Radar sea clutter parameter estimation method based on generalized Pareto distribution

Abstract

The invention relates to the technical field of radar signal processing, and provides a generalized Pareto distributed radar sea clutter parameter estimation method, which comprises the following steps of: obtaining a plurality of pieces of generalized Pareto distributed clutter data; constructing a fitness function based on an accumulative distribution function and a probability density function of the generalized Pareto distribution clutter data, and substituting the fitness function into a genetic algorithm; a global optimal particle of the generalized Pareto distribution clutter data is iteratively solved by combining a genetic algorithm and a particle swarm optimization algorithm, and when the number of iterations reaches a preset value or the global optimal particle keeps algebra equal to a preset algebra in the iteration process, iteration is stopped, and an optimal parameter value of generalized Pareto distribution is obtained; wherein the optimal parameter value is a global optimal particle when iteration is stopped, and the global optimal particle is a parameter enabling the fitness function value to reach the maximum; the parameter estimation method does not depend on a complex mathematical estimation expression, the parameter estimation precision is high, and the estimation range is wide.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and more specifically, to a radar sea clutter parameter estimation method based on generalized Pareto distribution. Background Art

[0002] The composite Gaussian model can well describe the statistical characteristics of sea clutter in high-resolution low-grinding angle radar detection scenarios, and has important practical value for realizing sea radar target detection and constant false alarm detection. According to different choices of texture distribution (mainly gamma distribution, inverse gamma distribution and inverse Gaussian distribution, etc.), the composite Gaussian model can be divided into K distribution, generalized Pareto distribution and IC-CG distribution. Among them, the generalized Pareto distribution has better performance in the statistical modeling of measured data in complex marine environments. In addition, the optimal detector of this distribution model is also the only feasible solution among the above three models. The accurate estimation of the distribution model parameters has a very important impact on the improvement of radar target detection performance. For different application scenarios, choosing a suitable parameter estimation method in actual engineering can achieve twice the result with half the effort.

[0003] When the traditional maximum likelihood estimation method is used for generalized Pareto distribution parameter estimation, it is necessary to solve the numerical calculation problem of the non-closed expression of the scale parameter, which leads to the low efficiency of this method. When solving the generalized Pareto distribution parameter estimation formula, the classical moment estimation method is affected by the domain of the gamma function, and the estimation range of the shape parameter is limited to a certain interval. For example, the second and fourth order moment estimation cannot solve the generalized Pareto distribution parameter estimation with a shape parameter less than 2. The prior art proposes a parameter estimation method of the first-order logarithmic moment, which expands the estimation range of the shape parameter to a situation greater than 1, and to a certain extent broadens the application scope of the generalized Pareto distribution. On the basis of the first-order logarithmic moment, the prior art also studies the logarithmic moment parameter estimation method with an order less than 1, and further expands the effective estimation range of the shape parameter of the generalized Pareto distribution to within 1. Although various logarithmic moment estimation methods have expanded the parameter estimation range of the generalized Pareto distribution, the presence of the Diagram function in the parameter estimation formula of this method leads to the fact that the estimation range of the shape parameter is still limited, and when the order is relatively low, the phenomenon of the non-closure of the parameter estimation expression will increase the complexity of the parameter estimation.

[0004] In summary, the existing traditional parameter estimation methods for generalized Pareto distribution have problems such as low estimation accuracy, limited estimation range, and non-closed expressions in parameter estimation formulas. Summary of the invention

[0005] In order to overcome the defects of low parameter estimation accuracy and limited estimation range in the above-mentioned prior art, the present invention provides a radar sea clutter parameter estimation method of generalized Pareto distribution with wide estimation range and high estimation result accuracy.

[0006] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0007] A generalized Pareto distribution radar sea clutter parameter estimation method comprises the following steps:

[0008] Obtain several pieces of generalized Pareto distribution clutter data;

[0009] Constructing a fitness function based on the cumulative distribution function and probability density function of the generalized Pareto distribution clutter data, and substituting the fitness function into a genetic algorithm;

[0010] Combining the genetic algorithm and the particle swarm optimization algorithm, the global optimal particle of the generalized Pareto distribution clutter data is iteratively solved. When the number of iterations reaches a preset value, or the number of generations of the global optimal particle during the iteration is equal to the preset number of generations, the iteration is stopped to obtain the optimal parameter value of the generalized Pareto distribution; wherein the optimal parameter value is the global optimal particle when the iteration is stopped, and the global optimal particle is the parameter that maximizes the value of the fitness function.

[0011] The present invention also proposes a generalized Pareto distribution radar sea clutter parameter estimation system, which is used to implement the generalized Pareto distribution radar sea clutter parameter estimation method mentioned above, and the system comprises:

[0012] A data acquisition module is used to acquire a number of generalized Pareto distribution clutter data;

[0013] A fitness function construction module, used to construct a fitness function based on the cumulative distribution function and probability density function of the generalized Pareto distribution clutter data, and substitute the fitness function into the genetic algorithm;

[0014] The optimal parameter value output module is used to combine the genetic algorithm and the particle swarm optimization algorithm to iteratively solve the global optimal particle of the generalized Pareto distribution clutter data. When the number of iterations reaches a preset value, or the number of generations of the global optimal particle during the iteration is equal to the preset number of generations, the iteration is stopped to obtain the optimal parameter value of the generalized Pareto distribution; wherein the optimal parameter value is the global optimal particle when the iteration is stopped, and the global optimal particle is the parameter that maximizes the value of the fitness function.

[0015] The present invention also proposes a computer device, comprising a memory and a processor, wherein the memory stores computer-readable instructions, and wherein when the computer-readable instructions are executed by the processor, the processor executes the steps of the above-mentioned generalized Pareto distribution radar sea clutter parameter estimation method.

[0016] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0017] The invention obtains a plurality of generalized Pareto distribution clutter data; constructs a fitness function based on the cumulative distribution function and probability density function of the generalized Pareto distribution clutter data, and substitutes the fitness function into a genetic algorithm; combines the genetic algorithm and the particle swarm optimization algorithm to iteratively solve the global optimal particle of the generalized Pareto distribution clutter data, and stops the iteration when the number of iterations reaches a preset value, or when the number of generations of the global optimal particle during the iteration is equal to the preset number of generations, to obtain the optimal parameter value of the generalized Pareto distribution; the parameter estimation method of the invention does not rely on complex mathematical estimation expressions, and has high parameter estimation accuracy and a wide estimation range. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of the radar sea clutter parameter estimation method of the generalized Pareto distribution proposed in Example 1;

[0019] Figure 2 This is a schematic diagram of the statistical characteristics of the generalized Pareto distribution under different parameters proposed in Example 1;

[0020] Figure 3 A schematic diagram of a PDF curve of a simulated generalized Pareto distribution proposed in Example 2;

[0021] Figure 4 A schematic diagram comparing the iterative processes of two different algorithms proposed in Example 2;

[0022] Figure 5 Schematic diagram of parameter estimation error curves of two different algorithms proposed in Example 2;

[0023] Figure 6 This is a schematic diagram of the framework of the parameter estimation system proposed in Example 3. DETAILED DESCRIPTION

[0024] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0025] In order to better illustrate the present embodiment, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product;

[0026] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0027] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0028] Example 1

[0029] This embodiment proposes a radar sea clutter parameter estimation method based on generalized Pareto distribution. Figure 1 Schematic diagram of the radar sea clutter parameter estimation method based on the generalized Pareto distribution proposed in this embodiment;

[0030] like Figure 1 As shown, the radar sea clutter parameter estimation method of the generalized Pareto distribution of this embodiment includes the following steps:

[0031] S1: Obtain several pieces of generalized Pareto distribution clutter data;

[0032] S2: constructing a fitness function based on the cumulative distribution function and probability density function of the generalized Pareto distribution clutter data, and substituting the fitness function into the genetic algorithm;

[0033] S3: Combining the genetic algorithm and the particle swarm optimization algorithm, iteratively solving the global optimal particle of the generalized Pareto distribution clutter data, when the number of iterations reaches a preset value, or when the number of generations of the global optimal particle during the iteration is equal to the preset number of generations, the iteration is stopped to obtain the optimal parameter value of the generalized Pareto distribution; wherein the optimal parameter value is the global optimal particle when the iteration is stopped, and the global optimal particle is the parameter that maximizes the value of the fitness function.

[0034] In the specific implementation process, a number of generalized Pareto distribution clutter data are obtained; a fitness function is constructed based on the cumulative distribution function and probability density function of the generalized Pareto distribution clutter data, and the fitness function is substituted into a genetic algorithm; the genetic algorithm and the particle swarm optimization algorithm are combined to iteratively solve the global optimal particle of the generalized Pareto distribution clutter data, and when the number of iterations reaches a preset value, or the number of generations of the global optimal particle during the iteration is equal to the preset number, the iteration is stopped to obtain the optimal parameter value of the generalized Pareto distribution; the parameter estimation method of the present invention does not rely on complex mathematical estimation expressions, and the parameter estimation accuracy is high and the estimation range is wide.

[0035] In an optional embodiment, the generalized Pareto distribution clutter data is obtained by simulating a generalized Pareto distribution random sequence using a sampling formula using a direct sampling method;

[0036] The expression of the sampling formula includes:

[0037]

[0038] In the formula, x i represents the i-th generalized Pareto distribution clutter data, a and b correspond to the shape parameter and scale parameter of the generalized Pareto distribution clutter data respectively, u i Represents x i The corresponding value range is a uniformly distributed random number in the range [0,1].

[0039] As an example, the parameters of the generalized Pareto distribution are set to a=3.5, b=0.5, and the number of clutter samples is 5×10 4 .

[0040] As an example, the generalized Pareto distribution is obtained by modulating the speckle component with the structure component. The structure component characterizes the average power of the sea clutter, while the speckle component reflects the texture characteristics of the sea surface. The probability density function (PDF) of the generalized Pareto distribution can be defined as:

[0041]

[0042] In the formula, f τ (τ; a, b) is the PDF of the structural component τ, which is a positive random process that obeys the inverse gamma distribution, that is:

[0043]

[0044] In the formula, a represents the shape parameter, which determines the degree of tailing of the statistical distribution. The larger the shape parameter a is, the more obvious the tailing phenomenon is; b represents the scale parameter, which reflects the power of the echo signal. u (x|τ) is the PDF of the speckle component u, which obeys the Rayleigh distribution, that is:

[0045]

[0046] The PDF of the generalized Pareto distribution is derived as:

[0047]

[0048] Where, parameters a and b are shape parameters and scale parameters, respectively. When shape parameter a→∞, the amplitude PDF of generalized Pareto distribution is approximately Rayleigh distribution, while when a→0, the amplitude tailing phenomenon of sea clutter gradually increases. In addition, the cumulative distribution function (CDF) of generalized Pareto distribution is:

[0049]

[0050] Figure 2 Schematic diagram of the statistical characteristics of the generalized Pareto distribution under different parameters proposed in this embodiment; when the shape parameter a and the scale parameter b are fixed respectively, the PDF curve of the generalized Pareto distribution changes with the changes of each parameter as shown in Figure 2 As shown. Figure 2 It can be seen that when the scale parameter b is fixed at 1.5, the peak of the PDF curve of the generalized Pareto distribution rises as the shape parameter increases, and the peak gradually moves in the direction of decreasing amplitude, and the tail becomes shorter. When the shape parameter a is fixed at 1.5, the peak of the PDF curve of the generalized Pareto distribution rises as the scale parameter increases, and the peak also moves in the direction of decreasing amplitude, and the tail gradually becomes shorter.

[0051] As an example, the basis for using the generalized Pareto distribution to complete the clutter statistical characteristics modeling is the accurate estimation of the dual parameters, thereby completing the maritime radar target detection process; the traditional generalized Pareto distribution parameter estimation methods include maximum likelihood estimation, moment estimation, and sequential statistics parameter estimation methods; maximum likelihood estimation is a classic parameter estimation method with extremely wide applications. This method has a relatively high parameter estimation accuracy and can achieve the Cramer-Laur lower bound; the log-likelihood function of the generalized Pareto distribution is as follows:

[0052]

[0053] Solve the derivatives of the above log-likelihood function with respect to the shape parameter a and the scale parameter b respectively, and set them equal to 0. Solve the likelihood function equation system to obtain the maximum likelihood estimate of the generalized Pareto distribution:

[0054]

[0055] The maximum likelihood estimation requires first obtaining the estimated value of the scale parameter b through numerical calculation methods, and then calculating the estimated result of the shape parameter a. The moment estimation method equates the origin moments of each order of the sample to the cumulative moments of the corresponding distribution PDF, and completes the parameter estimation process by solving the set of equations. The cumulative moment of the generalized Pareto distribution is calculated as follows:

[0056]

[0057] In the formula, variable λ = bx 2 The solution process involves the operation of the gamma function. From its properties, we can see that the above equation is valid only if a>r / 2 is satisfied, that is, the estimation range of the shape parameter will be limited. If the sea clutter sample data X=[x 1 ,x 2 ,…x n ], then the r-order sample origin moment of random data X is

[0058] From the derivation described in the example, it can be seen that the parameter estimation formula of maximum likelihood estimation is subject to complex numerical iterative calculation, which is relatively inefficient; the moment estimation method is limited by the estimation range of shape parameters, and the cumulative error of high-order moment samples leads to low parameter estimation accuracy; this application utilizes the advantages of intelligent algorithms in nonlinear optimization planning to establish a generalized Pareto distribution parameter estimation objective function that does not rely on complex mathematical parameter estimation formula calculations, thereby solving the problem of efficient and accurate parameter estimation of generalized Pareto distribution.

[0059] In an optional embodiment, the expression of the fitness function includes:

[0060]

[0061] In the formula, f fitness (θ) represents the fitness function, f(n;θ) and F(n;θ) represent the probability density function and cumulative distribution function of the nth generalized Pareto distribution clutter data, respectively, h(n) and H(n) represent the values ​​of the clutter statistical histogram of the nth generalized Pareto distribution clutter data on the probability density function curve and cumulative distribution function curve sampling interval, respectively, λ 1 and λ 2 Both represent weight coefficients, and N represents the total number of generalized Pareto distribution clutter data.

[0062] As an example, λ 1 =0.8,λ 2 =0.2.

[0063] In an optional embodiment, the step of searching for optimal parameters for the generalized Pareto distribution clutter data by combining a genetic algorithm and a particle swarm optimization algorithm includes:

[0064] Initialize the position and velocity of the particle swarm, where one particle of the particle swarm corresponds to a parameter value of the generalized Pareto distribution clutter data;

[0065] According to the fitness function, the fitness value of each particle in the particle swarm is calculated and the fitness value is regarded as the individual extreme value P of the particle. id , select the largest P in the particle swarm id As the global extreme value P gd ;

[0066] Update the weight factor using the inertia weight that decreases nonlinearly with the number of iterations;

[0067] The position and speed of the particle swarm are updated based on the particle swarm optimization algorithm; in each iteration, the speed and position of each particle are updated using the weight factor of the current iteration, the individual extreme value of the particle, and the global extreme value, and the fitness value of the particle of the current iteration is calculated, and the fitness value of the particle of the current iteration is compared with its individual extreme value P id Compare, if the current fitness value is greater than the individual extreme value P id , then use the current fitness value to update the individual extreme value P id , all particles complete the individual extreme value P id After updating, select the largest P in the particle swarm id As the new global extremum P gd ;

[0068] Determine whether the current number of iterations reaches the preset value, or whether the number of generations of the global optimal particle during the iteration is equal to the preset number of generations; wherein the global optimal particle is the global extreme value P gd The corresponding particles;

[0069] If yes, stop the iteration, and output the global optimal particle when the iteration is stopped as the optimal parameter value of the generalized Pareto distribution;

[0070] Otherwise, based on the genetic algorithm, after all particles have completed the position and velocity update, the hybridization pool size ratio P s The hybridization probability P among all particles decreases nonlinearly with the number of iterations. c A preset number of particles are selected, and particles are randomly selected as parent particles. The parent particles are hybridized with each other using the hybridization formula, and the parent particles are replaced with the child particles obtained by hybridization to form a new particle swarm. Based on the combination of genetic algorithm and particle swarm optimization algorithm, the optimal parameters of the new particle swarm are searched.

[0071] In an optional embodiment, the expression for updating the weight factor using the nonlinear decreasing inertia weight with the number of iterations includes:

[0072]

[0073] In the formula, k represents the current number of iterations, ω(k) represents the weight factor when the number of iterations is k, ωstart represents the initial inertia weight, ω end Represents the inertia weight when the iteration reaches the maximum number, N max Indicates the maximum number of iterations.

[0074] In an optional embodiment, the expression for updating the speed and position of each particle using the weight factor of the current iteration, the individual extreme value of the particle and the global extreme value includes:

[0075]

[0076] In the formula, represents the velocity of the particle numbered id at the kth iteration, represents the position of the particle numbered id at the kth iteration, ω(k) represents the weight factor when the number of iterations is k, and c 1 and c 2 Both represent learning factors, r 1 and r 2 is a random number distributed in the interval [0,1]. represents the individual extreme value of the particle numbered id at the kth iteration, Represents the global extreme value at the kth iteration, and k represents the current iteration number.

[0077] In an optional embodiment, the hybridization probability P that decreases nonlinearly with the number of iterations c The expressions include:

[0078]

[0079] Where P c1 represents the initial hybridization probability, P c2 represents the hybridization probability when the maximum number of iterations is reached, k represents the current number of iterations, and N max Indicates the maximum number of iterations.

[0080] In an optional embodiment, the expression of the hybridization formula includes:

[0081] child(x)=P c *parent 1 (x)+(1-P b )*parent 2 (x)

[0082]

[0083] In the formula, parent 1 (x) and parent 2 (x) represents the position of a parent particle and another parent particle respectively; parent1 (v) and parent 2 (v) represents the velocity of a parent particle and another parent particle respectively; child(x) and child(v) represent the position and velocity of the child particle respectively; P c represents the hybridization probability that decreases nonlinearly with the number of iterations.

[0084] As an example, the standard particle swarm optimization algorithm (PSO) is a swarm intelligence optimization algorithm suitable for solving complex nonlinear optimization problems. The PSO algorithm randomly initializes a group of particles (representing the potential global optimal solution) in the feasible solution space of the target object. The search activities of particles in space are affected by group cognition and their own factors, including three characteristics: position, speed, and fitness. In each iteration, particles complete the update of position and speed according to individual extreme values ​​and group extreme values.

[0085] As an exemplary illustration, in order to prevent particles from blindly searching and falling into the risk of local optimum, the speed and position of particles are usually limited to a certain range.

[0086] As an exemplary explanation, in the standard PSO algorithm, the inertia weight factor is a manifestation of the spatial search capability of each particle and is an important parameter that affects the particle search speed and search range; generally, a larger inertia weight is conducive to global search, while a smaller inertia weight is more conducive to local search, so the inertia weight that decreases with the number of iterations is conducive to balancing the capabilities of global search and local search, thereby improving the convergence performance of the algorithm; when considering the setting of the inertia weight of the PSO algorithm, the present application introduces an inertia weight that decreases nonlinearly with the number of iterations; the nonlinearly decreasing inertia weight can enable the particle to obtain a larger motion inertia at the initial stage, thereby enhancing the particle's global search capability; and when the particle approaches the optimal position, the particle's motion impulse is reduced, so that it moves within a small local range, thereby improving the search accuracy.

[0087] As an example, the standard PSO algorithm has the problem of premature particles and falling into local optimality, which affects the convergence accuracy of the algorithm. The selection and recombination operations in the genetic algorithm are introduced into the particle swarm optimization algorithm, and it is called the hybrid PSO algorithm, which greatly improves the premature convergence of the population. After all particles complete the position and speed update, according to the hybrid pool size ratio P s A certain number of particles are selected from the entire population for hybridization. Under the set hybridization probability P c In this case, two particles are randomly selected to participate in hybridization, and the new particles obtained by hybridization replace the parent particles, so that the particles jump out of the local optimal position; in addition, if the hybrid particle group adopts a fixed hybridization probability P c, which will cause repeated and invalid hybridization operations in the local range in the later stage of particle iteration, reduce the operation efficiency of the algorithm, and lead to the loss of the advantages of the hybridization operation. To address this problem, the present application adopts a nonlinearly decreasing hybridization probability, so that the parent generation hybridization probability shows a nonlinear decreasing trend with the increase of the number of iterations.

[0088] As an example, the introduction of nonlinear crossover probability not only enables particles to have stronger global search capabilities in the early stages of iteration, but also solves the problem of local search efficiency in the later stages of iteration.

[0089] As an exemplary illustration, generalized Pareto distributions with different parameters can describe the statistical characteristics of sea clutter under different background environments, and the differences in shape parameters and scale parameters are the main factors affecting the statistical characteristic curve of the generalized Pareto distribution. In order to better achieve the accurate fitting of the generalized Pareto distribution to the clutter data, the present application adopts the cumulative error at the point of the clutter data statistical histogram and the theoretical distribution curve as the objective function for the generalized Pareto distribution parameter estimation optimization. In addition, in order to balance the fitting difference between the PDF curve and the CDF curve of the clutter data, the two difference functions are mixed and weighted by appropriate weight coefficients to construct a fitness function, and then the hybrid PSO algorithm is used to complete the corresponding optimal parameter search task.

[0090] In this embodiment, the hybrid PSO algorithm is used to solve the problem that the particles of the standard PSO algorithm are prone to premature maturity and fall into the local optimum, and the simulation data is used to illustrate the parameter estimation performance advantage of the hybrid PSO algorithm; the nonlinear decreasing inertia weight ω and the hybrid probability P c , which improves the parameter estimation performance of the hybrid PSO algorithm and gives the optimal parameter setting scheme; the generalized Pareto distribution estimated by the hybrid PSO algorithm has a more stable fitting effect on sea clutter data and is not affected by the value range of the shape parameter.

[0091] Example 2

[0092] This embodiment proposes a specific implementation example based on the radar sea clutter parameter estimation method of the generalized Pareto distribution proposed in Example 1, and the implementation example is as follows:

[0093] The parameters of the generalized Pareto distribution are set to a = 3.5, b = 0.5, and the number of clutter samples is 5×10 4 ;

[0094] Figure 3 This is a schematic diagram of the PDF curve of the simulated generalized Pareto distribution proposed in this embodiment. Figure 3 The statistical characteristics of the simulation data are given.

[0095] The above simulation data is used to test the effect of the hybrid PSO algorithm and compare it with the performance of the standard PSO algorithm. The parameters of the hybrid PSO algorithm are set as follows: the population size is 20, the learning factor c 1 =c 2 =2, hybridization pool size ratio P s = 0.5, the minimum number of generations to keep the global optimal position is set to 15; the initial values ​​of the nonlinear decreasing inertia weight and the hybridization probability are both 0.9, and the end values ​​are both set to 0.4. In addition, the maximum number of iterations N max is 50.

[0096] In order to facilitate comparative analysis, the parameters of the standard PSO algorithm are set as follows: population size 20, learning factor c 1 =c 2 =2, inertia weight ω=0.4, and the maximum number of iterations is 50. The fitness function is constructed using the simulation data introduced above, and then the performance differences of the two algorithms when optimizing the target object are compared. Figure 3 The iterative process of the hybrid PSO algorithm and the standard PSO algorithm is given. Figure 3 It can be seen that the hybrid PSO algorithm can quickly converge to the global optimal position, while the standard particle swarm algorithm converges slowly and has local convergence. The output parameter estimation results of the optimal positions of the two algorithms in the figure are: a = 3.2748, b = 0.5729 (hybrid PSO algorithm), a = 3.2747, b = 0.5729 (standard PSO algorithm), indicating that the final parameter estimation results of the two algorithms are the same, but the standard PSO algorithm requires more computing time.

[0097] Figure 5 The following is a schematic diagram of the parameter estimation error curve of the two different algorithms proposed in this embodiment. The shape parameter / scale parameter is fixed, and the scale parameter / shape parameter is changed. The standard PSO algorithm and the hybrid PSO algorithm are used to search for the global optimal value of the fitness function of the generalized Pareto distribution parameter estimation, so as to obtain the corresponding parameter estimation values. First, the scale parameter b=0.3 is fixed, and the shape parameter of each group of clutter samples is changed from 0.1 to 10 at equal intervals. The number of samples of the simulated generalized Pareto distribution is 5×104. The experimental results are the average of 10 repeated experiments. The change curve of the absolute distance between the parameter estimation value and the actual value of the standard PSO algorithm and the hybrid PSO algorithm can be obtained as shown in the figure. Figure 5 (a) Observation Figure 5 (a) It can be seen that the estimation error of the shape parameter a increases with the increase of the simulation data parameter a, while the change of the scale parameter estimation error has experienced a trend of first decreasing and then increasing. In addition, the parameter estimation error of the standard PSO algorithm changes more dramatically when the shape parameter a is small, which shows that the parameter estimation robustness of the standard PSO algorithm is relatively poor.

[0098] The shape parameter a is fixed at 2.5, the scale parameter of the clutter sample varies from 0.1 to 10 at equal intervals, and the length of the simulation data remains unchanged. The parameter estimation curves of the two algorithms are also plotted ( Figure 5 (b)). Figure 5 (b) It can be seen that as the scale parameter increases, the parameter estimation error of the shape parameter a does not change significantly, and the parameter estimation error of the scale parameter b shows an upward trend. The standard PSO algorithm still shows a violent oscillation phenomenon, indicating that the particles of the algorithm are prone to premature maturation and cause the population to fall into a local optimal position. From the above experimental results, it can be seen that compared with the standard PSO algorithm, the hybrid PSO algorithm not only has higher parameter estimation accuracy, but also has better parameter estimation stability. Therefore, this application uses the hybrid PSO algorithm to complete the optimal parameter search task of the generalized Pareto distribution parameter estimation fitness function.

[0099] The basic steps of the hybrid PSO algorithm proposed in the present invention are:

[0100] S1: Initialize the particle swarm, including the particle swarm size N, the inertia weight ω of the particle update, and the learning factor c 1 and c 2 , and the hybridization pool size ratio P in the hybridization operation s , hybridization probability P c Etc. The position X and velocity V of each particle are set using uniformly distributed random numbers within a certain range;

[0101] S2: Calculate the fitness value corresponding to each particle according to the objective function, and then store the value in the P of each particle. id The fitness value of the optimal position is selected and stored in P gd middle;

[0102] S3: Update the weight factor ω using nonlinear decreasing inertia weight;

[0103] S4: According to the inertia weight of the current iteration, and algorithm parameters such as the learning factor, the particle speed and position are updated respectively using the position and speed update formulas proposed in Example 1;

[0104] S5: Calculate the fitness value of the particle in the current iteration and compare it with the particle's historical optimal position. Update the particle's P according to the fitness value. id , and then put all updated P id Compare with the global historical optimal position to update the population's P gd ;

[0105] S6: Update the hybridization probability P using nonlinear decreasing hybridization probability c ;

[0106] S7: Select P according to the hybridization probability s A specified number of particles are placed in the hybridization pool, and two particles in the pool are randomly selected in turn to participate in the hybridization. The position and velocity hybridization formulas of the hybrid offspring are updated, and the hybridization operation produces the same number of particles as the parent;

[0107] S8: Determine whether the termination condition of the algorithm is met. If the requirement is met, stop the population search task and save the global optimal position of the particle. Otherwise, return to step 3 to step 7 to continue searching.

[0108] There are two ways to terminate the particle swarm search in the hybrid PSO algorithm. One is to require the maximum number of iterations of the particles to be reached, and the other is to set the number of generations of the global optimal particle to be retained. Since the maximum number of iterations is determined according to the properties of the objective function, and each iteration of the particle has a certain degree of randomness, this application adopts the method of setting the number of generations of the global optimal particle to ensure that the particle can effectively search for the optimal position of the objective function.

[0109] Example 3

[0110] This embodiment proposes a generalized Pareto distribution radar sea clutter parameter estimation system, which is used to implement the generalized Pareto distribution radar sea clutter parameter estimation method proposed in Example 1; Figure 6 This is a schematic diagram of the framework of the parameter estimation system proposed in this embodiment.

[0111] The generalized Pareto distribution radar sea clutter parameter estimation system comprises:

[0112] A data acquisition module is used to acquire a number of generalized Pareto distribution clutter data;

[0113] A fitness function construction module, used to construct a fitness function based on the cumulative distribution function and probability density function of the generalized Pareto distribution clutter data, and substitute the fitness function into the genetic algorithm;

[0114] The optimal parameter value output module is used to combine the genetic algorithm and the particle swarm optimization algorithm to iteratively solve the global optimal particle of the generalized Pareto distribution clutter data. When the number of iterations reaches a preset value, or the number of generations of the global optimal particle during the iteration is equal to the preset number of generations, the iteration is stopped to obtain the optimal parameter value of the generalized Pareto distribution; wherein the optimal parameter value is the global optimal particle when the iteration is stopped, and the global optimal particle is the parameter that maximizes the value of the fitness function.

[0115] This embodiment also proposes a computer device, including a memory and a processor, wherein the memory stores computer-readable instructions, and when the computer-readable instructions are executed by the processor, the processor executes the steps of the radar sea clutter parameter estimation method of the generalized Pareto distribution described in Example 1.

[0116] It can be understood that the system and computer device of this embodiment improve the method of embodiment 1, and the options in the above embodiment 1 are also applicable to this embodiment, so they will not be described repeatedly here.

[0117] The same or similar reference numerals correspond to the same or similar components;

[0118] The terms used in the drawings to describe positional relationships are only used for illustrative purposes and should not be construed as limiting this patent;

[0119] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A radar sea clutter parameter estimation method based on generalized Pareto distribution, characterized in that: The following steps are involved: Obtain several pieces of generalized Pareto distribution clutter data; Constructing a fitness function based on the cumulative distribution function and probability density function of the generalized Pareto distribution clutter data, and substituting the fitness function into a genetic algorithm; Combining the genetic algorithm and the particle swarm optimization algorithm, the global optimal particle of the generalized Pareto distribution clutter data is iteratively solved. When the number of iterations reaches a preset value, or the number of generations of the global optimal particle during the iteration is equal to the preset number of generations, the iteration is stopped to obtain the optimal parameter value of the generalized Pareto distribution; wherein the optimal parameter value is the global optimal particle when the iteration is stopped, and the global optimal particle is the parameter that maximizes the value of the fitness function.

2. The radar sea clutter parameter estimation method based on generalized Pareto distribution according to claim 1, characterized in that: The generalized Pareto distribution clutter data is obtained by simulating the generalized Pareto distribution random sequence through a sampling formula using a direct sampling method; The expression of the sampling formula includes: In the formula, x i represents the i-th generalized Pareto distribution clutter data, a and b correspond to the shape parameter and scale parameter of the generalized Pareto distribution clutter data respectively, u i Represents x i The corresponding value range is a uniformly distributed random number in the range [0,1].

3. The radar sea clutter parameter estimation method based on generalized Pareto distribution according to claim 1, characterized in that: The expression of the fitness function includes: In the formula, f fitness (θ) represents the fitness function, f(n; θ) and F(n; θ) represent the probability density function and cumulative distribution function of the nth generalized Pareto distribution clutter data, respectively, h(n) and H(n) represent the values ​​of the clutter statistical histogram of the nth generalized Pareto distribution clutter data on the sampling interval of the probability density function curve and the cumulative distribution function curve, respectively, λ1 and λ2 represent weight coefficients, and N represents the total number of generalized Pareto distribution clutter data.

4. The radar sea clutter parameter estimation method based on generalized Pareto distribution according to any one of claims 1 to 3, characterized in that: Combining the genetic algorithm and the particle swarm optimization algorithm, the steps of searching for optimal parameters for the generalized Pareto distribution clutter data include: Initialize the position and velocity of the particle swarm, where one particle of the particle swarm corresponds to a parameter value of the generalized Pareto distribution clutter data; According to the fitness function, the fitness value of each particle in the particle swarm is calculated and the fitness value is regarded as the individual extreme value P of the particle. id , select the largest P in the particle swarm id As the global extreme value P gd ; Update the weight factor using the nonlinear decreasing inertia weight with the number of iterations; The position and speed of the particle swarm are updated based on the particle swarm optimization algorithm; in each iteration, the speed and position of each particle are updated using the weight factor of the current iteration, the individual extreme value of the particle, and the global extreme value, and the fitness value of the particle of the current iteration is calculated, and the fitness value of the particle of the current iteration is compared with its individual extreme value P id Compare, if the current fitness value is greater than the individual extreme value P id , then use the current fitness value to update the individual extreme value P id , all particles complete the individual extreme value P id After updating, select the largest P in the particle swarm id As the new global extremum P gd ; Determine whether the current number of iterations reaches the preset value, or whether the number of generations of the global optimal particle during the iteration is equal to the preset number of generations; wherein the global optimal particle is the global extreme value P gd The corresponding particles; If yes, stop the iteration, and output the global optimal particle when the iteration is stopped as the optimal parameter value of the generalized Pareto distribution; Otherwise, based on the genetic algorithm, after all particles have completed the position and velocity update, the hybridization pool size ratio P s The hybridization probability P among all particles decreases nonlinearly with the number of iterations. c A preset number of particles are selected, and particles are randomly selected as parent particles. The parent particles are hybridized with each other using the hybridization formula, and the parent particles are replaced with the child particles obtained by hybridization to form a new particle swarm. Based on the combination of genetic algorithm and particle swarm optimization algorithm, the optimal parameters of the new particle swarm are searched.

5. The radar sea clutter parameter estimation method based on generalized Pareto distribution according to claim 4, characterized in that: The expressions for updating the weight factor using the nonlinear decreasing inertia weight with the number of iterations include: In the formula, k represents the current iteration number, ω(k) represents the weight factor when the iteration number is k, and ω start represents the initial inertia weight, ω end Represents the inertia weight when the iteration reaches the maximum number, N max Indicates the maximum number of iterations.

6. The radar sea clutter parameter estimation method based on generalized Pareto distribution according to claim 4, characterized in that: The expressions for updating the velocity and position of each particle using the weight factor of the current iteration, the individual extremum of the particle, and the global extremum include: In the formula, represents the velocity of the particle numbered id at the kth iteration, represents the position of the particle numbered id at the kth iteration, ω(k) represents the weight factor when the number of iterations is k, c1 and c2 both represent learning factors, r1 and r2 are random numbers distributed in the interval [0,1], represents the individual extreme value of the particle numbered id at the kth iteration, Represents the global extreme value at the kth iteration, and k represents the current iteration number.

7. The radar sea clutter parameter estimation method based on generalized Pareto distribution according to claim 4, characterized in that: The hybridization probability P decreases nonlinearly with the number of iterations. c The expressions include: Where P c1 represents the initial hybridization probability, P c2 represents the hybridization probability when the iteration reaches the maximum number, k represents the current number of iterations, N max Indicates the maximum number of iterations.

8. The radar sea clutter parameter estimation method based on generalized Pareto distribution according to claim 4, characterized in that: The expression of the hybridization formula includes: child(x)=P c *parent1(x)+(1-P b )*parent2(x) In the formula, parent1(x) and parent2(x) represent the positions of a parent particle and another parent particle respectively; parent1(v) and parent2(v) represent the velocities of a parent particle and another parent particle respectively; child(x) and child(v) represent the position and velocity of the child particle respectively; P c represents the hybridization probability that decreases nonlinearly with the number of iterations.

9. A generalized Pareto distribution radar sea clutter parameter estimation system, used to implement the generalized Pareto distribution radar sea clutter parameter estimation method according to any one of claims 1 to 8, characterized in that: include: A data acquisition module is used to acquire a number of generalized Pareto distribution clutter data; A fitness function construction module is used to construct a fitness function based on the cumulative distribution function and probability density function of the generalized Pareto distribution clutter data, and substitute the fitness function into the genetic algorithm; The optimal parameter value output module is used to combine the genetic algorithm and the particle swarm optimization algorithm to iteratively solve the global optimal particle of the generalized Pareto distribution clutter data. When the number of iterations reaches a preset value, or the number of generations of the global optimal particle during the iteration is equal to the preset number of generations, the iteration is stopped to obtain the optimal parameter value of the generalized Pareto distribution; wherein the optimal parameter value is the global optimal particle when the iteration is stopped, and the global optimal particle is the parameter that maximizes the value of the fitness function.

10. A computer device comprising a memory and a processor, wherein the memory stores computer-readable instructions, characterized in that: When the computer-readable instructions are executed by the processor, the processor executes the steps of the radar sea clutter parameter estimation method based on generalized Pareto distribution according to any one of claims 1 to 8.

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