Method and apparatus for simulating sea clutter amplitude data with stable Alpha distribution

Abstract

This invention provides a method and apparatus for simulating positive alpha stable distribution sea clutter amplitude data, relating to the field of sea clutter data processing technology. The method includes: determining a probability density function based on the characteristic function, inverse Laplace transform, Merlin transform properties, and G function of the positive alpha stable distribution; determining a cumulative distribution function based on the probability density function; establishing a correspondence table between multiple target characteristic index parameters, multiple target comprehensive scale parameters, multiple target sea clutter amplitude values, and the values ​​of the cumulative distribution function; and determining the target sea clutter amplitude data matrix based on preset characteristic index parameters, preset scale parameters, a random number matrix, and the correspondence table. By utilizing the characteristic function, inverse Laplace transform, Merlin transform properties, and G function of the positive alpha stable distribution, a closed-loop representation of the probability density function of the positive alpha stable distribution is achieved, enabling the direct simulation and generation of positive alpha stable distribution sea clutter amplitudes.

Description

Technical Field

[0001] This invention relates to the field of sea clutter data processing technology, and in particular to a method and apparatus for simulating sea clutter amplitude data with a positive Alpha stable distribution. Background Technology

[0002] Maritime clutter detection has always been a hot topic in radar signal processing. Acquiring diverse and high-quality sea clutter data is fundamental to the design of maritime clutter detection algorithms. The sea clutter data received by radar is significantly affected by factors such as radar operating conditions, sea state, sea area, wind speed, wind direction, and wave height, resulting in highly variable statistical characteristics. A single statistical model cannot fully describe the characteristics of sea clutter, and the actual data acquisition process cannot obtain comprehensive sea clutter data. Therefore, sea clutter simulation is needed to expand sea clutter data. In Alpha stable distributions, the symmetric Alpha stable distribution is a commonly used model for sea clutter simulation. According to the sub-Gaussian theorem, the symmetric Alpha stable distribution can be expressed as the product of a complex Gaussian random process and a positive Alpha stable distribution random variable. It can comprehensively describe the amplitude distribution characteristics and correlations of sea clutter and can be considered a special form of the composite Gaussian distribution. However, because the probability density function of the Alpha stable distribution does not have a closed-form expression for elementary functions, simulation research on sea clutter data for this distribution family is very limited.

[0003] Currently, for simulating symmetric Alpha stable distribution data, the spherically invariant stochastic process method can be used. When simulating symmetric Alpha stable distribution data using the spherically invariant stochastic process method, its amplitude probability density function and autocorrelation function can be independently controlled. However, since the amplitude distribution of the symmetric Alpha stable distribution is still a special type of Alpha stable distribution, namely the positive Alpha stable distribution, and the positive Alpha stable distribution does not have a closed-form probability density function expression, it is impossible to directly simulate and generate positive Alpha stable distribution sea clutter amplitude data through the probability density function. Summary of the Invention

[0004] The purpose of this invention is to provide a method and apparatus for simulating positive alpha stable distribution sea clutter amplitude data, solving the problem that positive alpha stable distribution sea clutter amplitude data cannot be directly simulated and generated through probability density functions.

[0005] To address the aforementioned technical problems, the embodiments of the present invention provide the following technical solutions:

[0006] The first aspect of this invention provides a method for simulating positive alpha stable distribution sea clutter amplitude data, the method comprising:

[0007] The simulation parameters for symmetric Alpha stable distribution sea clutter data are obtained. The simulation parameters include the number of sea clutter range cells, the number of pulses, the preset characteristic index parameter, and the preset scale parameter.

[0008] Based on the preset alpha stable distribution feature function, preset parameter range, and initial comprehensive scale parameter, determine the feature function of the positive alpha stable distribution;

[0009] Based on the characteristic function, inverse Laplace transform, Merlin transform properties, and G function of the positive Alpha stable distribution, the probability density function is determined. The probability density function is used to indicate the closed representation of the positive Alpha stable distribution with respect to the G function.

[0010] Determine the cumulative distribution function based on the probability density function;

[0011] Based on the cumulative distribution function and the preset interval, establish a correspondence table between multiple target characteristic index parameters, multiple target comprehensive scale parameters, multiple target sea clutter amplitude values ​​and the corresponding cumulative distribution function values;

[0012] A random number matrix is ​​generated based on the number of sea clutter range cells, the number of pulses, and random distribution parameters;

[0013] Based on preset characteristic index parameters, preset scale parameters, random number matrix and corresponding relationship table, the target sea clutter amplitude data matrix is ​​determined, and the target sea clutter amplitude data matrix is ​​used to simulate sea clutter data.

[0014] A second aspect of this application provides a device for simulating positive alpha stable distribution sea clutter amplitude data, the device comprising:

[0015] The acquisition module is used to acquire simulation parameters of symmetric Alpha stable distribution sea clutter data. The simulation parameters include the number of sea clutter range cells, the number of pulses, the preset characteristic index parameter, and the preset scale parameter.

[0016] The first determining module is used to determine the characteristic function of the positive Alpha stable distribution based on the preset characteristic function of the Alpha stable distribution, the preset parameter range, and the initial comprehensive scale parameter.

[0017] The second determining module is used to determine the probability density function based on the characteristic function of the positive Alpha stable distribution, the inverse Laplace transform, the Merlin transform property, and the G function. The probability density function is used to indicate the closed representation of the positive Alpha stable distribution with respect to the G function.

[0018] The third determining module is used to determine the cumulative distribution function based on the probability density function;

[0019] A module is established to create a table of correspondences between multiple target characteristic index parameters, multiple target comprehensive scale parameters, multiple target sea clutter amplitude values ​​and the corresponding cumulative distribution function values, based on the cumulative distribution function and a preset interval.

[0020] The generation module is used to generate a random number matrix based on the number of sea clutter range cells, the number of pulses, and random distribution parameters;

[0021] The fourth determination module is used to determine the target sea clutter amplitude data matrix based on preset characteristic index parameters, preset scale parameters, random number matrix and corresponding relationship table. The target sea clutter amplitude data matrix is ​​used to simulate sea clutter data.

[0022] Compared to existing technologies, the present invention provides a method and apparatus for simulating positive Alpha stable distribution sea clutter amplitude data. This method acquires simulation parameters for symmetric Alpha stable distribution sea clutter data; determines the characteristic function of the positive Alpha stable distribution based on the preset characteristic function of the Alpha stable distribution, the preset parameter range, and the initial synthetic scale parameters; determines the probability density function based on the characteristic function of the positive Alpha stable distribution, the inverse Laplace transform, the Merlin transform properties, and the G function, whereby the probability density function indicates the closed representation of the positive Alpha stable distribution with respect to the G function; determines the cumulative distribution function based on the probability density function; establishes a correspondence table between multiple target characteristic index parameters, multiple target synthetic scale parameters, multiple target sea clutter amplitude values, and the corresponding cumulative distribution function values ​​based on the cumulative distribution function and a preset interval; generates a random number matrix based on the number of sea clutter range cells, the number of pulses, and the random distribution parameters; and determines the target sea clutter amplitude data matrix based on the preset characteristic index parameters, the preset scale parameters, the random number matrix, and the correspondence table. In this way, based on the characteristic function, inverse Laplace transform, Merlin transform properties, and G function of the positive Alpha stable distribution, the probability density function of the positive Alpha stable distribution can be expressed as a closed expression of the G function, realizing the closed representation of the probability density function of the positive Alpha stable distribution, so that the target sea clutter amplitude data matrix, i.e., the positive Alpha stable distribution sea clutter amplitude, can be directly simulated and generated. Attached Figure Description

[0023] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent upon reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of the invention are illustrated by way of example and not limitation, with the same or corresponding reference numerals denoteing the same or corresponding parts, wherein:

[0024] Figure 1 The flowchart of the simulation method for positive alpha stable distribution sea clutter amplitude data is illustrated schematically. Figure 1 ;

[0025] Figure 2 The flowchart of the simulation method for positive alpha stable distribution sea clutter amplitude data is illustrated schematically. Figure 2 ;

[0026] Figure 3 A schematic diagram illustrating the comparison of probability densities is shown.

[0027] Figure 4 A schematic diagram of sea clutter amplitude data under simulation parameters is shown.

[0028] Figure 5 A schematic diagram illustrating the comparison of probability density function curves is shown.

[0029] Figure 6 A schematic diagram of a device for simulating the amplitude of sea clutter with a stable positive Alpha distribution is shown. Detailed Implementation

[0030] Exemplary embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.

[0031] It should be noted that, unless otherwise stated, the technical or scientific terms used in this invention should have the ordinary meaning as understood by one of ordinary skill in the art.

[0032] The methods described in the embodiments of the present invention will be explained in detail below.

[0033] Figure 1 A flowchart illustrating the simulation method for positive Alpha stable distribution sea clutter amplitude data in an embodiment of the present invention is shown schematically. See [link / reference]. Figure 1 As shown, the method may include:

[0034] S101. Obtain simulation parameters for symmetrical Alpha stable distribution sea clutter data.

[0035] The simulation parameters include the number of sea clutter range cells, the number of pulses, preset characteristic index parameters, and preset scale parameters.

[0036] In this embodiment of the invention, it is necessary to obtain the quantity parameters of the sea clutter amplitude data to be simulated based on the simulation requirements of the sea clutter data volume, including the number of sea clutter range cells M and the number of pulses N. It is also necessary to obtain the simulation parameter values ​​of the Alpha stable distribution based on the statistical characteristics of the sea clutter amplitude, including the preset characteristic index parameter α′, the preset scale parameter σ′, the preset skewness parameter β′, and the preset position parameter μ′.

[0037] S102. Determine the characteristic function of the positive Alpha stable distribution based on the preset characteristic function of the Alpha stable distribution, the preset parameter range, and the initial comprehensive scale parameter.

[0038] The characteristic function of the presupposed Alpha stable distribution is the general form of the Alpha stable distribution characteristic function. The preset parameter range can include (0,1], 1, and 0.

[0039] S103. Determine the probability density function based on the characteristic function of the stable distribution of positive Alpha, the inverse Laplace transform, the Merlin transform, and the G function.

[0040] The probability density function is used to indicate the closed-loop representation of the positive Alpha stable distribution with respect to the G function.

[0041] The probability density function is the probability density function of the positive Alpha stable distribution with respect to the closed representation of the G function. Based on the characteristic function of the positive Alpha stable distribution, the inverse Laplace transform, the Merlin transform properties, and the G function, the probability density function of the positive Alpha stable distribution with respect to the closed representation of the G function is determined.

[0042] S104. Determine the cumulative distribution function based on the probability density function.

[0043] The cumulative distribution function is the cumulative distribution function of the positive Alpha stable distribution with respect to the closed representation of the G function. Based on the probability density function of the positive Alpha stable distribution with respect to the closed representation of the G function, the cumulative distribution function of the positive Alpha stable distribution with respect to the closed representation of the G function is determined.

[0044] S105. Based on the cumulative distribution function and the preset interval, establish a correspondence table between multiple target characteristic index parameters, multiple target comprehensive scale parameters, multiple target sea clutter amplitude values ​​and the corresponding cumulative distribution function values.

[0045] Based on the cumulative distribution function and preset interval of the positive Alpha stable distribution with respect to the closed characterization of the G function, a table is established to correspond to the values ​​of multiple target characteristic index parameters, multiple target comprehensive scale parameters, multiple target sea clutter amplitude values ​​and the corresponding cumulative distribution function values.

[0046] The preset intervals include a first preset interval, a second preset interval, and a third preset interval. The first preset interval is the interval corresponding to the initial characteristic index parameter, the second preset interval is the interval corresponding to the initial comprehensive scale parameter, and the third preset interval is the interval corresponding to the initial sea clutter amplitude value.

[0047] S106. Generate a random number matrix based on the number of sea clutter range cells, the number of pulses, and the random distribution parameters.

[0048] The random distribution parameter is (0,1).

[0049] S107. Determine the target sea clutter amplitude data matrix based on the preset characteristic index parameters, preset scale parameters, random number matrix, and corresponding relationship table.

[0050] The target sea clutter amplitude data matrix is ​​used to simulate sea clutter data.

[0051] Based on the above Figure 1 As can be seen from the implementation method, the embodiments of the present invention obtain simulation parameters for symmetric Alpha stable distribution sea clutter data; determine the characteristic function of positive Alpha stable distribution based on the preset characteristic function of Alpha stable distribution, preset parameter range, and initial synthetic scale parameters; determine the probability density function based on the characteristic function of positive Alpha stable distribution, inverse Laplace transform, Merlin transform properties, and G function, the probability density function being used to indicate the closed representation of positive Alpha stable distribution with respect to G function; determine the cumulative distribution function based on the probability density function; establish a correspondence table between multiple target characteristic index parameters, multiple target synthetic scale parameters, multiple target sea clutter amplitude values, and the corresponding cumulative distribution function values ​​based on the cumulative distribution function and preset intervals; generate a random number matrix based on the number of sea clutter range cells, the number of pulses, and random distribution parameters; and determine the target sea clutter amplitude data matrix based on the preset characteristic index parameters, preset scale parameters, random number matrix, and correspondence table. In this way, based on the characteristic function, inverse Laplace transform, Merlin transform properties, and G function of the positive Alpha stable distribution, the probability density function of the positive Alpha stable distribution can be expressed as a closed expression of the G function, realizing the closed representation of the probability density function of the positive Alpha stable distribution, so that the target sea clutter amplitude data matrix, i.e., the positive Alpha stable distribution sea clutter amplitude, can be directly simulated and generated.

[0052] As a refinement and extension of the above embodiments, Figure 2 The flowchart of the method for simulating sea clutter amplitude data with positive Alpha stable distribution in this embodiment of the invention. Figure 2 See Figure 2 As shown in the embodiment of the present invention, a method for simulating the amplitude data of sea clutter with a positive alpha stable distribution may include:

[0053] S201. Obtain simulation parameters for symmetrical Alpha stable distribution sea clutter data.

[0054] The simulation parameters include the number of sea clutter range cells, the number of pulses, preset characteristic index parameters, and preset scale parameters.

[0055] Step S201 is the same as step S101, so it will not be described again here.

[0056] S202. Determine the characteristic function of the positive Alpha stable distribution based on the preset characteristic function of the Alpha stable distribution, the preset parameter range, and the initial comprehensive scale parameter.

[0057] Before determining the feature function of the positive Alpha stable distribution based on the feature function of the preset Alpha stable distribution, the preset parameter range, and the initial comprehensive scale parameter, it is necessary to obtain the feature function of the preset Alpha stable distribution.

[0058] Specifically, the characteristic function of the presupposed Alpha stable distribution is the general form of the Alpha stable distribution characteristic function. The expression is:

[0059]

[0060] in, Let t be the feature function of the pre-defined alpha stable distribution, i be the imaginary unit, α be the initial feature exponent parameter and α∈(0,2], σ be the initial scale parameter and σ>0, β be the initial skewness parameter and β∈[-1,1], and μ be the initial location parameter and μ be the initial location parameter. It represents the set of real numbers.

[0061] Specifically, based on the preset alpha stable distribution feature function, preset parameter range, and initial comprehensive scale parameters, the feature function of the positive alpha stable distribution is determined, including:

[0062] Step A1: Obtain the characteristic function of the first positive Alpha stable distribution based on the preset Alpha stable distribution characteristic function and preset parameter range.

[0063] The characteristic function of the presupposed Alpha stable distribution is the general form of the Alpha stable distribution characteristic function. The preset parameter range can include (0,1], 1, and 0.

[0064] Based on the definition of a positive Alpha stable distribution, the characteristic function of the general form of the Alpha stable distribution is... The initial feature index parameter α is set to a preset range of α∈(0,1], the initial skewness parameter β is set to β=1, and the initial position parameter μ is set to μ=0. These parameter values ​​are then substituted into the feature function of the preset Alpha stable distribution. From the formula, we obtain the characteristic function φ of the first positive Alpha stable distribution. PαS 1(t):

[0065]

[0066] Where, φ PαS 1(t) is the characteristic function of the first positive Alpha stable distribution, t is the time variable, i is the imaginary unit, σ is the initial scale parameter, and α is the initial characteristic exponent parameter.

[0067] Step A2: Determine the characteristic function of the positive Alpha stable distribution based on the characteristic function of the first positive Alpha stable distribution and the initial integrated scale parameter.

[0068] Specifically, based on the characteristic function of the first positive alpha stable distribution and the initial integrated scale parameter, the characteristic function of the positive alpha stable distribution is determined, including:

[0069] The initial comprehensive scale parameter, i.e., the initial comprehensive scale parameter of a positive Alpha stable distribution, is expressed as γ = σ. α / cos(πα / 2), by rearranging terms, we get σ α =γ*cos(πα / 2), where σ α Substituting γ*cos(πα / 2) into the characteristic function φ of the first positive Alpha stable distribution obtained in step A1,... PαS From 1(t), we can obtain:

[0070]

[0071] Where, φ PαS 2(t) is the characteristic function of the stable distribution of the intermediate positive Alpha, γ is the initial comprehensive scale parameter, α is the initial characteristic exponent parameter, σ is the initial scale parameter, t is the time variable, and i is the imaginary unit;

[0072] By utilizing the relationship between the Laplace transform and the definition of the characteristic function, the formula for the characteristic function of the intermediate positive alpha stable distribution can be simplified to obtain the simplified characteristic function of the positive alpha stable distribution, i.e., the characteristic function φ of the positive alpha stable distribution. P ′ αS (t):

[0073] φ P ′ αS(t)=exp(-γt α );

[0074] Where, φ P ′ αS (t) is the characteristic function of the positive Alpha stable distribution, γ is the initial comprehensive scale parameter, α is the initial characteristic exponent parameter, and t is the time variable.

[0075] The following steps S203-S206 are specific operations for determining the probability density function based on the characteristic function of the stable distribution of positive Alpha, the inverse Laplace transform, the Merlin transform property, and the G function.

[0076] S203. Convert the initial feature index parameters into intermediate feature index parameters.

[0077] The intermediate feature index parameter is a fractional expression of the initial feature index parameter, and the feature function of the positive Alpha stable distribution includes the initial feature index parameter.

[0078] Converting initial feature index parameters to intermediate feature index parameters includes: converting initial feature index parameters into intermediate feature index parameters in fractional form.

[0079] α = v / u, v <u;

[0080] Where α is the initial feature index parameter, v is the first intermediate parameter, u is the second intermediate parameter, and v and u are positive integers.

[0081] S204. Perform an inverse Laplace transform on the characteristic function of the positive Alpha stable distribution to obtain the first probability density function.

[0082] The first probability density function is an integral form of the probability density function.

[0083] Taking the inverse Laplace transform of the characteristic function of the positive Alpha stable distribution, we obtain the first probability density function in integral form:

[0084]

[0085] Where f1(z) is the first probability density function, For the inverse Laplace transform, φ P ′ αS (t) is the characteristic function of a positive Alpha stable distribution, γ is the initial integrated scale parameter, α is the initial characteristic exponent parameter, z is the initial sea clutter amplitude value, t is the time variable, and exp(-γt) α ) is e of -γt α Power of 1.

[0086] S205. Based on the properties of the Merlin transform and the first probability density function, the second probability density function is obtained.

[0087] Specifically, according to the properties of Merlin transform, we can obtain: Substituting this formula into the formula for the first probability density function above, we get:

[0088]

[0089] Where f2(z) is the second probability density function, z is the initial sea clutter amplitude value, γ is the initial synthesis scale parameter, α is the initial characteristic index parameter, s is the seventh intermediate variable, i is the imaginary unit, and Γ(·) is the Gamma function.

[0090] S206. Determine the probability density function based on the intermediate characteristic index parameter, the second probability density function, the properties of the Gamma function, and the G function.

[0091] The probability density function is used to indicate the closed-loop representation of a positive alpha stable distribution with respect to the G function.

[0092] Specifically, the probability density function is determined based on the intermediate feature index parameter, the second probability density function, the properties of the Gamma function, and the G function, including:

[0093] Step B1: Substitute the intermediate feature index parameters into the second probability density function and perform variable substitution to obtain the third probability density function.

[0094] Substituting the intermediate characteristic exponent parameter α = v / u into the formula for the second probability density function f2(z) and performing variable substitution, i.e. s / u = t, we obtain the third probability density function:

[0095]

[0096] Where f3(z) is the third probability density function, z is the initial sea clutter amplitude value, u is the second intermediate parameter, i is the imaginary unit, t is the time variable, v is the first intermediate parameter, L1 is the integration path, Γ(·) is the Gamma function, and γ is the initial synthesis scale parameter.

[0097] Step B2: Based on the properties of the Gamma function, the G function, and the third probability density function, determine the probability density function using the following first formula:

[0098]

[0099] Among them, a h =(u-h+1) / u, b j= (v-j+1) / v, h = 1, 2, ..., u, j = 1, 2, ..., v, f(z) is the probability density function, z is the initial sea clutter amplitude value, γ is the initial composite scale parameter, v is the first intermediate parameter, u is the second intermediate parameter, a u b is the third intermediate parameter. v The fourth intermediate parameter, To use the Meijer G function with parameters (0, u, u, v), a h b is the h-th third intermediate parameter. j This is the j-th fourth intermediate parameter.

[0100] Specifically, based on the properties of the Gamma function, that is... And the G function simplifies the formula for the probability density function, yielding the probability density function, which is the probability density function of the positive alpha stable distribution with respect to the closed-form representation of the G function:

[0101]

[0102] S207. Determine the cumulative distribution function based on the probability density function.

[0103] Specifically, determining the cumulative distribution function based on the probability density function includes:

[0104] Step C1: Determine the first cumulative distribution function based on the probability density function and the integral relationship between the probability density function and the cumulative distribution function.

[0105] The formula for the first cumulative distribution function is:

[0106]

[0107] Where F1(z) is the first cumulative distribution function, f(x) is the probability density function, and to distinguish it from z in F1(z), f(z) in step B2 is replaced with f(x), x is the independent variable of the function, v is the first intermediate parameter, u is the second intermediate parameter, and a u b is the third intermediate parameter. v The fourth intermediate parameter, The Meijer G function with parameters (0, u, u, v) is used, and γ is the initial synthesis scale parameter.

[0108] Step C2: Based on the first cumulative distribution function, the cumulative distribution function, i.e., the cumulative distribution function representing the positive Alpha stable distribution with respect to the closure of the G function, is obtained using the following second formula:

[0109]

[0110] Where, a′ h=(u-h+1) / u, b j ′=(vj) / v, h=1,2,...,u, j=1,2,...,v, F(z) is the cumulative distribution function, z is the initial sea clutter amplitude value, γ is the initial composite scale parameter, v is the first intermediate parameter, u is the second intermediate parameter, a u ′ is the fifth intermediate parameter, b v ′ is the sixth intermediate parameter. To use the Meijer G function with parameters (0, u, u, v), a′ h b is the h-th fifth intermediate parameter. j ′ represents the j-th sixth intermediate parameter.

[0111] S208. Based on the cumulative distribution function and the preset interval, establish a correspondence table between multiple target characteristic index parameters, multiple target comprehensive scale parameters, multiple target sea clutter amplitude values ​​and the corresponding cumulative distribution function values.

[0112] The preset intervals include the first preset interval, the second preset interval, and the third preset interval, and the cumulative distribution function includes the initial characteristic index parameter, the initial sea clutter amplitude value, and the initial composite scale parameter.

[0113] Specifically, based on the cumulative distribution function and preset intervals, a correspondence table is established between multiple target characteristic index parameters, multiple target comprehensive scale parameters, multiple target sea clutter amplitude values, and the corresponding cumulative distribution function values, including:

[0114] Step D1: Based on the initial feature index parameters and the first preset interval, obtain multiple target feature index parameters at preset time intervals.

[0115] The first preset interval is [0,1].

[0116] Specifically, the initial feature index parameter α is set to a value between the first preset interval [0,1], and is taken at 0.01 intervals starting from a preset time of 0.01, thus obtaining multiple target feature index parameter values ​​α. p That is, the initial characteristic index parameter α takes values ​​of 0.01, 0.02, 0.03...0.99, 1, for a total of 100 values, denoted as α. p , where p = 1, 2, ..., 100, and p is the number of initial characteristic index parameters α.

[0117] The preset time can also be 0.02; there is no limitation on the preset time here.

[0118] Step D2: Based on the initial integrated scale parameters and the second preset interval, obtain multiple target integrated scale parameters at preset time intervals.

[0119] The second preset interval can be [0,10] or [0,20], and there is no limitation on the second preset interval here.

[0120] Specifically, the initial comprehensive scale parameter γ is set between the second preset interval [0,10], and the value is taken once every 0.01 starting from the preset time 0.01 to obtain multiple target comprehensive scale parameter values ​​γ. q That is, the initial comprehensive scaling parameter γ takes values ​​of 0.01, 0.02, 0.03...9.99, 10, for a total of 1000 values, denoted as γ. q , where q = 1, 2, ..., 1000, and q is the number of initial integrated scale parameters γ.

[0121] Step D3: Based on the initial sea clutter amplitude value and the third preset interval, obtain multiple target sea clutter amplitude values ​​at preset time intervals.

[0122] The third preset interval can be [0, 1000] or [0, 2000], and there is no limitation on the third preset interval here.

[0123] Specifically, the initial simulated clutter amplitude value z is set between [0, 1000], and the value is taken every 0.01 seconds starting from a preset time of 0.01 to obtain multiple target clutter amplitude values ​​z. r That is, the initial clutter amplitude value z takes values ​​of 0.01, 0.02, 0.03...999.99, 1000, for a total of 100,000 values, denoted as z. r , where r = 1, 2, ... 100000, and r is the number of initial simulated clutter amplitude values ​​z.

[0124] Step D4: Establish a three-dimensional parameter matrix based on multiple target characteristic index parameters, multiple target comprehensive scale parameters, and multiple target sea clutter amplitude values.

[0125] Each element in the three-dimensional parameter matrix contains a target feature index parameter, a target comprehensive scale parameter, and a target sea clutter amplitude value.

[0126] Specifically, using multiple different target feature index parameter values ​​α p Different integrated scale parameters γ for multiple targets q Different target sea clutter amplitude values ​​z r Construct a 100×1000×100000 three-dimensional parameter matrix, where each element of the matrix is ​​(α... p ,γ q ,z r ).

[0127] Step D5: Substitute each element in the three-dimensional parameter matrix into the cumulative distribution function to obtain the value of the cumulative distribution function corresponding to each element.

[0128] Specifically, iterate through each element in the three-dimensional parameter matrix, and set each element (α) p ,γ q ,z r Substituting these values ​​into the formula for the cumulative distribution function, we can calculate the value of the cumulative distribution function F(z) for each element. r ; α = α p ,γ=γ q The values ​​of these cumulative distribution functions obtained are different.

[0129] Step D6: Associate each element with the value of the corresponding cumulative distribution function to establish a correspondence table.

[0130] Specifically, each element is associated with the value of the corresponding cumulative distribution function, such that each element (α) in the three-dimensional parameter matrix... p ,γ q ,z r ) and the corresponding cumulative distribution function value F(z) r ; α = α p ,γ=γ q This establishes a one-to-one correspondence between each element in the three-dimensional parameter matrix and the corresponding cumulative distribution function value, thus creating a table showing the relationship between each element and the value of the cumulative distribution function.

[0131] S209. Generate a random number matrix based on the number of sea clutter range cells, the number of pulses, and the random distribution parameters.

[0132] Specifically, a random number matrix is ​​generated based on the number of sea clutter range cells, the number of pulses, and random distribution parameters, including:

[0133] Step E1: Generate a zero matrix of a preset length based on the number of sea clutter range cells, the number of pulses, and the zero matrix.

[0134] The zero matrix of the preset length includes multiple zero elements. The preset length is M×N.

[0135] Specifically, based on the number of sea clutter range cells M, the number of pulses N, and the zero matrix, a zero matrix of preset length M×N is generated:

[0136]

[0137] Where D is a zero matrix of preset length, M is the number of sea clutter range cells, and N is the number of pulses.

[0138] Step E2: Generate multiple random numbers based on the random distribution parameters.

[0139] The number of random numbers is the same as the number of zero elements. The random distribution parameter is (0,1), and the generated random numbers are uniformly distributed.

[0140] Generate M×N random numbers that are uniformly distributed with random distribution parameters (0,1).

[0141] Step E3: Replace each of the zero elements row by row with a random number to obtain a random number matrix.

[0142] The zero elements are replaced row by row with multiple random numbers to obtain a random number matrix. Alternatively, following the principle of left-to-right and top-to-bottom, multiple random numbers are used to sequentially replace the zero elements in a zero matrix of a preset length, resulting in a uniformly distributed random number matrix D1 with random distribution parameters (0,1).

[0143]

[0144] Where D1 is the random number matrix, Rnd1 is the first random number, M is the number of sea clutter range cells, and N is the number of pulses.

[0145] The following steps S209-S210 are specific operations for determining the target sea clutter amplitude data matrix based on preset characteristic index parameters, preset scale parameters, random number matrix and corresponding relationship table.

[0146] S210. Determine the first feature index parameter and the first comprehensive scale parameter based on the preset feature index parameter and the preset scale parameter.

[0147] Specifically, based on the preset feature index parameter α′, the corresponding first feature index parameter, i.e., the feature index parameter of the positive Alpha stable distribution, is determined.

[0148]

[0149] in, α is the first feature index parameter, and α′ is the preset feature index parameter.

[0150] According to the first characteristic index parameter And a preset scale parameter σ′ is used to determine the corresponding first comprehensive scale parameter, which is the comprehensive scale parameter of the positive Alpha stable distribution.

[0151]

[0152] in, σ′ is the first comprehensive scale parameter, and σ′ is the preset scale parameter. This is the parameter of the first characteristic index.

[0153] S211. Determine the target sea clutter amplitude data matrix based on the first characteristic index parameter, the first comprehensive scale parameter, the random number matrix, and the corresponding relationship table.

[0154] The target sea clutter amplitude data matrix is ​​used to simulate sea clutter data.

[0155] Specifically, based on the first characteristic index parameter, the first comprehensive scale parameter, the random number matrix, and the corresponding relationship table, the target sea clutter amplitude data matrix is ​​determined, including:

[0156] Step F1: Compare the first feature index parameter with multiple target feature index parameters in the corresponding relation table to determine the second feature index parameter.

[0157] Among them, the second characteristic index parameter To be related to the first characteristic index parameter The parameters with the smallest difference.

[0158] The first characteristic index parameter Multiple target feature index parameters α in the corresponding relationship table p Compare and find the corresponding table with closest α p Recorded as

[0159] Step F2: Compare the first comprehensive scale parameter with the multiple target comprehensive scale parameters in the corresponding relationship table to determine the second comprehensive scale parameter.

[0160] Among them, the second comprehensive scale parameter To be consistent with the first comprehensive scale parameter The parameters with the smallest difference.

[0161] The first comprehensive scale parameter The comprehensive scale parameter γ of multiple targets in the corresponding relationship table q Compare and find the corresponding table with closest γ q Recorded as

[0162] Step F3: Replace all target feature index parameters in the correspondence table with the second feature index parameters, and replace all target comprehensive scale parameters in the correspondence table with the second comprehensive scale parameters.

[0163] The corresponding relationship table as well as

[0164] Step F4: Based on the second characteristic index parameter, the second comprehensive scale parameter, and the corresponding multiple target sea clutter amplitude values, update the values ​​of all cumulative distribution functions in the corresponding relationship table to obtain the updated values ​​of all cumulative distribution functions.

[0165] According to the second characteristic index parameter Second comprehensive scale parameter Given the corresponding target sea clutter amplitude values, update the cumulative distribution function values ​​in the corresponding relationship table to obtain all updated cumulative distribution function values.

[0166] Step F5: Compare each element in the random number matrix with the values ​​of all updated cumulative distribution functions in the corresponding relation table to determine the final sea clutter amplitude value corresponding to each element, thereby determining the target sea clutter amplitude data matrix.

[0167] The final sea clutter amplitude value is the sea clutter amplitude value corresponding to the cumulative distribution function value that differs from each element the least.

[0168] For each element in the random number matrix D1, match it with all the updated cumulative distribution function values ​​in the corresponding relation table. By comparison, the value of the cumulative distribution function that is closest to each element in the random number matrix is ​​determined. The final sea clutter amplitude value z is determined from the value of the closest cumulative distribution function. r The final sea clutter amplitude value z can be obtained. r denoted as z mn Where m = 1, 2, ..., M, n = 1, 2, ..., N, z mn For each element in the target sea clutter amplitude data matrix, M is the number of sea clutter range cells, and N is the number of pulses.

[0169] The target sea clutter amplitude data matrix Z will be constructed based on the final sea clutter amplitude value corresponding to each element:

[0170] Z = [z mn ] M×N ;

[0171] Where Z is the target sea clutter amplitude data matrix.

[0172] Furthermore, after obtaining the target sea clutter amplitude data matrix, the sea clutter data with a symmetrical alpha stable distribution can be simulated more accurately based on these target sea clutter amplitude data matrices, thereby achieving the purpose of accurate sea clutter simulation. This can expand the sea clutter data so that the radar can identify targets based on the sea clutter data.

[0173] Figure 3A schematic diagram illustrating the probability density comparison is provided. Based on simulation parameters (number of sea clutter range cells, number of pulses, preset characteristic index parameters, and preset scale parameters), simulation parameters for the positive Alpha stable distribution are obtained and further substituted into the probability density function of the positive Alpha stable distribution expressed with respect to the G function closure. The independent variable interval of the probability density function is set to [1:1000] with a 1-interval. The probability density function image is plotted and compared with the probability density function image of the ideal positive Alpha stable distribution. The results are as follows: Figure 3 As shown. From Figure 3 It can be seen that the probability density function value calculated using the probability density function of the positive Alpha stable distribution with respect to the closed representation of the G function in this invention is very close to the probability density value of the ideal positive Alpha stable distribution, and the relative entropy (Kullback-Leibler Divergence, KL distance) is 5.81 × 10⁻⁶. -4 This demonstrates that the method and related calculations of the present invention can accurately characterize the positive Alpha stable distribution probability density value.

[0174] Figure 4 A schematic diagram of sea clutter amplitude data under simulated parameters is shown. This invention generates sea clutter amplitude data under simulated parameters and further plots the data. The horizontal axis represents different range cell numbers, the vertical axis represents different echo pulses, and the color represents the amplitude of the generated sample. The sea clutter amplitudes under different range cells and different echo pulses are compared, and the results are as follows: Figure 4 As shown. From Figure 4 It can be seen that the amplitude of sea clutter generated varies under different distance cells and echo pulses.

[0175] Figure 5 A schematic diagram illustrating the comparison of probability density function curves is provided. Using embodiments of the present invention, sea clutter amplitude data under simulated parameters is generated, and histogram statistics are further performed on the data to obtain the empirical probability density function of the simulated data. The empirical probability density function curve is plotted and compared with the ideal probability density function curve. The results are as follows: Figure 5 As shown. From Figure 5 It can be seen that the empirical probability density curve of sea clutter amplitude generated by the embodiments of the present invention matches the ideal probability density function curve, indicating that the method of simulating positive Alpha stable distribution sea clutter amplitude data in the embodiments of the present invention is effective.

[0176] The present invention provides a method for simulating the amplitude data of positive alpha-stable sea clutter distributions. Utilizing the inverse Laplace transform, Merlin transform, and the definition of the G function, the probability density function of a positive alpha-stable distribution is expressed as a closed-form expression of the G function. This overcomes the limitation that the probability density function of a positive alpha-stable distribution lacks a closed-form expression of elementary functions. Furthermore, the introduction of the G function provides feasibility and convenience for calculating the probability density function of a positive alpha-stable distribution and for simulating symmetric alpha-stable sea clutter data using the spherically invariant random process method. The method directly generates sea clutter amplitude data using the Monte Carlo method, which is simpler than indirect methods and eliminates the need for cumbersome parameter conversions.

[0177] Based on the same inventive concept, as an implementation of the above-mentioned method for simulating the amplitude data of positive Alpha stable distribution sea clutter, this embodiment of the invention also provides a device for simulating the amplitude data of positive Alpha stable distribution sea clutter. Figure 6 This is a structural diagram of the device in an embodiment of the present invention. See also: Figure 6 As shown, the simulation device for positive Alpha stable distribution sea clutter amplitude data may include:

[0178] The acquisition module 601 is used to acquire simulation parameters of symmetric Alpha stable distribution sea clutter data. The simulation parameters include the number of sea clutter range cells, the number of pulses, preset characteristic index parameters, and preset scale parameters.

[0179] The first determining module 602 is used to determine the characteristic function of the positive Alpha stable distribution based on the preset characteristic function of the Alpha stable distribution, the preset parameter range, and the initial comprehensive scale parameter.

[0180] The second determining module 603 is used to determine the probability density function based on the characteristic function of the positive Alpha stable distribution, the inverse Laplace transform, the Merlin transform property and the G function. The probability density function is used to indicate the closed representation of the positive Alpha stable distribution with respect to the G function.

[0181] The third determining module 604 is used to determine the cumulative distribution function based on the probability density function;

[0182] Module 605 is established to create a table of correspondences between multiple target characteristic index parameters, multiple target comprehensive scale parameters, multiple target sea clutter amplitude values ​​and the corresponding cumulative distribution function values, based on the cumulative distribution function and preset intervals.

[0183] The generation module 606 is used to generate a random number matrix based on the number of sea clutter range cells, the number of pulses, and random distribution parameters;

[0184] The fourth determining module 607 is used to determine the target sea clutter amplitude data matrix based on preset characteristic index parameters, preset scale parameters, random number matrix and corresponding relationship table. The target sea clutter amplitude data matrix is ​​used to simulate sea clutter data.

[0185] The first determining module 602 is specifically used to obtain the characteristic function of the first positive Alpha stable distribution based on the characteristic function of the preset Alpha stable distribution and the preset parameter range; and to determine the characteristic function of the positive Alpha stable distribution based on the characteristic function of the first positive Alpha stable distribution and the initial comprehensive scale parameter.

[0186] The second determining module 603 is specifically used to convert the initial feature index parameters into intermediate feature index parameters, which are fractional expressions of the initial feature index parameters; to perform an inverse Laplace transform on the feature function of the positive Alpha stable distribution to obtain a first probability density function, which is an integral form of the probability density function; to obtain a second probability density function based on the Merlin transform property and the first probability density function; and to determine the probability density function based on the intermediate feature index parameters, the second probability density function, the property of the Gamma function, and the G function.

[0187] The second determining module 603 determines the probability density function based on the intermediate feature index parameter, the second probability density function, the properties of the Gamma function, and the G function. This includes: substituting the intermediate feature index parameter into the second probability density function and performing variable substitution to obtain the third probability density function; and determining the probability density function using the following first formula based on the properties of the Gamma function, the G function, and the third probability density function:

[0188]

[0189] Among them, a h =(u-h+1) / u, b j = (v-j+1) / v, h = 1, 2, ..., u, j = 1, 2, ..., v, f(z) is the probability density function, z is the initial sea clutter amplitude value, γ is the initial composite scale parameter, v is the first intermediate parameter, u is the second intermediate parameter, a u b is the third intermediate parameter. v The fourth intermediate parameter, To use the Meijer G function with parameters (0, u, u, v), a h b is the h-th third intermediate parameter. j This is the j-th fourth intermediate parameter.

[0190] The third determining module 604 is specifically used to determine the first cumulative distribution function based on the probability density function and the integral relationship between the probability density function and the cumulative distribution function; and to obtain the cumulative distribution function based on the first cumulative distribution function using the following second formula:

[0191]

[0192] Where, a′ h =(u-h+1) / u, b j ′=(vj) / v, h=1,2,...,u, j=1,2,...,v, F(z) is the cumulative distribution function, z is the initial sea clutter amplitude value, γ is the initial composite scale parameter, v is the first intermediate parameter, u is the second intermediate parameter, a u ′ is the fifth intermediate parameter, b v ′ is the sixth intermediate parameter. To use the Meijer G function with parameters (0, u, u, v), a′ h b is the h-th fifth intermediate parameter. j ′ represents the j-th sixth intermediate parameter.

[0193] Module 605 is specifically used to: acquire multiple target feature index parameters according to initial feature index parameters and a first preset interval at preset time intervals; acquire multiple target comprehensive scale parameters according to initial comprehensive scale parameters and a second preset interval at preset time intervals; acquire multiple target sea clutter amplitude values ​​according to initial sea clutter amplitude values ​​and a third preset interval at preset time intervals; establish a three-dimensional parameter matrix based on multiple target feature index parameters, multiple target comprehensive scale parameters, and multiple target sea clutter amplitude values, where each element in the three-dimensional parameter matrix contains one target feature index parameter, one target comprehensive scale parameter, and one target sea clutter amplitude value; substitute each element in the three-dimensional parameter matrix into the cumulative distribution function to obtain the value of the cumulative distribution function corresponding to each element; and associate each element with the value of the corresponding cumulative distribution function to establish a correspondence table, wherein the preset intervals include the first preset interval, the second preset interval, and the third preset interval, and the cumulative distribution function includes the initial feature index parameters, the initial sea clutter amplitude value, and the initial comprehensive scale parameter.

[0194] The generation module 606 is specifically used to generate a zero matrix of a preset length based on the number of sea clutter range cells, the number of pulses, and the zero matrix. The zero matrix of the preset length includes multiple zero elements. Based on the random distribution parameters, multiple random numbers are generated, and the number of random numbers is the same as the number of zero elements. The multiple zero elements are replaced row by row with multiple random numbers to obtain a random number matrix.

[0195] The fourth determining module 607 is specifically used to determine the first characteristic index parameter and the first comprehensive scale parameter based on the preset characteristic index parameter and the preset scale parameter; and to determine the target sea clutter amplitude data matrix based on the first characteristic index parameter, the first comprehensive scale parameter, the random number matrix and the corresponding relationship table.

[0196] The fourth determining module 607 determines the target sea clutter amplitude data matrix based on the first characteristic index parameter, the first comprehensive scale parameter, the random number matrix, and the correspondence table. This includes: comparing the first characteristic index parameter with multiple target characteristic index parameters in the correspondence table to determine a second characteristic index parameter, which is the parameter with the smallest difference from the first characteristic index parameter; comparing the first comprehensive scale parameter with multiple target comprehensive scale parameters in the correspondence table to determine a second comprehensive scale parameter, which is the parameter with the smallest difference from the first comprehensive scale parameter; and replacing all multiple target characteristic index parameters in the correspondence table with the first characteristic index parameter. The second characteristic index parameter is used, and multiple target integrated scale parameters in the corresponding relationship table are replaced with the second integrated scale parameter. Based on the second characteristic index parameter, the second integrated scale parameter, and the corresponding multiple target sea clutter amplitude values, the values ​​of all cumulative distribution functions in the corresponding relationship table are updated to obtain the values ​​of all updated cumulative distribution functions. Each element in the random number matrix is ​​compared with the values ​​of all updated cumulative distribution functions in the corresponding relationship table to determine the final sea clutter amplitude value corresponding to each element, thereby determining the target sea clutter amplitude data matrix. The final sea clutter amplitude value is the sea clutter amplitude value corresponding to the cumulative distribution function value that differs the least from each element.

[0197] It should be noted that the above description of the embodiment of the positive alpha stable distribution sea clutter amplitude data simulation device is similar to the description of the above embodiment of the positive alpha stable distribution sea clutter amplitude data simulation method, and has similar beneficial effects. For technical details not disclosed in the embodiments of the positive alpha stable distribution sea clutter amplitude data simulation device of the present invention, please refer to the description of the embodiment of the positive alpha stable distribution sea clutter amplitude data simulation method of the present invention for understanding.

[0198] The above are merely specific embodiments 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 scope of the technology 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 simulating the amplitude data of sea clutter with a positive Alpha stable distribution, characterized in that, The method for simulating sea clutter amplitude data with a stable positive Alpha distribution includes: The simulation parameters for obtaining symmetric Alpha stable distribution sea clutter data are as follows: the number of sea clutter range cells, the number of pulses, the preset characteristic index parameter, and the preset scale parameter. Based on the preset alpha stable distribution feature function, preset parameter range, and initial comprehensive scale parameter, determine the feature function of the positive alpha stable distribution; Based on the characteristic function, inverse Laplace transform, Merlin transform property, and G function of the positive Alpha stable distribution, a probability density function is determined, which is used to indicate the closed representation of the positive Alpha stable distribution with respect to the G function. Determine the cumulative distribution function based on the probability density function; Based on the cumulative distribution function and the preset interval, establish a correspondence table between multiple target characteristic index parameters, multiple target comprehensive scale parameters, multiple target sea clutter amplitude values ​​and the corresponding cumulative distribution function values; A random number matrix is ​​generated based on the number of sea clutter range cells, the number of pulses, and the random distribution parameters; The target sea clutter amplitude data matrix is ​​determined based on the preset feature index parameter, the preset scale parameter, the random number matrix, and the correspondence table. The target sea clutter amplitude data matrix is ​​used to simulate sea clutter data.

2. The method for simulating positive Alpha stable distribution sea clutter amplitude data according to claim 1, characterized in that, The step of determining the feature function of a positive Alpha stable distribution based on the preset feature function of the Alpha stable distribution, the preset parameter range, and the initial comprehensive scale parameter includes: Based on the feature function of the preset Alpha stable distribution and the preset parameter range, the feature function of the first positive Alpha stable distribution is obtained; The characteristic function of the positive alpha stable distribution is determined based on the characteristic function of the first positive alpha stable distribution and the initial comprehensive scale parameter.

3. The method for simulating positive Alpha stable distribution sea clutter amplitude data according to claim 1, characterized in that, The characteristic function of the positive alpha stable distribution includes an initial characteristic exponent parameter. The determination of the probability density function based on the characteristic function of the positive alpha stable distribution, the inverse Laplace transform, the Merlin transform property, and the G function includes: The initial feature index parameter is converted into an intermediate feature index parameter, which is a fractional expression of the initial feature index parameter. The characteristic function of the positive Alpha stable distribution is subjected to the inverse Laplace transform to obtain the first probability density function, which is an integral form of the probability density function. Based on the Merlin transform property and the first probability density function, the second probability density function is obtained; The probability density function is determined based on the intermediate feature index parameter, the second probability density function, the properties of the Gamma function, and the G function.

4. The method for simulating sea clutter amplitude data with a positive Alpha stable distribution according to claim 3, characterized in that, The step of determining the probability density function based on the intermediate feature index parameter, the second probability density function, the properties of the Gamma function, and the G function includes: Substitute the intermediate feature index parameter into the second probability density function and perform variable substitution to obtain the third probability density function; Based on the properties of the Gamma function, the G function, and the third probability density function, the probability density function is determined using the following first formula: Among them, a h =(u-h+1) / u, b j = (v-j+1) / v, h = 1, 2, ..., u, j = 1, 2, ..., v, f(z) is the probability density function, z is the initial sea clutter amplitude value, γ is the initial composite scale parameter, v is the first intermediate parameter, u is the second intermediate parameter, a u b is the third intermediate parameter. v The fourth intermediate parameter, To use the Meijer G function with parameters (0, u, u, v), a h For the h-th third intermediate parameter, b j This is the j-th fourth intermediate parameter.

5. The method for simulating sea clutter amplitude data with a positive Alpha stable distribution according to claim 4, characterized in that, Determining the cumulative distribution function based on the probability density function includes: The first cumulative distribution function is determined based on the probability density function and the integral relationship between the probability density function and the cumulative distribution function. Based on the first cumulative distribution function, the cumulative distribution function is obtained using the following second formula: Where, a′ h =(u-h+1) / u, b j ′=(vj) / v, h=1,2,...,u, j=1,2,...,v, F(z) is the cumulative distribution function, z is the initial sea clutter amplitude value, γ is the initial composite scale parameter, v is the first intermediate parameter, u is the second intermediate parameter, a u ′ is the fifth intermediate parameter, b v ′ is the sixth intermediate parameter. To use the Meijer G function with parameters (0, u, u, v), a′ h For the h-th fifth intermediate parameter, b j ′ represents the j-th sixth intermediate parameter.

6. The method for simulating sea clutter amplitude data with a positive Alpha stable distribution according to claim 1, characterized in that, The preset intervals include a first preset interval, a second preset interval, and a third preset interval. The cumulative distribution function includes an initial characteristic index parameter, an initial sea clutter amplitude value, and the initial synthetic scale parameter. The step of establishing a correspondence table between multiple target characteristic index parameters, multiple target synthetic scale parameters, multiple target sea clutter amplitude values, and the corresponding values ​​of the cumulative distribution function, based on the cumulative distribution function and the preset intervals, includes: Based on the initial feature index parameters and the first preset interval, the plurality of target feature index parameters are obtained at preset time intervals. Based on the initial integrated scale parameters and the second preset interval, the plurality of target integrated scale parameters are obtained at the preset time interval; Based on the initial sea clutter amplitude value and the third preset interval, the amplitude values ​​of the plurality of target sea clutter are obtained at the preset time interval. A three-dimensional parameter matrix is ​​established based on the multiple target feature index parameters, the multiple target comprehensive scale parameters, and the multiple target sea clutter amplitude values. Each element in the three-dimensional parameter matrix contains one target feature index parameter, one target comprehensive scale parameter, and one target sea clutter amplitude value. Substitute each element in the three-dimensional parameter matrix into the cumulative distribution function to obtain the value of the cumulative distribution function corresponding to each element; Each element is associated with the corresponding value of the cumulative distribution function to establish the correspondence table.

7. The method for simulating sea clutter amplitude data with a positive Alpha stable distribution according to claim 1, characterized in that, The step of generating a random number matrix based on the number of sea clutter range cells, the number of pulses, and random distribution parameters includes: Based on the number of sea clutter range cells, the number of pulses, and the zero matrix, a zero matrix of a preset length is generated, wherein the zero matrix of the preset length includes multiple zero elements; Based on the random distribution parameters, multiple random numbers are generated, and the number of the multiple random numbers is the same as the number of the multiple zero elements; The plurality of zero elements are replaced row by row with the plurality of random numbers to obtain the random number matrix.

8. The method for simulating sea clutter amplitude data with a positive Alpha stable distribution according to claim 1, characterized in that, The step of determining the target sea clutter amplitude data matrix based on the preset feature index parameter, the preset scale parameter, the random number matrix, and the correspondence table includes: The first feature index parameter and the first comprehensive scale parameter are determined based on the preset feature index parameter and the preset scale parameter; The target sea clutter amplitude data matrix is ​​determined based on the first characteristic index parameter, the first comprehensive scale parameter, the random number matrix, and the correspondence table.

9. The method for simulating sea clutter amplitude data with a positive Alpha stable distribution according to claim 8, characterized in that, The step of determining the target sea clutter amplitude data matrix based on the first characteristic index parameter, the first comprehensive scale parameter, the random number matrix, and the correspondence table includes: The first feature index parameter is compared with the plurality of target feature index parameters in the correspondence table to determine the second feature index parameter, which is the parameter that differs from the first feature index parameter the smallest. The first comprehensive scale parameter is compared with the plurality of target comprehensive scale parameters in the corresponding relationship table to determine the second comprehensive scale parameter, which is the parameter that differs from the first comprehensive scale parameter the least. Replace all the target feature index parameters in the correspondence table with the second feature index parameters, and replace all the target comprehensive scale parameters in the correspondence table with the second comprehensive scale parameters; Based on the second characteristic index parameter, the second comprehensive scale parameter, and the corresponding multiple target sea clutter amplitude values, update the values ​​of all cumulative distribution functions in the corresponding relationship table to obtain the updated values ​​of all cumulative distribution functions; Each element in the random number matrix is ​​compared with the value of all updated cumulative distribution functions in the correspondence table to determine the final sea clutter amplitude value corresponding to each element, thereby determining the target sea clutter amplitude data matrix. The final sea clutter amplitude value is the sea clutter amplitude value corresponding to the cumulative distribution function value that differs from each element the least.

10. A device for simulating sea clutter amplitude data with a positive Alpha stable distribution, characterized in that, The positive Alpha stable distribution sea clutter amplitude data simulation device includes: The acquisition module is used to acquire simulation parameters of symmetric Alpha stable distribution sea clutter data. The simulation parameters include the number of sea clutter range cells, the number of pulses, preset characteristic index parameters, and preset scale parameters. The first determining module is used to determine the characteristic function of the positive Alpha stable distribution based on the preset characteristic function of the Alpha stable distribution, the preset parameter range, and the initial comprehensive scale parameter. The second determining module is used to determine the probability density function based on the characteristic function, inverse Laplace transform, Merlin transform property, and G function of the positive Alpha stable distribution. The probability density function is used to indicate the closed representation of the positive Alpha stable distribution with respect to the G function. The third determining module is used to determine the cumulative distribution function based on the probability density function; A module is established to create a correspondence table between multiple target characteristic index parameters, multiple target comprehensive scale parameters, multiple target sea clutter amplitude values ​​and the corresponding values ​​of the cumulative distribution function, based on the cumulative distribution function and a preset interval. The generation module is used to generate a random number matrix based on the number of sea clutter range cells, the number of pulses, and random distribution parameters; The fourth determining module is used to determine the target sea clutter amplitude data matrix based on the preset feature index parameter, the preset scale parameter, the random number matrix and the correspondence table. The target sea clutter amplitude data matrix is ​​used to simulate sea clutter data.

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