WW-distributed radar sea clutter parameter estimation method

Abstract

The invention relates to the technical field of radar signal processing, and provides a WW-distributed radar sea clutter parameter estimation method, which comprises the following steps of: obtaining a plurality of pieces of radar clutter data; constructing a distribution model of the radar clutter data based on dual Weibull distribution; solving a parameter reference value of the distribution model based on a Kmeans algorithm; taking an expectation for maximizing the parameters of the distribution model as an objective function, iteratively solving the objective function by using an expectation condition maximization algorithm, and when the number of iterations reaches a preset value or the objective function reaches a maximum value, ending iteration to obtain an optimal parameter estimation value of the distribution model; the problems of parameter acquisition difficulty and local convergence caused by many WW distribution parameters are solved, and the WW distribution parameters can be efficiently and accurately estimated.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and more specifically, to a method for estimating radar sea clutter parameters of WW distribution. Background Art

[0002] Errors in searching for distribution model parameters will lead to a decrease in the detection performance of the radar constant false alarm rate (CFAR) detection algorithm, thus affecting its application in this field. Common radar clutter distribution models include Rayleigh distribution, lognormal distribution, Weibull distribution, and K distribution. With the development of surveillance radar systems and their application in complex scenarios, relevant researchers have proposed a composite structure WW distribution (double Weibull distribution, Weibull-Weibull) model, which can accurately describe the amplitude distribution characteristics of sea clutter. However, the mathematical form of the WW distribution is complex and has many parameters, which makes it difficult to search for distribution parameters. According to the characteristics of the WW distribution model, an optimization model for parameter search is established. Optimizing the parameter search algorithm is one of the important ways to achieve effective detection of targets in WW distribution clutter environments.

[0003] The use of intelligent algorithms to search for parameters of WW distribution and to find the optimal model for searching the parameters of WW distribution are hot topics in current research. The prior art proposes to extract parameters using the method of minimum mean square error, but the accuracy of the parameters obtained by this method is not high and overfitting is prone to occur. The prior art also proposes to use particle swarm optimization algorithm and genetic algorithm to search for parameters of WW distribution respectively. The model parameters obtained by these two methods are relatively accurate, but they need to be continuously iterated and optimized, with large amount of calculation and easy to fall into the problem of local optimum. The prior art also uses cuckoo search algorithm to obtain the optimal parameter value of WW distribution. By establishing the optimal parameter search model, good results are achieved, but when the data sample size is large, the algorithm operation efficiency is low. The application of intelligent algorithms to the parameter search of WW distribution can improve the accuracy of parameter acquisition, but it also leads to the problems of local convergence and algorithm complexity. Therefore, according to the characteristics of WW distribution, it is of great significance to seek an efficient and accurate WW distribution parameter search method and to estimate the WW distribution parameters efficiently and accurately. Summary of the invention

[0004] In order to overcome the defect of the prior art that WW distribution parameters cannot be estimated efficiently and accurately, the present invention provides a WW distributed radar sea clutter parameter estimation method that can estimate WW distribution parameters efficiently and accurately.

[0005] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0006] A method for estimating radar sea clutter parameters of WW distribution comprises the following steps:

[0007] Obtain several pieces of radar clutter data;

[0008] Constructing a distribution model of the radar clutter data based on a dual Weibull distribution;

[0009] Solving the parameter reference values ​​of the distribution model based on the Kmeans algorithm;

[0010] The objective function is to maximize the expectation of the parameters of the distribution model, and the objective function is iteratively solved using the expectation condition maximization algorithm. When the number of iterations reaches a preset value, or the objective function reaches a maximum value, the iteration is terminated to obtain the optimal estimated values ​​of the parameters of the distribution model.

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

[0012] A data acquisition module, used to acquire a number of radar clutter data;

[0013] A distribution model building module, used for building a distribution model of the radar clutter data based on a double Weibull distribution;

[0014] A reference value solving module, used for solving the parameter reference value of the distribution model based on the Kmeans algorithm;

[0015] The parameter estimation module is used to maximize the expectation of the parameters of the distribution model as the objective function, and iteratively solve the objective function using the expectation condition maximization algorithm. When the number of iterations reaches a preset value, or when the objective function reaches a maximum value, the iteration is terminated to obtain the optimal estimated values ​​of the parameters of the distribution model.

[0016] 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 WW distributed radar sea clutter parameter estimation method.

[0017] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0018] The present invention obtains a plurality of radar clutter data; constructs a distribution model of the radar clutter data based on a double Weibull distribution; solves parameter reference values ​​of the distribution model based on a Kmeans algorithm; takes maximizing the expectation of the parameters of the distribution model as an objective function, iteratively solves the objective function using an expectation condition maximization algorithm, and terminates the iteration when the number of iterations reaches a preset value or the objective function reaches a maximum value, thereby obtaining optimal estimated values ​​of the parameters of the distribution model, solving the problems of difficulty in parameter acquisition and local convergence caused by more WW distribution parameters, and being able to efficiently and accurately estimate WW distribution parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a schematic diagram of the radar sea clutter parameter estimation method of WW distribution proposed in Example 1;

[0020] Figure 2 A schematic diagram comparing the WW distribution and the Weibull distribution under different parameters proposed in Example 1;

[0021] Figure 3 This is a schematic diagram of the Kmeans clustering process proposed in Example 1;

[0022] Figure 4 Schematic diagram of the iterative process of initializing parameters of Kmeans clustering proposed in Example 1;

[0023] Figure 5 This is a schematic diagram of the search results of various parameters of the WW distribution proposed in Example 2;

[0024] Figure 6 A comparative schematic diagram of the WW distribution PDF curve search results proposed in Example 2;

[0025] Figure 7 A comparison chart of search results of various algorithms proposed in Example 2 under different initial parameter conditions;

[0026] Figure 8 It is a table of parameter search accuracy when the number of clutter data samples is different as proposed in Example 2;

[0027] Fig. 9 This is a table of parameter search accuracy when the weight factor k value is different as proposed in Example 2;

[0028] Fig.10 This is a schematic diagram of the framework of the parameter estimation system proposed in Example 3. DETAILED DESCRIPTION

[0029] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0030] 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;

[0031] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0032] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0033] Example 1

[0034] This embodiment proposes a method for estimating radar sea clutter parameters of WW distribution. Figure 1 Schematic diagram of the WW distribution radar sea clutter parameter estimation method proposed in this embodiment;

[0035] like Figure 1 As shown, the radar sea clutter parameter estimation method of WW distribution in this embodiment includes the following steps:

[0036] S1: Obtain several pieces of radar clutter data;

[0037] S2: constructing a distribution model of the radar clutter data based on double Weibull distribution;

[0038] S3: solving the parameter reference values ​​of the distribution model based on the Kmeans algorithm;

[0039] S4: Taking maximizing the expectation of the parameters of the distribution model as the objective function, the expectation condition maximization algorithm is used to iteratively solve the objective function. When the number of iterations reaches a preset value, or the objective function reaches a maximum value, the iteration is terminated to obtain the optimal estimated values ​​of the parameters of the distribution model.

[0040] In a specific implementation process, a number of radar clutter data are obtained; a distribution model of the radar clutter data is constructed based on a double Weibull distribution; a parameter reference value of the distribution model is solved based on a Kmeans algorithm; and the objective function is to maximize the expectation of the parameters of the distribution model, and the objective function is iteratively solved using an expectation condition maximization algorithm. When the number of iterations reaches a preset value, or when the objective function reaches a maximum value, the iteration is terminated to obtain the optimal estimated value of the parameter of the distribution model, thereby solving the problem of difficulty in parameter acquisition and local convergence caused by a large number of WW distribution parameters, and being able to efficiently and accurately estimate the WW distribution parameters.

[0041] In an optional embodiment, the expression of the distribution model of the radar clutter data includes:

[0042] f WW (x) = (1-k)f W1 (x; α 1 ,β1 )+kf W2 (x; α 2 ,β 2 )

[0043]

[0044] In the formula, f WW (x) represents the distribution model of radar clutter data; k represents the weight coefficient; f W1 represents the first Weibull distribution function, f W1 (x; α 1 ,β 1 ) indicates that the input data is x and the parameters include α 1 and β 1 f W1 ;f W2 represents the second Weibull distribution function, f W2 (x; α 2 ,β 2 ) indicates that the input data is x and the parameters include α 2 and β 2 f W2 .

[0045] As an example, the sea surface echo is mainly composed of the scattering contributions of a large number of basic scatterers and a few strong echoes. The echo signal generated by the basic scatterers (i.e., Bragg / whitecap scatterers) is the main component of sea clutter, and its power varies with the movement of the sea surface, while a few strong echoes (discrete spikes) are caused by breaking waves on the sea surface. Different from the KA distribution, which models the spike component as a Class A model, the WW distribution models both the Bragg / whitecap scatterer and the discrete sea spike component with a Weibull distribution, α 1 and α 2 Greater than zero, indicating the shape parameter of the distribution inclination, which can be used to characterize different sea conditions; β 1 and β 2 is greater than zero, indicating the scale parameter of the median of the distribution, which determines the mean square value of the Weibull distribution. The WW distribution is composed of two independent single Weibull distributions mixed with certain weights. The expression of the distribution model is obtained by weighted summation of the two clutter models; where f W1 (x; α 1 ,β 1 ) and f W2 (x; α 2 ,β 2 ) represent the PDF (probability density function) of Prague / Whitecap and Sea Peak respectively, and the corresponding parameter vector is θ 1 =(α 1 ,β 1) and θ 2 =(α 2 ,β 2 ); k is the weight of the two components in the mixed distribution. The larger the k value, the larger the clutter peak component. The weight factor k and the proportional coefficient ρ in the distribution model determine the peak component. The proportional coefficient can be expressed by the following formula:

[0046]

[0047] Where Γ(·) is the gamma function; if k = 0 or ρ = 1, the WW distribution degenerates into a single Weibull distribution. Compared with the KA distribution, the WW distribution can not only fit the sea clutter peak more accurately, but also has a closed expression, which is more practical in practical applications such as sea clutter analysis and suppression, and detection algorithm design.

[0048] As an example, Figure 2 This is a schematic diagram comparing the WW distribution and the Weibull distribution under different parameters proposed in this embodiment. Figure 2 (a) shows the situation when k = 0.01 and the proportionality coefficient ρ takes different values. Figure 2 (b) shows the different values ​​of the weight coefficient k when ρ = 8; Figure 2 The 1-CDF (Cumulative Distribution Function) curves of WW distribution and Weibull distribution are compared. Figure 2 It can be seen that the difference between the two distributions in the tailing area is mainly controlled by the parameters k and ρ. ρ mainly controls the degree of deviation of the WW distribution from the Weibull distribution, while k affects both the degree of deviation and the position of deviation. The larger the k value, the more obvious the tailing phenomenon of the WW distribution. Usually, k values ​​within 0.2 are sufficient to describe the peak components of various types of sea clutter. The average intensity ρ only affects the degree of deviation, so its value range is relatively wide. By setting the parameters k and ρ, various types of sea clutter can be fitted in a wide range.

[0049] In an optional embodiment, the step of solving the parameter reference value of the distribution model based on the Kmeans algorithm includes:

[0050] The log-likelihood function of the distribution model is used as a clustering criterion function, and the clustering criterion function is iteratively solved by using a Kmeans algorithm. When the number of iterations reaches a preset value, or when the clustering criterion function reaches a maximum value, the iteration is terminated, and the radar clutter data is clustered and divided into two types of Weibull distribution clusters;

[0051] Parameter search is performed on radar clutter data in two types of Weibull distribution clusters respectively to obtain parameter reference values ​​of the distribution model.

[0052] In an optional embodiment, the expression of the clustering criterion function includes:

[0053]

[0054] Where X represents the set of radar clutter data obtained, L(X|θ) represents the clustering criterion function, and also represents the function with X as input data and θ as parameter, where θ includes θ 1 and θ 2 ; N represents the total number of radar clutter data in X; k represents the weight coefficient; x i represents the i-th radar clutter data in X, f W1 (x i |θ 1 ) represents x i As input and θ 1 is the first Weibull distribution function in the distribution model with parameters; f W2 (x i |θ 2 ) represents x i As input and θ 2 The second Weibull distribution function in the distribution model with parameter .

[0055] As an example, θ 1 Including α 1 and β 1 θ 2 Including α 2 and β 2 .

[0056] In an optional embodiment, parameter searches are performed on radar clutter data in two types of Weibull distribution clusters respectively, and expressions of parameter reference values ​​of the distribution model obtained include:

[0057]

[0058] In the formula, represents the parameter reference value of the distribution model, Represents the first Weibull distribution function in the distribution model The corresponding parameter reference value, Represents the second Weibull distribution function in the distribution model Corresponding parameter reference value; X represents the set of radar clutter data obtained, x i represents the i-th radar clutter data in X, N represents the total number of radar clutter data in X, represents the clustering criterion function value when the radar clutter data is clustered into two types of Weibull distribution clusters, L(X|θ (g+1) ) represents the clustering criterion function value corresponding to the parameter reference value.

[0059] As an example, Kmeans is a commonly used data clustering method. It first needs to distribute the input data into K different distribution clusters according to the set distance metric, and then calculate the center point of each distribution cluster; according to the new center point position, the sample data is divided into the center point closest to it, so as to determine the new distribution cluster, and then continue to repeatedly calculate the center point position and classify until convergence. Usually Kmeans clustering uses the sum of squared errors as the distance metric for classification, also known as the clustering criterion function, as shown in the following formula:

[0060]

[0061] Where dist is the Euler distance, and different distance functions can also be used here; c k is the center of the kth distribution cluster; in order to solve the problem of WW distribution data clustering, the data samples are divided into two types of Weibull distribution clusters, and the log-likelihood function of WW distribution is used as the clustering criterion function; the purpose of Kmeans clustering is to make the likelihood function approach the theoretical maximum value continuously, and finally obtain the initialization parameters that meet the requirements. The likelihood function of WW distribution is as follows:

[0062]

[0063] From this formula, we can see that by judging the value of the probability density function, the random variable x i Assign to the corresponding Weibull distribution cluster, thereby increasing the value of the log-likelihood function, as shown in the following formula:

[0064]

[0065] In the formula, m represents the number of iterations of Kmeans clustering, I i is the introduced characteristic function, representing the random variable x i After the data classification is completed, the parameters of the data in the two distribution clusters are searched separately to obtain the m+1th Kmeans clustering value of the WW distribution parameter, as shown in the following formula:

[0066]

[0067] The WW distribution is actually the superposition of two independent Weibull distributions, and there is an intersection between the two Weibull distributions with different parameters. Kmeans clustering is an absolute classification method that ignores the correlation between data. Therefore, the parameter values ​​obtained using the Kmeans clustering idea are inconsistent with the theoretical values, but this value can be used as the initialization parameter of the ECM algorithm to solve the problem that the algorithm may converge locally; Figure 3The schematic diagram of the Kmeans clustering process proposed in this embodiment is as follows: Figure 3 shown.

[0068] In an optional embodiment, the expression of the objective function includes:

[0069]

[0070] Where, T g represents the objective function; θ (m-1) represents the parameters of the distribution model after m-1 iterations of the expected conditional maximization algorithm. When m-1 = 0, θ (m-1) is equal to the parameter reference value of the distribution model obtained by solving the Kmeans algorithm; n represents the total number of radar clutter data involved in the iterative solution, f WW (x i ) indicates that the input data is x i distribution model, k represents the weight coefficient.

[0071] As an example, the basic principle of the ECM (Expectation-Conditional Maximization) algorithm can be expressed as given observation data X, assuming that the weight factor k is a latent variable, and searching for the value of each parameter by iterating between expected values ​​and sequentially conditionally maximizing. (0) In this case, the steps of searching the WW distribution parameters by the ECM algorithm include:

[0072] 1) Find the expectation in step E, assuming θ (m) represents the mth iteration solution, and the expectation is calculated according to the following formula:

[0073]

[0074] 2) Maximize Q(θ in the M step (m) ,θ (m-1) ), find θ (m) Make Q(θ (m) ,θ (m-1) ) respectively about the parameter α 1 ,β 1 ,α 2 ,β 2 , k is derived and set equal to 0 to obtain the m+1th parameter search value, as shown in the following formula:

[0075]

[0076] 3) Since the formula in step 2) is a complex transcendental equation system, it is not easy to find θ (m)First,

[0077] Under the same condition, find the value that makes Q(θ (m) ,θ (m-1) ) to a great extent Then in Under the condition of (m) ,θ (m-1) ) to maximize The other parameters are obtained in the same way. In this paper, the M step is decomposed into 5 conditional maximizations, that is, k = 5. The specific solution expressions of each parameter in the mth iteration are as follows:

[0078]

[0079] To facilitate calculation According to calculate and We can get:

[0080]

[0081] Finally, consider and The conditional maximization of , the formula in step 2) can be obtained as follows:

[0082]

[0083] About α j The derivative is:

[0084]

[0085] According to the Newton iteration method formula:

[0086]

[0087] Therefore, we can obtain:

[0088]

[0089] In this embodiment, in order to solve the problem of difficulty in searching parameters and local convergence of WW distribution, a Kmeans-ECM algorithm is proposed to search parameters of WW distribution; Kmeans clustering is applied to the parameter initialization of the ECM algorithm, which not only effectively solves the local convergence problem caused by random initialization parameters, but also improves the operation efficiency of the algorithm. The effectiveness of the algorithm is verified by simulation data, and the algorithm can obtain good accuracy.

[0090] Example 2

[0091] This embodiment verifies the effectiveness of the radar sea clutter parameter estimation method for WW distribution proposed in Embodiment 1. The verification example is as follows:

[0092] The parameters obtained by the Kmeans clustering algorithm are used as the initialization parameters of the ECM algorithm. In order to verify the effectiveness of this method, the performance of the Kmeans-ECM algorithm in extracting WW distribution parameters is verified through Monte Carlo simulation experiments. Among them, the parameter values ​​of the WW distribution simulation random sequence are set to

[0093] k=0.2,α 1 =1.2,β 1 =1.5,α 2 =2.5,β 2 =3.5. The parameter search performance is verified by using the data generated by simulation. By analyzing the convergence conditions of the algorithm, the algorithm is terminated by setting the maximum number of iterations. The Kmeans clustering method is used to obtain the value of the initialization parameter. Figure 3 A typical iterative process of obtaining the initialization parameters of the ECM algorithm using the Kmeans clustering algorithm is given. The number of samples of the simulated random sequence is 3000. Through multiple experimental analyses, the specific parameter settings that meet the requirements are obtained: the maximum number of iterations is set to 30, and the maximum likelihood function convergence condition is set to the difference between the results of the previous and next two iterations is less than 10 -3 .

[0094] Figure 4 Schematic diagram of the iterative process of Kmeans clustering initialization parameters proposed in this embodiment, Figure 4 It can be seen that through the Kmeans clustering iteration method, the parameters of the WW distribution can basically approach the theoretical expected values ​​quickly, and the deviation of individual parameters from the theoretical expected values ​​is caused by the error of the simulation sequence. Using the results obtained by the clustering method as the initialization parameters of the ECM algorithm can not only effectively avoid the problem of local convergence of the algorithm, but also reduce the number of iterations of the ECM algorithm and improve the operation speed of the ECM algorithm.

[0095] Then, the WW distribution parameter values ​​obtained by clustering are used as the initialization parameters of the ECM algorithm, and the ECM algorithm is run to complete the search of WW distribution parameters. Through multiple experimental analyses, the maximum number of iterations of the ECM algorithm is set to 500 to meet the accuracy requirements.

[0096] Figure 5 This is a schematic diagram of the search results of various parameters of the WW distribution proposed in this embodiment. Figure 5 The results of various parameters obtained after 50 Monte Carlo tests. Figure 5 It can be seen that there are outliers in the results of the parameter search. After analysis, it can be seen that this is caused by the random errors of the simulation sample sequence.

[0097] Figure 6 This is a comparative schematic diagram of the WW distribution PDF curve search results proposed in this embodiment. Figure 6 The PDF (probability density function) curves of the WW distribution obtained from a simulation experiment are compared. To compare the search performance of the two algorithms, their initialization parameters are set to k( 0 )=0.3, where the Kmeans-ECM algorithm does not need to initialize the weight factor, and this value initialization is only for the ECM algorithm. Figure 6 It can be seen that the PDF curve searched by the Kmeans-ECM algorithm is closer to the theoretical WW distribution PDF curve.

[0098] Three groups of initial parameters are randomly selected to analyze the impact of the ECM algorithm on the WW distribution parameter search performance after the Kmeans clustering algorithm is introduced. The actual values ​​of the parameters of the WW distribution random sequence are k=0.2, α 1 =1.2,β 1 =1.5,α 2 =2.5,β 2 =3.5, Figure 7 This is a comparison table of search results of various algorithms proposed in this embodiment under different initial parameter conditions. The parameter search results are as follows: Figure 7 As shown in the figure, it can be seen that the search performance of the Kmeans-ECM algorithm is improved compared with the ECM algorithm, and the local convergence problem caused by the random initialization parameters of the ECM algorithm is effectively solved.

[0099] Figure 8 This is a table of parameter search accuracy when the number of clutter data samples proposed in this embodiment is different. Figure 8 is the search accuracy of each parameter of WW distribution when the weight factor k=0.2 and the number of samples is different. The search results are given by the Monte Carlo simulation test method with two indicators: mean error (ME) and root mean square error (RMSE), where the number of Monte Carlo tests is 50 times in total. Figure 8 It can be seen that in the process of searching for parameters of simulation data, since there are differences between the PDF curve of simulation data and the theoretical curve, the parameter search algorithm proposed in this paper has certain differences between the parameter search values ​​and actual values ​​for different simulation sequences, but the difference is not large. As the number of samples increases, the parameter results obtained by the search are getting closer and closer to the true value.

[0100] When the weight factor k takes different values ​​and the other parameters remain unchanged, the simulation generates three groups of clutter data sets that obey the WW distribution. Each data set contains 50 sets of random sequences that obey the WW distribution. Table 3 shows the search error of each parameter of the WW distribution, where k represents the value of the weight factor and the length of the clutter data is 3000.

[0101] Fig. 9 This is a table of parameter search accuracy when the weight factor k value is different in this embodiment. Figure 8 and Fig. 9 It can be seen that the Kmeans-ECM algorithm has a relatively ideal effect in parameter search for random sequences that obey WW distribution. The algorithm can not only obtain good accuracy, but also has a fast operation speed, which can meet the application needs of actual engineering.

[0102] Example 3

[0103] This embodiment provides a specific implementation example of the method for estimating radar sea clutter parameters of WW distribution described in Embodiment 1.

[0104] like Figure 2 As shown in the figure, the overall idea of ​​applying Kmeans clustering to the initialization of WW distribution model parameters is shown. The detailed steps are as follows:

[0105] S1: Randomly select two sets of initial parameters θ 1 and θ 2 , respectively calculate n The probability density function value of the point random sequence under each Weibull distribution parameter, that is, f W (X|θ j ){X=(x 1 ,x 2 ,…,x n ) T ,j=1,2};

[0106] S2: The value of the Weibull distribution probability density function is used as the distance from the n-point random sequence to each cluster center. According to formula (9), x i It is assigned to the distribution cluster cluster(j) determined by the cluster center closest to it.

[0107]

[0108] S3: Update the weight factor according to the classification. The Weibull distribution parameter corresponding to the j-th random sequence sample is θ j =(α j ,β j ), the data capacity of each type of distribution cluster ω j The ratio of the total random sequence capacity ω is used as the new weight factor of WW distribution, that is, k * =ω j / ω.

[0109] S4: Perform moment estimation of Weibull distribution parameters on the random sequences of each distribution cluster, and obtain two sets of new Weibull distribution parameters to update the values ​​of WW distribution parameters. The calculation expression for moment estimation of Weibull distribution parameters on the random sequences of each distribution cluster includes:

[0110]

[0111] S5: Calculate the maximum likelihood function value for the WW distribution after the parameters are updated, and compare it with the maximum likelihood function value obtained in the previous iteration to determine whether it converges; wherein the calculation expression for calculating the maximum likelihood function value for the WW distribution after the parameters are updated includes:

[0112]

[0113] S6: Repeat S2 to S5 until the maximum likelihood function convergence condition or the maximum number of iterations is met.

[0114] Figure d is a parameter search flow chart of the Kmeans-ECM algorithm proposed in this embodiment; the specific process of the Kmeans-ECM algorithm for WW distribution parameter search is shown in Figure d. (0) In this case, the steps of searching the WW distribution parameters by the ECM algorithm are the same as those described in Example 1.

[0115] Example 4

[0116] This embodiment proposes a WW distributed radar sea clutter parameter estimation system, which is used to implement the WW distributed radar sea clutter parameter estimation method proposed in Embodiment 1; Fig.10 This is a schematic diagram of the framework of the parameter estimation system proposed in this embodiment.

[0117] The WW distributed radar sea clutter parameter estimation system comprises:

[0118] A data acquisition module, used to acquire a number of radar clutter data;

[0119] A distribution model building module, used for building a distribution model of the radar clutter data based on a double Weibull distribution;

[0120] A reference value solving module, used for solving the parameter reference value of the distribution model based on the Kmeans algorithm;

[0121] The parameter estimation module is used to maximize the expectation of the parameters of the distribution model as the objective function, and iteratively solve the objective function using the expectation condition maximization algorithm. When the number of iterations reaches a preset value, or when the objective function reaches a maximum value, the iteration is terminated to obtain the optimal estimated values ​​of the parameters of the distribution model.

[0122] In an optional embodiment, the step of solving the parameter reference value of the distribution model based on the Kmeans algorithm includes:

[0123] The log-likelihood function of the distribution model is used as a clustering criterion function, and the clustering criterion function is iteratively solved by using a Kmeans algorithm. When the number of iterations reaches a preset value, or when the clustering criterion function reaches a maximum value, the iteration is terminated, and the radar clutter data is clustered and divided into two types of Weibull distribution clusters;

[0124] Parameter search is performed on radar clutter data in two types of Weibull distribution clusters respectively to obtain parameter reference values ​​of the distribution model.

[0125] In an optional embodiment, the expression of the objective function includes:

[0126]

[0127] Where, T g represents the objective function; θ (m-1) represents the parameters of the distribution model after m-1 iterations of the expected conditional maximization algorithm. When m-1 = 0, θ (m-1) is equal to the parameter reference value of the distribution model obtained by solving the Kmeans algorithm; n represents the total number of radar clutter data involved in the iterative solution, f WW (x i ) indicates that the input data is x i distribution model, k represents the weight coefficient.

[0128] 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 method for estimating radar sea clutter parameters of WW distribution described in Example 1.

[0129] It can be understood that the system and computer device of this embodiment improve the method of embodiment 1, and the options in embodiment 1 are also applicable to this embodiment, so they will not be described again here.

[0130] The same or similar reference numerals correspond to the same or similar components;

[0131] 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;

[0132] 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 method for estimating radar sea clutter parameters of WW distribution, characterized in that: The following steps are involved: Obtain several pieces of radar clutter data; Constructing a distribution model of the radar clutter data based on a dual Weibull distribution; Solving the parameter reference values ​​of the distribution model based on the Kmeans algorithm; The objective function is to maximize the expectation of the parameters of the distribution model, and the objective function is iteratively solved using the expectation condition maximization algorithm. When the number of iterations reaches a preset value, or the objective function reaches a maximum value, the iteration is terminated to obtain the optimal estimated values ​​of the parameters of the distribution model.

2. The method for estimating radar sea clutter parameters of WW distribution according to claim 1, characterized in that: The expression of the distribution model of the radar clutter data includes: f WW (x)=(1-k)f W1 (x;α1,β1)+kf W2 (x;α2,β2) In the formula, f WW (x) represents the distribution model of radar clutter data; k represents the weight coefficient; f W1 represents the first Weibull distribution function, f W1 (x; α1, β1) means f with input data x and parameters including α1 and β1 W1 ;f W2 represents the second Weibull distribution function, f W2 (x; α2, β2) means f with input data x and parameters including α2 and β2 W2 .

3. The method for estimating radar sea clutter parameters of WW distribution according to claim 1, characterized in that: The step of solving the parameter reference value of the distribution model based on the Kmeans algorithm includes: The log-likelihood function of the distribution model is used as a clustering criterion function, and the clustering criterion function is iteratively solved by using a Kmeans algorithm. When the number of iterations reaches a preset value, or when the clustering criterion function reaches a maximum value, the iteration is terminated, and the radar clutter data is clustered and divided into two types of Weibull distribution clusters; Parameter search is performed on radar clutter data in two types of Weibull distribution clusters respectively to obtain parameter reference values ​​of the distribution model.

4. The method for estimating radar sea clutter parameters of WW distribution according to claim 3, characterized in that: The expression of the clustering criterion function includes: Where X represents the set of radar clutter data obtained, L(X|θ) represents the clustering criterion function, which also represents a function with X as input data and θ as parameter, where θ includes θ1 and θ2; N represents the total number of radar clutter data in X; k represents the weight coefficient; x i represents the i-th radar clutter data in X, f W1 (x i |θ1) represents x i is the first Weibull distribution function in the distribution model with θ1 as input; f W2 (x i |θ2) represents x i The second Weibull distribution function in the distribution model with θ2 as input and θ2 as parameter.

5. The method for estimating radar sea clutter parameters of WW distribution according to claim 3, characterized in that: Parameter searches are performed on radar clutter data in two types of Weibull distribution clusters respectively, and expressions of parameter reference values ​​of the distribution model obtained include: In the formula, represents the parameter reference value of the distribution model, Represents the first Weibull distribution function in the distribution model The corresponding parameter reference value, Represents the second Weibull distribution function in the distribution model Corresponding parameter reference value; X represents the set of radar clutter data obtained, x i represents the i-th radar clutter data in X, N represents the total number of radar clutter data in X, represents the clustering criterion function value when the radar clutter data is clustered into two types of Weibull distribution clusters, Indicates the clustering criterion function value corresponding to the parameter reference value.

6. The method for estimating radar sea clutter parameters of WW distribution according to any one of claims 1 to 5, characterized in that: The expression of the objective function includes: Wherein, Tg represents the objective function; θ (m-1) represents the parameters of the distribution model after m-1 iterations of the expected conditional maximization algorithm. When m-1 = 0, θ (m-1) is equal to the parameter reference value of the distribution model obtained by the Kmeans algorithm; n represents the total number of radar clutter data involved in the iterative solution, and f WW (x i ) indicates that the input data is x i distribution model, k represents the weight coefficient.

7. A WW distributed radar sea clutter parameter estimation system, used to implement the WW distributed radar sea clutter parameter estimation method according to any one of claims 1 to 9, characterized in that: include: A data acquisition module, used to acquire a number of radar clutter data; A distribution model building module, used for building a distribution model of the radar clutter data based on a double Weibull distribution; A reference value solving module, used for solving the parameter reference value of the distribution model based on the Kmeans algorithm; The parameter estimation module is used to maximize the expectation of the parameters of the distribution model as the objective function, and iteratively solve the objective function using the expectation condition maximization algorithm. When the number of iterations reaches a preset value, or when the objective function reaches a maximum value, the iteration is terminated to obtain the optimal estimated values ​​of the parameters of the distribution model.

8. The radar sea clutter parameter estimation system for WW distribution according to claim 7, characterized in that: The step of solving the parameter reference value of the distribution model based on the Kmeans algorithm includes: The log-likelihood function of the distribution model is used as a clustering criterion function, and the clustering criterion function is iteratively solved by using a Kmeans algorithm. When the number of iterations reaches a preset value, or when the clustering criterion function reaches a maximum value, the iteration is terminated, and the radar clutter data is clustered and divided into two types of Weibull distribution clusters; Parameter search is performed on radar clutter data in two types of Weibull distribution clusters respectively to obtain parameter reference values ​​of the distribution model.

9. The radar sea clutter parameter estimation system for WW distribution according to claim 7, characterized in that: The expression of the objective function includes: Wherein, Tg represents the objective function; θ (m-1) represents the parameters of the distribution model after m-1 iterations of the expected conditional maximization algorithm. When m-1 = 0, θ (m-1) is equal to the parameter reference value of the distribution model obtained by the Kmeans algorithm; n represents the total number of radar clutter data involved in the iterative solution, and f WW (x i ) indicates that the input data is x i distribution model, k represents the weight coefficient.

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 method for estimating radar sea clutter parameters of WW distribution according to any one of claims 1 to 6.

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