Radar sea clutter amplitude trailing distribution modeling method

Abstract

The invention belongs to the technical field of radar sea clutter modeling, and discloses a radar sea clutter amplitude trailing distribution modeling method, which comprises the following steps: acquiring clutter amplitude value data; deriving a probability density function of amplitude trailing based on the clutter amplitude value data, and constructing a two-parameter exponential distribution model for describing clutter amplitude trailing based on the probability density function; performing parameter estimation on the two-parameter exponential distribution model to obtain model estimation parameters; and obtaining actually measured amplitude trailing data, fitting the actually measured amplitude trailing data based on the model estimation parameters to obtain fitting data, and adjusting and optimizing the two-parameter exponential distribution model based on the fitting data to obtain an optimized two-parameter exponential distribution model. According to the technical scheme, the accuracy of target detection of a radar system can be improved, and a foundation is laid for sea surface target detection under complex sea conditions.

Description

Technical Field

[0001] The invention belongs to the technical field of radar sea clutter modeling, and in particular relates to a radar sea clutter amplitude tailing distribution modeling method. Background Art

[0002] When detecting targets at sea, radar is often interfered by sea clutter. When the radar resolution is high or the sea conditions are high, breaking waves, whitecaps, etc. will produce strong scattered echoes, forming clutter false alarms, which will have an adverse effect on radar target detection. The sea clutter amplitude distribution is an important aspect of describing the characteristics of sea clutter and is an important basis for radar detection threshold setting and statistical testing.

[0003] At present, the research on the amplitude distribution of sea clutter is mostly focused on the analysis of the overall amplitude distribution. However, the amplitude distribution characteristics of sea clutter in different radar systems in different scenarios are usually inconsistent, which brings challenges to the setting of radar detection thresholds and the design of detectors. Although 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, the fitting effect of the amplitude tail part is not ideal; the composite distribution model introduces different texture component models (such as inverse Gamma distribution, inverse Gaussian distribution, etc.) to model sea clutter, which improves the fitting effect to a certain extent, but there is still a problem of limited applicable scenarios.

[0004] Considering that the radar false alarm probability is usually controlled at a low level, at this time, the radar detection threshold only needs to be obtained according to 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 specialized modeling studies on amplitude tail distribution, especially the lack of a more universal model for the modeling of sea clutter amplitude tail in different scenarios. Summary of the invention

[0005] The object of the present invention is to provide a radar sea clutter amplitude tailing distribution modeling method to solve the problems existing in the above-mentioned prior art.

[0006] To achieve the above object, the present invention provides a radar sea clutter amplitude tailing distribution modeling method, comprising:

[0007] Obtain clutter amplitude value data;

[0008] Derivation of a probability density function of the amplitude tail based on the clutter amplitude value data, and construction of a two-parameter exponential distribution model for describing the clutter amplitude tail based on the probability density function;

[0009] Performing parameter estimation on the two-parameter exponential distribution model to obtain model estimation parameters;

[0010] Acquire measured amplitude tailing data, fit the measured amplitude tailing data based on the model estimation parameters to obtain fitting data, adjust and optimize the two-parameter exponential distribution model based on the fitting data to obtain an optimized two-parameter exponential distribution model.

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

[0012] Each clutter amplitude value acquisition process is treated as an independent experiment, and binomial distribution is used to describe the probability that the amplitude value data falls into the tailing interval. The binomial distribution is converted into a Poisson distribution. After the conversion is completed, an event and a corresponding probability are set. The event is that a number of data points in the amplitude value data fall into a preset interval.

[0013] After the event definition is completed, the absence of data points in the preset interval is used as the initial condition, and the probability corresponding to the initial condition is solved. The distribution function of the amplitude tail is derived based on the probability corresponding to the initial condition, and the distribution function is derived to obtain the probability density 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] Where F(y) represents the distribution function of the amplitude tail, η represents the lower limit of the amplitude tail, that is, the position parameter, y represents the tail amplitude value, and the value range is y∈(η,∞), P(Y≤η) is the probability that the no-tail data falls into the interval (η,∞), Y is the amplitude tail, 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] Where p(y) is the probability density function of the amplitude tailing, y represents the amplitude tailing value, and its value range is y∈(η,∞), η represents the lower limit of the amplitude tailing, e represents the natural logarithm, and λ represents the shape parameter.

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

[0021] Acquire tailing data located at the tail of the distribution in the clutter amplitude value data;

[0022] Calculate the first-order moment data and the second-order moment data of the tailing 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] Where m1 is the first-order moment of the tailing data, m2 is the second-order moment of the tailing data, N1 is the amount of tailing amplitude data, and y i Indicates the value of each tailing 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:

[0028]

[0029] Where m1 is the first-order moment of the tailing data, m2 is the second-order moment of the tailing data, is the parameter estimate of the shape parameter λ, is the parameter estimate of the location 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 fitting data, and the two-parameter exponential distribution model is adjusted and optimized based on the goodness of fit to obtain an optimized two-parameter exponential distribution model.

[0032] The technical effects of the present invention are:

[0033] The invention can more effectively distinguish target signals from background noise by more accurately modeling the amplitude tail distribution of sea clutter, effectively reduce the fitting error of the clutter amplitude tail, improve the accuracy of radar system in detecting targets, and lay a foundation for sea surface target detection under complex sea conditions; through parameter estimation and measured data fitting, the method can adapt to different radar systems and operating conditions, and enhance the universality and applicability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0035] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0036] Figure 1 is an implementation flow chart of a radar sea clutter amplitude tailing distribution modeling method in an embodiment of the present invention;

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

[0038] Figure 3 It is a fitting effect diagram of the tailing distribution of IPIX measured data in an embodiment of the present invention. DETAILED DESCRIPTION

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

[0040] It should be understood that the terms described in the present invention are only for describing special embodiments and are not intended to limit the present invention. In addition, for the numerical range in the present invention, it should be understood that each intermediate value between the upper and lower limits of the scope is also specifically disclosed. Each smaller range between the intermediate value in any stated value or stated range and any other stated value or intermediate value in the described range is also included in the present invention. The upper and lower limits of these smaller ranges can be independently included or excluded in the scope.

[0041] Unless otherwise indicated, all technical and scientific terms used herein have the same meanings as those of ordinary skill in the art generally understood by the present invention. Although the present invention describes only preferred methods, any method similar or equivalent to that described herein may also be used in the implementation or testing of the present invention. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods related to the documents. In the event of a conflict with any incorporated document, the content of this specification shall prevail.

[0042] It will be apparent to those skilled in the art that various modifications and variations may be made to the specific embodiments of the present invention description without departing from the scope or spirit of the present invention. Other embodiments derived from the present invention description will be apparent to those skilled in the art. The present application description and examples are exemplary only.

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

[0044] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0045] Embodiment 1

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

[0047] In view of the problem that the existing technology cannot well describe the radar sea clutter tail distribution in different scenarios, this embodiment proposes a radar sea clutter amplitude tail distribution modeling method, uses measured data to derive a two-parameter exponential distribution model for the sea clutter amplitude tail, and verifies the effectiveness of the model.

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

[0049] Step 1, derivation of a two-parameter exponential distribution model, specifically includes the following sub-steps:

[0050] Step (a), treat each amplitude value as an independent experiment, and use P k represents the probability that k values ​​fall into the tailing interval (η,∞), then the probability that k values ​​fall into the tailing interval among N observations is:

[0051]

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

[0053]

[0054] Step (b), let the event {N(η,y)=k1} represent that there are k1 data points in the amplitude value that fall into the interval (η,y], and its probability is expressed as Indicates that y∈(η,∞) represents the tail amplitude value, N(η,y) is the amount of data in the amplitude interval (η,y], so:

[0055] Step (c), according to the condition: for sufficiently small Δy, when k1=1, P1(y,y+Δy)=λΔy+ο(Δy), when k1≥2, {N(y,y+Δy)=k1}, the probability of occurrence twice or more is negligible compared to the probability of occurrence once. Consider P0(η,y), that is, the probability when there is no data point 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), consider P0(η,η)=P{N(η,η)=0}=1 as the initial condition and solve:

[0061] P0(η,y)=e -λ(y-η) ,y∈(η,∞)

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

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

[0064] Where F(y) represents the distribution function of the amplitude tail, η represents the lower limit of the amplitude tail, that is, the position parameter, y represents the tail amplitude value, and the value range is y∈(η,∞), P(Y≤η) is the probability that the no-tail data falls into the interval (η,∞), Y is the amplitude tail, e represents the natural logarithm, and λ represents the shape parameter.

[0065] Step (f), by taking the derivative of the above equation, we can get the probability density function p(y) of the tail 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 order moments m1 and m2 of the trailing data.

[0069]

[0070] Where m1 is the first-order moment of the tailing data, m2 is the second-order moment of the tailing data, N1 is the amount of tailing amplitude data, and y i Indicates the value of each tailing amplitude.

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

[0072]

[0073] In the formula, is the parameter estimate of the shape parameter λ, is the parameter estimate of the location parameter η.

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

[0075] Step (a), according to the false alarm probability P fa Filter the amplitude tailing data.

[0076] Step (b), fitting the amplitude tailing data according to the model parameters in step 2.

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

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

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

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

[0081] The above is only a preferred specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A radar sea clutter amplitude tailing distribution modeling method, characterized in that: include: Obtain clutter amplitude value data; Derivation of a probability density function of the amplitude tail based on the clutter amplitude value data, and construction of a two-parameter exponential distribution model for describing the clutter amplitude tail based on the probability density function; Performing parameter estimation on the two-parameter exponential distribution model to obtain model estimation parameters; Acquire measured amplitude tailing data, fit the measured amplitude tailing data based on the model estimation parameters to obtain fitting data, adjust and optimize the two-parameter exponential distribution model based on the fitting data to obtain an optimized two-parameter exponential distribution model.

2. A radar sea clutter amplitude tailing distribution modeling method according to claim 1, characterized in that: The probability density function of amplitude tailing derived based on the clutter amplitude value data specifically includes: Each clutter amplitude value acquisition process is treated as an independent experiment, and binomial distribution is used to describe the probability that the amplitude value data falls into the tailing interval. The binomial distribution is converted into a Poisson distribution. After the conversion is completed, an event and a corresponding probability are set. The event is that a number of data points in the amplitude value data fall into a preset interval. After the event definition is completed, the absence of data points in the preset interval is used as the initial condition, and the probability corresponding to the initial condition is solved. The distribution function of the amplitude tail is derived based on the probability corresponding to the initial condition, and the distribution function is derived to obtain the probability density function.

3. A radar sea clutter amplitude tailing distribution modeling method according to claim 2, characterized in that: The distribution function of the amplitude tail is specifically: F(y)=P(η<Y≤y)=1-P(Y≤η)=1-e -λ(y-η) ,y∈(η,∞) Where F(y) represents the distribution function of the amplitude tail, η represents the lower limit of the amplitude tail, that is, the position parameter, y represents the tail amplitude value, and the value range is y∈(η,∞), P(Y≤η) is the probability that the no-tail data falls into the interval (η,∞), Y is the amplitude tail, e represents the natural logarithm, and λ represents the shape parameter.

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

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

6. A radar sea clutter amplitude tailing distribution modeling method according to claim 5, characterized in that: The calculation process of the statistical data specifically includes: Where m1 is the first-order moment of the tailing data, m2 is the second-order moment of the tailing data, N1 is the amount of tailing amplitude data, and y i Indicates the value of each tailing amplitude.

7. The radar sea clutter amplitude tailing distribution modeling method according to claim 5, 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: Where m1 is the first-order moment of the tailing data, m2 is the second-order moment of the tailing data, is the parameter estimate of the shape parameter λ, is the parameter estimate of the location parameter η.

8. The radar sea clutter amplitude tailing 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 fitting data, and the two-parameter exponential distribution model is adjusted and optimized based on the goodness of fit to obtain an optimized two-parameter exponential distribution model.

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