporated by way of citation to disclose and describe the methods associated with those references. In the event of any conflict with any incorporated reference, the content of this specification shall prevail.

[0042] Various modifications and variations can be made to the specific embodiments described in this specification without departing from the scope or spirit of the invention, as will be apparent to those skilled in the art. Other embodiments derived from this specification will also be obvious to those skilled in the art. This application specification and embodiments are merely exemplary.

[0043] The terms “include,” “including,” “have,” “contain,” etc., used in this article are all open-ended terms, meaning that they include but are not limited to.

[0044] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0045] Example 1

[0046] like Figure 1 - Figure 3 As shown in the figure, this embodiment provides a method for modeling the amplitude trailing distribution of radar sea clutter, including: acquiring clutter amplitude value data; deriving the probability density function of the amplitude trailing based on the clutter amplitude value data; constructing a two-parameter exponential distribution model to describe the clutter amplitude trailing based on the probability density function; estimating the parameters of the two-parameter exponential distribution model to obtain model estimation parameters; acquiring measured amplitude trailing data; fitting the measured amplitude trailing data based on the model estimation parameters to obtain fitted data; and adjusting and optimizing the two-parameter exponential distribution model based on the fitted data to obtain an optimized two-parameter exponential distribution model.

[0047] This embodiment addresses the problem that existing technologies cannot adequately describe the distribution of radar sea clutter tails under different scenarios. It proposes a modeling method for radar sea clutter amplitude tail distribution, derives a two-parameter exponential distribution model for sea clutter amplitude tails using measured data, and verifies the effectiveness of the model.

[0048] Figure 1 The flowchart of the radar sea clutter amplitude tail distribution modeling method in this embodiment includes:

[0049] Step 1, Derivation of the Two-Parameter Exponential Distribution Model, specifically includes the following sub-steps:

[0050] Step (a) treats each amplitude value as an independent experiment, and uses P according to the binomial distribution. k Let represent the probability that k values ​​fall within the tailing interval (η,∞). Then, the probability that k values ​​fall within the tailing interval in N observations is:

[0051]

[0052] As the number of values ​​increases, when N→∞, letting λ1=Np, the above equation can be simplified to a Poisson distribution:

[0053]

[0054] Step (b): Let the event {N(η,y)=k1} represent that k1 data points fall within the interval (η,y) in the amplitude range, and its probability be expressed as... Let N(η,y) represent the tail amplitude value, where y∈(η,∞) represents the amount of data within the amplitude interval (η,y]. Therefore:

[0055] Step (c), based on the condition: for sufficiently small Δy, when k1=1, we have P1(y,y+Δy)=λΔy+ο(Δy); when k1≥2, the probability of {N(y,y+Δy)=k1} occurring twice or more is negligible compared to the probability of it occurring once. Consider P0(η,y), that is, the probability when there are no data points in the interval (η,y):

[0056] P0(η,y+Δy)=P{N(η,y+Δy)=0}

[0057] =P{N(η,y)+N(y,y+Δy)=0}

[0058] =P{N(η,y)=0,N(y,y+Δy)=0}

[0059] =P0(η,y)[1-λΔy+ο(Δy)]

[0060] Step (d) takes P0(η,η)=P{N(η,η)=0}=1 as the initial condition and solves it to get:

[0061] P0(η,y)=e -λ(y-η) ,y∈(η,∞)

[0062] In step (e), the probability that the data without tails falls into the interval (η,∞) can be expressed as P(Y≤η)=P0(η,y),y∈(η,∞), and thus the distribution function F(y) of the amplitude tail Y is obtained as:

[0063] F(y)=P(η<Y≤y)=1-P(Y≤η)=1-e -λ(y-η) ,y∈(η,∞)

[0064] In the formula, F(y) represents the distribution function of amplitude tailing, η represents the lower limit of amplitude tailing, i.e., the position parameter, y represents the tailing amplitude value, with a value range of y∈(η,∞), P(Y≤η) is the probability that the data without tailing falls into the interval (η,∞), Y is the amplitude tailing, e represents the natural logarithm, and λ represents the shape parameter.

[0065] Step (f), differentiating the above equation, yields the probability density function p(y) of the trailing amplitude:

[0066] p(y)=λe -λ(y-η) ,y∈(η,∞)

[0067] Step 2, model parameter estimation, specifically includes the following sub-steps:

[0068] Step (a) Calculate the first and second moments m1 and m2 of the trailing data.

[0069]

[0070] In the formula, m1 is the first moment of the trailing data, m2 is the second moment of the trailing data, N1 is the amount of trailing amplitude data, and y i This represents the value for each trailing amplitude.

[0071] Step (b) further involves estimating the parameters of the two-parameter exponential distribution.

[0072]

[0073] In the formula, For parameter estimation of shape parameter λ, This is a parameter estimate for the position parameter η.

[0074] Step 3, fitting the measured data, specifically includes the following sub-steps:

[0075] Step (a), based on the false alarm probability P fa Filter data with trailing amplitude.

[0076] Step (b) involves fitting the amplitude tailing data based on the model parameters from step 2.

[0077] Figure 2 This is a fitting effect diagram of the SDRDSP measured data provided in this embodiment. The data is selected from the experimental data of the "Radar Maritime Detection Data Sharing Program (SDRDSP)" of the Naval Aviation University, file name 20210104163843_01_staring.mat. The specific parameters are as follows: pure clutter data of range cells 500-1000 are selected, and the false alarm rate is set to P. fa =0.001, filter out clutter tail data.

[0078] Figure 3 This is a fitting effect diagram of the IPIX measured data provided in this embodiment. The data used is IPIX radar test data, filename 19980223_165836_antstep.cdf. Specific parameters are as follows: This set of data is pure sea clutter data, and the false alarm rate is set to P. fa =0.01, filter out clutter tail data.

[0079] As can be seen from the above steps, the method proposed in this embodiment is more suitable for modeling the amplitude tail distribution of sea clutter compared with other extreme value distribution models.

[0080] This embodiment, by more accurately modeling the amplitude tail distribution of sea clutter, can more effectively distinguish target signals from background noise, effectively reduce the fitting error of clutter amplitude tail, improve the accuracy of radar system target detection, and lay the foundation for sea surface target detection under complex sea conditions. Through parameter estimation and fitting of measured data, this method can adapt to different radar systems and operating conditions, enhancing the universality and applicability of the model.

[0081] The above description is merely a preferred embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for modeling the amplitude tail distribution of radar sea clutter, characterized in that, include: Obtain clutter amplitude data; Based on the clutter amplitude data, the probability density function of amplitude tail is derived, and a two-parameter exponential distribution model for describing clutter amplitude tail is constructed based on the probability density function. The parameters of the two-parameter exponential distribution model are estimated to obtain the model estimated parameters. Obtain measured amplitude trailing data, fit the measured amplitude trailing data based on the model estimation parameters to obtain fitted data, and adjust and optimize the two-parameter exponential distribution model based on the fitted data to obtain the optimized two-parameter exponential distribution model. The derivation of the probability density function for amplitude tailing based on the clutter amplitude data specifically includes: Each clutter amplitude measurement process is treated as an independent experiment, and a binomial distribution is used to describe the probability of amplitude data falling into the tailing interval. The binomial distribution is transformed into a Poisson distribution. After the transformation, an event and its corresponding probability are set. The event is that a number of data points in the amplitude data fall into a preset interval. After the event is defined, the absence of data points in the preset interval is taken as the initial condition, and the probability corresponding to the initial condition is solved. Based on the probability corresponding to the initial condition, the distribution function of amplitude tailing is derived, and the probability density function is obtained by differentiating the distribution function. The distribution function for the amplitude tail is specifically as follows: F(y)=P(η<Y≤y)=1-P(Y≤η)=1-e -λ(y-η) ,y∈(η,∞) In the formula, F(y) represents the distribution function of amplitude tailing, η represents the lower limit of amplitude tailing, i.e., the position parameter, y represents the tailing amplitude value, with a value range of y∈(η,∞), P(Y≤η) is the probability that the data without tailing falls into the interval (η,∞), Y is the amplitude tailing, e represents the natural logarithm, and λ represents the shape parameter.

2. The radar sea clutter amplitude tail distribution modeling method according to claim 1, characterized in that, The probability density function is specifically: p(y)=λe -λ(y-η) ,y∈(η,∞) In the formula, p(y) is the probability density function of amplitude tailing, y represents the amplitude value of the tail, the range of values ​​is y∈(η,∞), η represents the lower limit of amplitude tailing, e represents the natural logarithm, and λ represents the shape parameter.

3. The radar sea clutter amplitude tail distribution modeling method according to claim 1, characterized in that, The parameter estimation of the two-parameter exponential distribution model specifically includes: Obtain the trailing data located at the end of the distribution in the clutter amplitude value data; Calculate the first and second moments of the trailing data to obtain statistical data; The parameters of the two-parameter exponential distribution model are estimated based on the statistical data.

4. The radar sea clutter amplitude tail distribution modeling method according to claim 3, characterized in that, The calculation process of the statistical data specifically includes: In the formula, m1 is the first moment of the trailing data, m2 is the second moment of the trailing data, N1 is the amount of trailing amplitude data, and y i This represents the value for each trailing amplitude.

5. The radar sea clutter amplitude tail distribution modeling method according to claim 3, characterized in that, The parameters of the two-parameter exponential distribution model are estimated based on the statistical data, and the specific calculation formula is as follows: In the formula, m1 is the first moment of the trailing data, and m2 is the second moment of the trailing data. For parameter estimation of shape parameter λ, This is a parameter estimate for the position parameter η.

6. The radar sea clutter amplitude tail distribution modeling method according to claim 1, characterized in that, The adjustment and optimization process of the two-parameter exponential distribution model specifically includes: The goodness of fit of the two-parameter exponential distribution model is evaluated based on the fitted data, and the two-parameter exponential distribution model is adjusted and optimized based on the goodness of fit to obtain the optimized two-parameter exponential distribution model.

Images