A variable trailing Rice Sea clutter amplitude distribution model and its parameter estimation method

Abstract

The application discloses a variable tailing Rayleigh sea clutter amplitude distribution model and a parameter estimation method thereof. Firstly, sea clutter data is acquired by a sea detection radar or a synthetic aperture radar, a bivariate truncated non-zero mean stable distribution complex wave model is constructed, and a variable tailing Rayleigh amplitude distribution model is derived based on the model. The model includes four key parameters for accurately describing the amplitude distribution characteristics of the sea clutter signal. Then, a theoretical characteristic function and an empirical characteristic function of the variable tailing Rayleigh amplitude distribution model are constructed, and the four key parameters are estimated by approximating the theoretical characteristic function to the empirical characteristic function. Finally, the probability density function of the variable tailing Rayleigh amplitude distribution is calculated by using the estimated parameters, and the fitting effect is evaluated by comparing with the empirical histogram of the measured data. The method can effectively improve the precision of the sea clutter amplitude modeling, has wide practical application value, and is especially applicable to the fields of ocean detection and radar signal processing.

Description

Technical Field

[0001] This invention relates to the field of marine exploration technology, and in particular to a variable-tailed Rice Sea clutter amplitude distribution model and its parameter estimation method. Background Technology

[0002] With the continuous development of marine exploration technology, the study of sea clutter signals has become one of the key issues in the application of marine exploration radar and synthetic aperture radar (SAR). Sea clutter refers to the backscattered echo from the sea surface received when radar electromagnetic waves illuminate the sea surface. Due to the influence of various factors such as platform parameters, measurement conditions, marine environment, and meteorological factors, the characteristics of sea clutter are usually complex and variable. For marine exploration systems, accurate modeling of sea clutter amplitude distribution is fundamental to improving radar performance, optimizing signal processing, and enhancing target detection capabilities. Therefore, sea clutter amplitude modeling and its parameter estimation are of great significance.

[0003] Currently, sea clutter models can be mainly classified into three categories: empirical distribution models, composite Gaussian distribution models, and mixed distribution models. The tailing degree of empirical distribution models and composite Gaussian distribution models is generally relatively fixed. For example, Rayleigh and Rice distributions have relatively light tailing, while log-normal and heavy-tailed models exhibit excessively heavy tailing. The K-distribution has a moderate tailing. This means that these models are only applicable to sea clutter data under specific conditions, lacking universality and easily leading to mismatches between measured data and models, thus affecting the performance of radar applications based on clutter amplitude distributions.

[0004] Hybrid distribution models, such as the KA and KK distributions, introduce additional components to describe the "peak" phenomenon in sea clutter, thus theoretically allowing for a more flexible fit to the tail of the clutter distribution and effectively improving the modeling's versatility. However, the KA and KK distributions have a large number of unknown parameters, and the parameters are coupled, which greatly increases the complexity of parameter estimation and is not conducive to practical applications.

[0005] Therefore, constructing a universal sea clutter amplitude distribution model applicable to different radar parameters and environmental conditions, and developing a simple and effective parameter estimation algorithm to better meet the needs of practical engineering applications, are key technical problems that urgently need to be solved in this field. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a variable trailing Rice Sea clutter amplitude distribution model and its parameter estimation method.

[0007] To achieve the above-mentioned objectives, the technical solution adopted by the present invention is as follows:

[0008] A variable-tailed Rice Sea clutter amplitude distribution model and its parameter estimation method include the following steps:

[0009] S1. Obtain sea clutter data from maritime surveillance radar or SAR.

[0010] S2. Construct a bivariate truncated non-zero mean stable distribution complex wave model, and derive a variable trailing Rice amplitude distribution model based on this model. This model includes four key parameters: characteristic index, scale parameter, position parameter, and truncation depth parameter, which are used to accurately describe the amplitude distribution characteristics of sea clutter signals.

[0011] S3. Construct the formulas for the theoretical and empirical characteristic functions of the variable trailing Rice amplitude distribution model. The theoretical characteristic function is determined by the four key parameters of the model, while the empirical characteristic function is calculated based on the acquired sea clutter amplitude data.

[0012] S4. By approximating the theoretical characteristic function using empirical characteristic functions, four key parameters of the variable-tailed Rice amplitude distribution model are estimated. Specifically, the position parameter is estimated based on the properties of the Bessel function; the characteristic exponent and truncation depth parameters are estimated by constructing an optimization problem and solving it using the Gauss-Hermitian quadrature method; the scale parameter is further estimated using the other estimated parameters.

[0013] S5. Substitute the estimated model parameters into the amplitude model to calculate the probability density function of the variable-tailed Rice amplitude distribution. Evaluate the fitting effect by comparing it with the empirical histogram of the measured data, and output the model fitting result.

[0014] Furthermore, in S1, for maritime detection radar, the amplitude sequence corresponding to a fixed range cell or a fixed pulse cell is analyzed and denoted as r = [r1, r2, ..., r...]. L ], where L is the number of pulses in the sample sequence data;

[0015] For SAR sea clutter data, analyze the two-dimensional image and rearrange the two-dimensional data into one-dimensional data, also denoted as r = [r1, r2, ..., r]. L ].

[0016] Furthermore, the characteristic function of the complex wave model described in S2 is:

[0017]

[0018] Where ξ1 and ξ2 represent the two components of the frequency vector. Let α be the amplitude of the frequency vector, α∈(0,2] be the characteristic exponent, γ>0 be the scale parameter, δ1∈(-∞,+∞) and δ2∈(-∞,+∞) be the edge distribution position parameters of the real and imaginary parts, and η>0 be the truncation depth parameter; j(δ1ξ1+δ2ξ2) embodies the mean information of the complex wave signal in the time domain.

[0019] Furthermore, in S2, a two-dimensional Fourier transform is performed on the characteristic function to obtain the joint probability density function of the real and imaginary parts of the clutter:

[0020]

[0021] in, This represents a double integration over two directions ξ1 and ξ2 in the frequency space;

[0022] x re x im Represents the real and imaginary parts of the clutter;

[0023] Furthermore, the corresponding variable tail amplitude distribution probability density function is derived in S2 based on the joint probability density function:

[0024]

[0025] in, This represents the clutter amplitude. Let J0(·) be the position parameter amplitude, J0(·) be the first-order 0th-order Bessel function, and s be a variable in the frequency space.

[0026] Furthermore, based on the characteristic function of the complex wave model of S2 The derivation in S3 yields information about the frequency domain magnitude variable. Theoretical characteristic function The calculation formula is

[0027]

[0028] Furthermore, based on the measured data of S1, r = [r1, r2, ..., r...] L In S3, the empirical characteristic function is calculated. Defined as:

[0029]

[0030] Where, r i Let L represent the i-th clutter amplitude in the measured data, and L be the number of data samples.

[0031] Furthermore, S4 utilizes Based on the property that J0(2.405)=0, the position parameter δ is estimated, and its estimated value is:

[0032]

[0033] Where s′ is the minimum s value obtained through numerical calculation, satisfying

[0034] Furthermore, in S4, to estimate the feature exponent α and the truncation depth parameter ηη, we first base it on the theoretical feature function. and empirical characteristic function Construct the following formula:

[0035]

[0036]

[0037] Where s ref =1 / C, This represents the amplitude signal power.

[0038] Furthermore, in S4, the characteristic exponent α and the truncation depth parameter η are estimated by solving the following optimization problem:

[0039]

[0040] Among them, {s k ;k = 1, 2, ..., K} are the positive zeros of the 2Kth order Hermitian polynomial, {w k ; k = 1, 2, ..., K} are the corresponding weighted values.

[0041] Furthermore, the estimated scaling parameter γ in S4 is:

[0042]

[0043] in, This represents an estimated value of the scaling parameter; This represents an estimated value of the characteristic index; Represents the estimated cutoff depth parameter of Power; It is related to the characteristic index A related factor; s ref Indicates the reference frequency; It is the product of the cutoff depth and the reference frequency; This represents the estimated value of the location parameter; ln(.) represents the natural logarithm.

[0044] This invention also discloses a variable-tailed Rice Sea clutter amplitude distribution model and its parameter estimation system. This system can be used to implement the aforementioned variable-tailed Rice Sea clutter amplitude distribution model and its parameter estimation method, specifically including:

[0045] The sea clutter data acquisition module is used to acquire sea clutter data from maritime surveillance radar or synthetic aperture radar (SAR).

[0046] The ocean clutter model building module is used to build a bivariate truncated non-zero mean stable distribution complex wave model and the corresponding variable tail Rice amplitude distribution model, and initialize the relevant model parameters, including characteristic exponent, scale parameter, position parameter and truncation depth parameter.

[0047] The amplitude model characteristic function construction module is used to construct the calculation formulas for the theoretical and empirical characteristic functions of the variable trailing Rice amplitude distribution model. The theoretical characteristic function is determined by the four key parameters of the model, while the empirical characteristic function can be calculated based on the acquired sea clutter amplitude data.

[0048] The parameter estimation module is used to estimate the position parameter, characteristic exponent, cutoff depth parameter, and scale parameter in the amplitude model by approximating the theoretical characteristic function using the empirical characteristic function of the amplitude model. The position parameter is estimated by using the properties of the Bessel function, the characteristic exponent and cutoff depth parameter are solved by constructing an optimization problem and using the Gauss-Hermite quadrature method, and the scale parameter is estimated by using the other parameters obtained from the estimation.

[0049] The fitting result evaluation module is used to substitute the estimated model parameters into the amplitude model, calculate the probability density function of the variable tail Rice amplitude distribution, and compare it with the empirical histogram of the measured data to evaluate the fitting effect of the model.

[0050] The display module is used to present the fitting results and evaluation effects to the user in the form of graphs, tables or other visualizations, so as to make it easy to intuitively view the parameter estimation results and the model fitting effect.

[0051] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-mentioned variable trailing Rice Sea clutter amplitude distribution model construction and parameter estimation method.

[0052] The present invention also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the above-mentioned variable trailing Rice Sea clutter amplitude distribution model construction and parameter estimation method.

[0053] Compared with the prior art, the advantages of the present invention are as follows:

[0054] Improving the accuracy of sea clutter amplitude distribution modeling: The variable trailing Rice amplitude distribution model proposed in this invention takes into account both the diversity of measured clutter amplitude distribution trailing and the non-zero mean of clutter real and imaginary part signals, which can effectively improve the accuracy and versatility of amplitude modeling under different radar parameters and environmental conditions.

[0055] Optimized parameter estimation process: This invention constructs theoretical and empirical characteristic functions of a variable trailing Rice amplitude distribution model, using the latter to approximate the former, thus effectively estimating various parameters in the sea clutter amplitude model. In particular, it accurately estimates the characteristic exponent and cutoff depth parameters using the Gauss-Hermitian quadrature method, thereby obtaining more accurate scale parameter estimates and avoiding estimation errors that may exist in traditional methods.

[0056] Applicable to various radar systems and sea clutter types: This invention is applicable to sea clutter data acquired by different types of radar systems (such as maritime detection radar, SAR, etc.), and has strong versatility, adapting to sea clutter characteristics under different sea conditions and frequency bands.

[0057] Improving the accuracy and operability of sea clutter signal analysis: The variable tail Rice amplitude distribution model constructed by this invention and the estimation method based on characteristic functions can not only accurately describe the statistical characteristics of sea clutter signals, but also provide reliable numerical support for subsequent radar data processing, image analysis and marine exploration, thereby improving the overall performance of marine exploration. Attached Figure Description

[0058] Figure 1 This is a flowchart of a radar sea clutter amplitude distribution analysis method with variable trailing Rice distribution provided in an embodiment of the present invention.

[0059] Figure 2 These are two 300*300 sea clutter images of a certain area obtained by COSMO-SkyMed SAR in an embodiment of the present invention; (a) in the image is Example 1, and (b) is Example 2.

[0060] Figure 3 This is an embodiment of the variable tail Rice distribution constructed in this invention. Figure 2 The probability density function fitting results of two measured sea clutter data images; (a) in the figure is Example 1, and (b) is Example 2. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0062] A method for estimating parameters of a sea clutter amplitude model includes the following steps:

[0063] S1, Sea Clutter Data Acquisition and Processing

[0064] Sea clutter data can typically be acquired by maritime surveillance radar and synthetic aperture radar (SAR). For maritime surveillance radar, the amplitude sequence corresponding to a fixed range cell or a fixed pulse cell is usually analyzed, denoted as r = [r1, r2, ..., r...].L [], where L is the number of pulses in the sample sequence data. For SAR sea clutter data, two-dimensional images are usually analyzed. In this case, the two-dimensional data can be rearranged into one-dimensional data, also denoted as r = [r1, r2, L, r] L ].

[0065] This paper uses two 300*300 sea clutter images from a COSMO-SkyMed SAR image of a certain region as examples to illustrate model validation and parameter estimation methods. The COSMO-SkyMed SAR is a satellite-borne system with an orbital altitude of 619.6 km and a frequency of 9.65 GHz (X-band). The two sea clutter images are selected from the Venezueela-Maracaibo file (row index 3049-3348, column index 201:500) and the Italy-DeltaPo file (row index 221-520, column index 1012:1311). Figure 2 Their amplitude grayscale images were plotted.

[0066] Rearrange the two images into a 1*90000 sequence r = [r1, r2, ..., r...] L ], where L = 90000.

[0067] S2. Constructing a bivariate truncated non-zero mean stable distribution complex wave model and its variable tail amplitude model. The characteristic function of the bivariate truncated non-zero mean stable distribution complex wave model is:

[0068]

[0069] in It is a frequency vector. Let α be the amplitude of the frequency vector, α∈(0,2] be the feature index, γ>0 be the scale parameter, δ1∈(-∞,+∞) and δ2∈(-∞,+∞) be the position parameters corresponding to the two edge distributions of the real and imaginary parts, respectively, and η>0 be the truncation depth parameter.

[0070] Performing a two-dimensional Fourier transform on the characteristic function of a bivariate truncated non-zero mean stable distribution yields the joint probability density function of the real and imaginary parts.

[0071]

[0072] Where x re and x im These are the real and imaginary parts of the clutter, respectively.

[0073] Based on the joint probability density function of the real and imaginary parts, the corresponding probability density function of the variable tail amplitude distribution is derived as follows:

[0074]

[0075] in This represents the clutter amplitude. Let J0 be the position parameter magnitude, and J0(·) be the first-order 0th-order Bessel function.

[0076] The amplitude model constructed in this invention is named the Variable Tail Rice Distribution to reflect its adjustable tail characteristics and consideration of the non-zero mean of the real and imaginary parts of clutter. When η→+∞, i.e., without truncation, the constructed Variable Tail Rice Distribution degenerates into a Heavy Tail Rice Distribution. When η→+∞ and δ=0, the constructed Variable Tail Rice Distribution degenerates into a Heavy Tail Rayleigh Distribution. When η→+∞, δ=0 and α=2, the constructed Variable Tail Rice Distribution degenerates into a Rayleigh Distribution.

[0077] S3. Construct the theoretical and empirical characteristic function calculation formulas for the variable-tailed Rice distribution with respect to the frequency vector magnitude variable, respectively.

[0078]

[0079] in ξ1=s cos(θ ξ ), ξ2=s ​​sin(θ) ξ ), R and Φ r X represents the random variables of clutter amplitude and phase, respectively. re =R cosΦ r and X im =R sinΦ r These are random variables representing the real and imaginary parts of the clutter, respectively. This is an empirical approximation of the theoretical expectation.

[0080] S4. Construct a parameter estimation method for the variable trailing amplitude model based on characteristic functions to fit the measured data.

[0081] Estimate the location parameter δ: using And using the property that J0(2.405)=0, the estimated value of δ is Where s′ is defined by numerical calculation formula (5). The minimum value of s.

[0082] Estimate the characteristic exponent α and the truncation depth parameter η. The theoretical characteristic function is based on the variable-tailed Rice distribution. and empirical characteristic function Construct the following formula

[0083]

[0084] Where s ref =1 / C, Let be the amplitude signal power. Then, the estimates of α and η can be obtained by solving the following Gaussian-Hermitian quadrature optimization problem:

[0085]

[0086] Where {s k ;k=1,L,K} are the positive zeros of the 2K-order Hermitian polynomial, {w k ;k = 1, L, K} are the corresponding weighting values, and in this invention, K = 10 is used. The Gauss-Hermitian quadrature optimization problem is solved using the classic simplex algorithm, with the initial point set as [α0, η0] = [1, 1].

[0087] Estimating the scaling parameter γ: using approximate The estimated value of γ can be obtained.

[0088]

[0089] Table 1 lists the variable trailing Rice amplitude model for... Figure 2 Parameter estimation results for two SAR images.

[0090] S5, Output model fitting results

[0091] Estimated parameters Substitute the results into equation (3) to calculate the probability density function of the variable trailing Rice amplitude distribution. Compare the results with the empirical histogram of the measured data to evaluate the fitting performance.

[0092] The probability density function fitting result of the measured data in this embodiment is as follows: Figure 3 As shown.

[0093] As can be seen, the fitting performance of this invention is significantly improved compared to existing technologies (K-distribution and heavily tailed Rice distribution). Specifically, compared to the K-distribution, the overall fitting performance of this invention is significantly improved; and compared to the heavily tailed Rice distribution, this invention significantly enhances the fitting performance at the tail. This advantage is mainly due to the fact that this invention takes into account the case of non-zero mean of the real and imaginary parts of clutter and can adapt to clutter with various degrees of tailing.

[0094] To highlight the advantages of the model constructed in this invention, the following comparison of two existing technologies was made.

[0095] ① Comparison Model 1: Typical K-distribution Where K v-1 (·) represents the modified Bessel function of the second kind of order v-1, where v and λ are the shape parameter and scale parameter, respectively.

[0096] ② Comparison Model 2: Heavy Tail Rice Distribution (a special case of the variable tail Rice distribution constructed in this invention when the truncation depth parameter η→+∞).

[0097] The table below shows the parameter estimation results for different models.

[0098]

[0099] In another embodiment of the present invention, a variable-tailed Rice Sea clutter amplitude distribution model and its parameter estimation system are provided. This system can be used to implement the aforementioned variable-tailed Rice Sea clutter amplitude distribution model and its parameter estimation method, specifically including:

[0100] The sea clutter data acquisition module is used to acquire sea clutter data from maritime surveillance radar or synthetic aperture radar (SAR).

[0101] The ocean clutter model building module is used to build a bivariate truncated non-zero mean stable distribution complex wave model and the corresponding variable tail Rice amplitude distribution model, and initialize the relevant model parameters, including characteristic exponent, scale parameter, position parameter and truncation depth parameter.

[0102] The amplitude model characteristic function construction module is used to construct the calculation formulas for the theoretical and empirical characteristic functions of the variable trailing Rice amplitude distribution model. The theoretical characteristic function is determined by the four key parameters of the model, while the empirical characteristic function can be calculated based on the acquired sea clutter amplitude data.

[0103] The parameter estimation module is used to estimate the position parameter, characteristic exponent, cutoff depth parameter, and scale parameter in the amplitude model by approximating the theoretical characteristic function using the empirical characteristic function of the amplitude model. The position parameter is estimated by using the properties of the Bessel function, the characteristic exponent and cutoff depth parameter are solved by constructing an optimization problem and using the Gauss-Hermite quadrature method, and the scale parameter is estimated by using the other parameters obtained from the estimation.

[0104] The fitting result evaluation module is used to substitute the estimated model parameters into the amplitude model, calculate the probability density function of the variable tail Rice amplitude distribution, and compare it with the empirical histogram of the measured data to evaluate the fitting effect of the model.

[0105] The display module is used to present the fitting results and evaluation effects to the user in the form of graphs, tables or other visualizations, so as to make it easy to intuitively view the parameter estimation results and the model fitting effect.

[0106] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve corresponding method flows or corresponding functions. The processor described in this embodiment can be used for operating the variable trailing Ricean clutter amplitude distribution model and its parameter estimation method.

[0107] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory). This computer-readable storage medium is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

[0108] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the variable trailing Rice Sea clutter amplitude distribution model and its parameter estimation method in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by a processor.

[0109] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0110] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0111] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0112] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0113] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the implementation methods of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the present invention.

Claims

1. A variable-tail Rician sea clutter amplitude distribution model and its parameter estimation method, characterized in that, Comprising the following steps: S1, obtain sea clutter data from the sea detection radar or synthetic aperture radar SAR, and the measured data is denoted as r = [r1, r2, …, r L ], wherein L is the number of pulses of the sample sequence data; S2, a bivariate truncated non-zero mean stable complex wave model is constructed, and a variable-tailed Lévy amplitude distribution model is derived therefrom, which includes four key parameters: characteristic exponent, scale parameter, location parameter and truncation depth parameter; The characteristic function of the complex wave model is: where ξ1, ξ2 represent two components of the frequency vector, is the frequency vector amplitude, a e (0, 2] is the characteristic index, γ > 0 is the scale parameter, δ1 e (-∞, +∞) and δ2 e (-∞, +∞) are the edge distribution position parameters of the real and imaginary parts, η > 0 is the truncation depth parameter; j(δ1ξ1+δ2ξ2) embodies the mean value information of the complex wave signal in the time domain; S3, the calculation formula of the theoretical characteristic function and the empirical characteristic function of the variable-tailed Lévy amplitude distribution model is constructed; wherein the theoretical characteristic function is determined by the four key parameters of the model, and the empirical characteristic function is calculated based on the obtained sea clutter amplitude data, specifically: Characteristic function of the complex wave model according to S2 Theoretical characteristic function of the frequency domain amplitude variable derived in S3 The calculation formula is According to the measured data r = [r1, r2,..., r L ], the empirical characteristic function is calculated in S3 as: where r i represents the ith clutter amplitude in the measured data, and L is the number of data samples; S4, the four key parameters of the variable-tailed Lévy amplitude distribution model are estimated by approximating the theoretical characteristic function with the empirical characteristic function, specifically, the estimation of the location parameter is based on the properties of the Bessel function; the characteristic exponent and the truncation depth parameter are estimated by constructing an optimization problem and using the Gauss-Hermite quadrature method to solve; the scale parameter is further estimated by using the estimated other parameters; S5, the estimated model parameters are substituted into the amplitude model to calculate the probability density function of the variable-tailed Lévy amplitude distribution; by comparing with the empirical histogram of the measured data, the fitting effect is evaluated, and the fitting result of the model is output.

2. The variable-tail Rayleigh sea clutter amplitude distribution model and parameter estimation method thereof according to claim 1, characterized in that: In S1, for a maritime detection radar, the amplitude sequence corresponding to a fixed range cell or a fixed pulse cell is analyzed and denoted as r = [r1, r2, ..., r L ], where L is the number of pulses in the sample sequence data; For the SAR sea clutter data, analyze the two-dimensional image, rearrange the two-dimensional data into one-dimensional data, also denoted as r = [rl, r2,..., r L ].

3. The variable-tail Rayleigh sea clutter amplitude distribution model and parameter estimation method thereof according to claim 2, characterized in that: In S2, the two-dimensional Fourier transform of the characteristic function is performed to obtain the joint probability density function of the real part and the imaginary part of the clutter: wherein denotes a double integration over two directions in frequency space, ξ1and ξ2. x re ,x im denotes the real and imaginary parts of the clutter.

4. The variable-tail Rayleigh sea clutter amplitude distribution model and parameter estimation method thereof according to claim 3, characterized in that: In S2, the corresponding variable-tailed amplitude distribution probability density function is derived based on the joint probability density function: wherein is the clutter amplitude, is the position parameter amplitude, J0(·) is the first kind 0th order Bessel function, and s is a variable in the frequency space.

5. The variable-tail Rayleigh sea clutter amplitude distribution model and parameter estimation method thereof according to claim 4, characterized in that: S4 utilizes and the property of J0(2.405) = 0, the position parameter δ is estimated with an estimate of: where s ′ is the minimum s value obtained by numerical calculation, satisfying 6. The variable-tail Rayleigh sea clutter amplitude distribution model and parameter estimation method thereof according to claim 5, characterized in that: In S4, to estimate the characteristic exponent a and the cutoff depth parameter h, first construct the following equation based on the theoretical characteristic function and the empirical characteristic function ​ where s ref = 1 / C, is the amplitude signal power.

7. The variable-tail Rayleigh sea clutter amplitude distribution model and parameter estimation method thereof according to claim 6, characterized in that: In S4, the characteristic exponent α and the truncation depth parameter η are estimated by solving the following optimization problem: where {s k are the positive zeros of the 2Korder Hermite polynomials, and {w k are the corresponding weight values.

8. The variable-tail Rayleigh sea clutter amplitude distribution model and parameter estimation method thereof according to claim 7, characterized in that: In S4, the scale parameter γ is estimated, and its estimated value is: wherein represents an estimate of a scale parameter; represents an estimate of a characteristic exponent; represents an estimated cut-off depth parameter to the power of s; is a factor related to the characteristic exponent s ref represents a reference frequency; is the product of the cut-off depth and the reference frequency; represents an estimate of a location parameter; ln(.) represents the natural logarithm.​ 9. A variable-tailed Lévy sea clutter amplitude distribution model and a parameter estimation system thereof, which can be used to implement the variable-tailed Lévy sea clutter amplitude distribution model and the parameter estimation method thereof according to any one of claims 1 to 8, specifically comprising: a sea clutter data acquisition module for acquiring sea clutter data from a sea detection radar or a synthetic aperture radar (SAR); a sea clutter model construction module for constructing a bivariate truncated non-zero mean stable complex wave model and a corresponding variable-tailed Lévy amplitude distribution model, and initializing related model parameters, including characteristic exponent, scale parameter, location parameter and truncation depth parameter; an amplitude model characteristic function construction module for constructing the calculation formula of the theoretical characteristic function and the empirical characteristic function of the variable-tailed Lévy amplitude distribution model, wherein the theoretical characteristic function is determined by the four key parameters of the model, and the empirical characteristic function can be calculated based on the obtained sea clutter amplitude data; a parameter estimation module for estimating the location parameter, the characteristic exponent, the truncation depth parameter and the scale parameter in the amplitude model by approximating the theoretical characteristic function with the empirical characteristic function of the amplitude model, wherein the location parameter is estimated by the properties of the Bessel function, the characteristic exponent and the truncation depth parameter are estimated by constructing an optimization problem and using the Gauss-Hermite quadrature method to solve, and the scale parameter is estimated by using the estimated other parameters; The fitting result evaluation module is configured to substitute the estimated model parameters into the amplitude model, calculate a probability density function of the variable-tail Rayleigh amplitude distribution, and compare the probability density function with an empirical histogram of the measured data to evaluate the fitting effect of the model. The display module is configured to display the fitting result and the evaluation effect in a graphical, tabular or other visualized form to the user, so as to intuitively view the parameter estimation result and the fitting effect of the model.

10. A computer device, comprising: The computer program is stored in the memory and executable on the processor, and the processor executes the program to implement the variable-tail Rayleigh sea clutter amplitude distribution model construction and parameter estimation method according to any one of claims 1 to 8.

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