A k-distributed clutter parameter estimation method based on a GBDT model

Abstract

The application discloses a K-distributed clutter parameter estimation method based on a GBDT model, and comprises the following steps: (1) obtaining a sea clutter sequence; (2) extracting features; (3) constructing a feature vector; (4) estimating a shape parameter; (5) estimating a scale parameter; and (6) calculating a KSD value. The application estimates the shape parameter through autonomous learning of the GBDT model and estimates the scale parameter by using specific quantile points dependent on the shape parameter, integrates the advantages of high estimation accuracy of moment estimation and anti-exceptional sample of quantile estimation, and thus realizes the accuracy of parameter estimation and the robustness in a complex clutter environment.

Description

TECHNICAL FIELD

[0001] The application relates to a signal processing technology, in particular to a K-distributed clutter parameter estimation method based on a GBDT model. BACKGROUND

[0002] In actual radar detection environment, there are islands, targets and the like, resulting in a large number of abnormal samples in sea clutter. At this time, the clutter is divided into pure clutter, abnormal clutter and mixed clutter. At present, the K-distribution is a recognized medium and low resolution sea clutter amplitude model, so it is necessary to study the estimation method of the shape parameter and the scale parameter in the K-distribution.

[0003] At present, scholars at home and abroad have developed three types of parameter estimation methods. The first type is a probability density function (PDF) based method, such as the moment estimation method and the maximum likelihood method. This kind of method has high estimation accuracy, but in the abnormal clutter environment, the estimation performance is seriously lost. The second type is a cumulative density function (CDF) based method, which can maintain robust performance in abnormal clutter environment, such as the three quantile method. Due to the existence of the Bessel function in the CDF, the mathematical expression of the quantile point cannot be obtained, and the auxiliary table method is required. The third type is a nonlinear model based estimation method. Some scholars propose to use neural networks to establish the relationship between the histogram and the parameter, so as to obtain the estimation value of the shape parameter, but this method requires the clutter to have unit average power. However, converting the parameter estimation into a nonlinear optimization problem is still a potential effective method. Therefore, in view of the complexity and diversity of the actual environment, it is urgent to develop an estimation method with the characteristics of resisting abnormal samples and high estimation accuracy. SUMMARY

[0004] The purpose of the application is to provide a K-distributed clutter parameter estimation method based on a GBDT model, so as to realize fast and robust parameter estimation.

[0005] Technical scheme: The K-distributed clutter parameter estimation method based on the GBDT model comprises the following steps:

[0006] (1) Obtain the sea clutter sequence: assume that the radar receives N sea clutter sequences, denoted as {z1, z2, …, z N}, and take the modulus of the sea clutter sequence to obtain the sea clutter amplitude sequence {r1, r2, …, r N}.

[0007] (1.1) Assume that the radar receives N sea clutter sequences, denoted as {z1, z2, …, z N}, and model the sequence as a compound Gaussian model.

[0008] (1.2) According to the sea clutter sequence, the sea clutter amplitude sequence is calculated as { |z1|, |z2|, …, |zN|}, where || represents the modulus of complex number; according to the compound Gaussian model, the sea clutter amplitude sequence obeys K distribution, and its probability density function is: N

[0009]

[0010] where r represents the sea clutter amplitude variable, v is the shape parameter, b is the scale parameter, Γ(·) is the gamma function, and K v (·) is the second kind of modified Bessel function of order v.

[0011] (2) Feature extraction: according to the sea clutter amplitude sequence in step (1), the sample moment of the lth order m l is calculated; four moment ratio values are extracted to form the moment feature ξ M ; the sea clutter amplitude sequence is sorted from small to large, and the sample quantile of the pth order r p is calculated; nine quantile ratio values are extracted to form the quantile feature ξ P .

[0012] (2.1) According to the sea clutter amplitude sequence in step (1), the sample moment of the lth order m l is calculated:

[0013]

[0014] When the sample number N of the sea clutter sequence tends to infinity, the sample moment tends to the theoretical moment; then, four moment ratio values are extracted to form the moment feature ξ M :

[0015]

[0016] where m 0.5 , m1, m2, m3, and m4 represent the 0.5th order moment, the 1st order moment, the 2nd order moment, the 3rd order moment, and the 4th order moment, respectively.

[0017] (2.2) The sea clutter amplitude sequence in step (1) is sorted from small to large and re-represented as {r1, r2, …, rN}, and the pth sample quantile r N is calculated: p

[0018] r p = r [N×p] , p ∈ [0, 1]

[0019] where [] represents the integer; when N tends to infinity, the sample quantile tends to the theoretical quantile; then, nine quantile ratio values are extracted to form the quantile feature ξ​​P :

[0020]

[0021] Thus, both the moment ratio and the quantile ratio are proved to be independent of the scale parameter and only related to the shape parameter.

[0022] (3) Construct the feature vector: combine the moment features and the quantile features in step (2) to construct a 13-dimensional feature vector M P T , T denotes transpose.

[0023] According to the features extracted in step (2), combine the moment features and the quantile features to construct a 13-dimensional feature vector:

[0024] M P T

[0025] , T denotes transpose.

[0026] (4) Estimate the shape parameter: first, establish the GBDT model, simulate K-distributed clutter under different shape parameters, obtain a large number of feature vectors according to steps (2) and (3), and establish the training data set Ω; then input the training data set Ω into the GBDT model for iterative learning to obtain the optimal parameter model of GBDT; finally, input the feature vector ξ in step (3) into the GBDT model with the optimal parameters to output the estimated value of the shape parameter

[0027] (4.1) Set the number of decision trees M = 500, the depth of each decision tree D = 7, and cascade all the decision trees to build the GBDT model.

[0028] (4.2) Simulate K-distributed clutter sequences under different shape parameters; set the shape parameter v to traverse the value range from 0.1 to 20 at a step of 0.1; for a given v j value, generate N = 10000 sequences conforming to the K distribution, and calculate the feature vector according to step (3) to obtain 1 sample, denoted as {ξ j , v j}; considering the strong non-Gaussianity of clutter under small shape parameters, when v ≤ 1.5, 8000 samples are generated for each shape parameter; when v > 1.6, 150 samples are generated for each shape parameter; finally, all the samples are combined to form the training data set Ω = { {ξ j , v j}, j = 1, 2, …, 147750}. ​​​​​

[0029] (4.3) Take the training set Ω in step (4.2) as input, and train the GBDT model built in step (4.1) to obtain the optimal parameters f of GBDT after iterative update M .

[0030] (4.4) Take the feature vector ξ in step (3) as input, and input it into the GBDT model with the optimal parameters to output the estimated value of the shape parameter

[0031]

[0032] where f M is the optimal parameter of GBDT obtained in step (4.3).

[0033] (5) Estimate the scale parameter: according to the cumulative probability density function F(r; v, b) of the K distribution, let into F(r; v, b) to obtain a specific quantile that depends on the shape parameter; according to the estimated value of the shape parameter in step (4) determine the estimated value of the scale parameter

[0034] (5.1) According to the probability density function of the K distribution in step (1.2), calculate the cumulative probability density function of the K distribution:

[0035]

[0036] (5.2) Let into F(r; v, b) to obtain a specific quantile that depends on the shape parameter:

[0037]

[0038] (5.3) Take the shape parameter estimate value in step (4.4) into θ(v) to obtain a specific quantile; therefore, the estimated value of the scale parameter is determined as:

[0039]

[0040] (6) Calculate the KSD value: combine the sea clutter amplitude sequence and the obtained parameter estimates to calculate the Kolmogorov-Smirnov distance, i.e. KSD, to measure the accuracy of the parameter estimates.

[0041] Combine the sea clutter amplitude sequence and the obtained parameter estimates to calculate the Kolmogorov-Smirnov distance, i.e. KSD:

[0042]

[0043] Where F(r; v, b) is the true cumulative distribution function, which can be replaced by the empirical cumulative distribution function; the smaller the KSD value, the higher the accuracy of parameter estimation.

[0044] A computer storage medium storing a computer program that, when executed by a processor, implements the aforementioned method for estimating K-distribution clutter parameters based on a GBDT model.

[0045] A computer device includes a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the above-described method for estimating K-distribution clutter parameters based on the GBDT model.

[0046] Beneficial effects: Compared with the prior art, the present invention has the following advantages: The present invention combines moment features and quantile features, and learns shape parameters autonomously with the help of the GBDT model, thereby achieving the accuracy of parameter estimation and robustness in complex clutter environments. Attached Figure Description

[0047] Figure 1 This is a flowchart of the steps of the method described in this invention;

[0048] Figure 2 This is an amplitude distribution diagram of the measured radar data;

[0049] Figure 3 The result of fitting the K-distribution to region A;

[0050] Figure 4 The result of fitting the K-distribution to region B;

[0051] Figure 5 This is the fitting result of the K-distribution for region C. Detailed Implementation

[0052] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0053] like Figure 1 As shown, a method for estimating K-distribution clutter parameters based on the GBDT model includes the following steps:

[0054] (1) Obtaining the sea clutter sequence: Assume that the radar receives N sea clutter sequences, denoted as {z1, z2, ..., z...} N}, take the modulus of the sea clutter sequence to obtain the sea clutter amplitude sequence {r1,r2,…,r}. N}

[0055] (1.1) Assume that the radar receives N sea clutter sequences, denoted as {z1, z2, ..., z...} N} and model the sequence as a compound Gaussian model.

[0056] (1.2) According to the sea clutter sequence, the sea clutter amplitude sequence is calculated as { |z1|, |z2|, …, |z N}, where || represents the modulus of complex number; according to the compound Gaussian model, the sea clutter amplitude sequence is subject to K distribution, and the probability density function is:

[0057]

[0058] where r represents the sea clutter amplitude variable, v is the shape parameter, b is the scale parameter, Γ(·) is the gamma function, and K v (·) is the second modified Bessel function of order v.

[0059] (2) Feature extraction: according to the sea clutter amplitude sequence in step (1), the sample moment m l of the lth order is calculated; four moment ratio values are extracted to form the moment feature ξ M ; the sea clutter amplitude sequence is sorted from small to large, and the sample quantile r p of the pth order is calculated; nine quantile ratio values are extracted to form the quantile feature ξ P .

[0060] (2.1) According to the sea clutter amplitude sequence in step (1), the sample moment m l of the lth order is calculated:

[0061]

[0062] When the sample number N of the sea clutter sequence tends to infinity, the sample moment tends to the theoretical moment; then, four moment ratio values are extracted to form the moment feature ξ M :

[0063]

[0064] where m 0.5 , m1, m2, m3, m4 represent the 0.5th order moment, the 1st order moment, the 2nd order moment, the 3rd order moment, and the 4th order moment, respectively.

[0065] (2.2) The sea clutter amplitude sequence in step (1) is sorted from small to large and re-marked as {r1, r2, …, r N}, and the pth sample quantile r p is calculated:

[0066] r p = r [N×p] , p ∈ [0, 1]

[0067] where [.] denotes the integer part; when N tends to infinity, the sample quantile tends to the theoretical quantile; then, extract 9 quantile ratios to form the quantile feature ξ P :

[0068]

[0069] It is proved that both the moment ratio and the quantile ratio are independent of the scale parameter, and only related to the shape parameter.

[0070] (3) Construct the feature vector: combine the moment feature and the quantile feature in step (2) to construct a 13-dimensional feature vector ξ = [ξ M , ξ P ] T , T denotes the transpose.

[0071] According to the features extracted in step (2), combine the moment feature and the quantile feature to construct a 13-dimensional feature vector:

[0072] ξ = [ξ M , ξ P ] T

[0073] where T denotes the transpose.

[0074] (4) Estimate the shape parameter: first, establish the GBDT model, simulate K-distributed clutter under different shape parameters, obtain a large number of feature vectors according to steps (2) and (3), and establish the training data set Ω; then input the training data set Ω into the GBDT model for iterative learning to obtain the optimal parameter model of GBDT; finally, input the feature vector ξ in step (3) into the GBDT model with the optimal parameters to output the estimated value of the shape parameter

[0075] (4.1) Set the number of decision trees M = 500, the depth of each decision tree D = 7, and cascade all the decision trees to build the GBDT model.

[0076] (4.2) Simulate K-distributed clutter sequences under different shape parameters; set the shape parameter v to traverse the value range from 0.1 to 20 with a step of 0.1; for a given v j value, generate N = 10000 sequences conforming to the K distribution, and calculate the feature vector according to step (3) to obtain 1 sample, denoted as {ξ j , v j}; considering the strong non-Gaussianity of clutter under small shape parameters, when v ≤ 1.5, 8000 samples are generated for each shape parameter; when v > 1.6, 150 samples are generated for each shape parameter; finally, all the samples form the training data set Ω = { {ξj , v j}, j = 1, 2, …, 147750}.

[0077] (4.3) Take the training set Ω in step (4.2) as input, train the GBDT model built in step (4.1), and update the optimal parameters f M of GBDT.

[0078] (4.4) Take the feature vector ξ in step (3) as input, and input it into the GBDT model with optimal parameters, and output the estimated value of the shape parameter

[0079]

[0080] where f M is the optimal parameter of GBDT obtained in step (4.3).

[0081] (5) Estimate the scale parameter: according to the cumulative probability density function F(r; v, b) of K distribution, let into F(r; v, b) to obtain a specific quantile that depends on the shape parameter; according to the estimated value of the shape parameter , determine the estimated value of the scale parameter

[0082] (5.1) According to the probability density function of K distribution in step (1.2), calculate the cumulative probability density function of K distribution:

[0083]

[0084] (5.2) Let into F(r; v, b) to obtain a specific quantile that depends on the shape parameter:

[0085]

[0086] (5.3) Take the shape parameter estimate in step (4.4) into θ(v) to obtain a specific quantile; therefore, the estimated value of the scale parameter is:

[0087]

[0088] (6) Calculate the KSD value: combine the sea clutter amplitude sequence and the obtained parameter estimates to calculate the Kolmogorov-Smirnov distance, i.e. KSD, to measure the accuracy of the parameter estimates.

[0089] Kolmogorov-Smirnov distance, KSD, is calculated based on the sea clutter amplitude sequence and the obtained parameter estimation value:

[0090]

[0091] where F(r;v,b) is the real cumulative distribution function, which can be replaced by the empirical cumulative distribution function; the smaller the KSD value, the higher the accuracy of the parameter estimation.

[0092] The effect of the present application is further illustrated below in combination with experimental results of measured data.

[0093] (1) Experimental data

[0094] The present example uses measured data collected by a shore-based radar in a dwell mode. The polarization mode of the radar is HH polarization, the pulse repetition frequency is 1000 Hz, and the range resolution is 30 m.

[0095] (2) Simulation experiment

[0096] The shape parameter and scale parameter of the measured sea clutter data are estimated by using the estimator of the present application and 1-2 order moment estimator, 2-4 order moment estimator, and quantile estimator, respectively, and the results are shown in Figures 2 to 5

[0097] Figure 2 is the range-time amplitude graph of the measured data, and regions A, B, and C are selected, and the proportion of outliers in each region is 5.74%, 2.41%, and 0%, respectively. Therefore, the three regions represent abnormal clutter, mixed clutter, and pure clutter, respectively.

[0098] Figure 3 is the K distribution fitting curve of region A, the abscissa represents the sea clutter amplitude value, and the ordinate represents the probability density value. At this time, the shape parameter of the K distribution is small, indicating that the clutter has strong non-Gaussian characteristics. At the same time, a large number of abnormal samples are contained in this clutter environment. In the abnormal clutter environment, the KSD values corresponding to the 1-2 order moment estimator and the 2-4 order moment estimator are the largest, and the performance of the estimator is severely lost. Compared with the moment estimator, the KSD value of the quantile estimator is significantly smaller, and has good anti-outlier characteristics. The KSD value of the estimator of the present application is the smallest, indicating that it has better anti-outlier characteristics, and has a performance improvement of 15% compared with the quantile estimator.

[0099] Figure 4 ​is the K distribution fitting curve of region B. The shape parameter of K distribution is moderate and contains certain outliers, and the clutter belongs to mixed clutter. Relative to the abnormal environment, the performance of the four estimators under the mixed clutter is improved. However, the two matrix estimators are still affected by outliers, and the performance is lost to a certain extent. And, relative to the three quantile estimators, the performance of the estimator of the application is improved by 50%.

[0100] Figure 5 is the K distribution fitting curve of region C. The shape parameter of K distribution is larger, the clutter tends to be Gaussian distribution, and there is no outlier, which belongs to pure clutter. It can be seen that the performance of the 1-2 order moment estimator and the 2-4 order moment estimator is obviously improved, and has the optimal detection performance, which is due to the optimality of the moment estimation under the pure Gaussian clutter. At this time, the performance of the three quantile point estimator is the worst, because the detector only uses three quantile point information in the clutter sequence, and a large amount of information is wasted. The performance of the estimator of the application is between the 1-2 order moment estimator and the 2-4 order moment estimator, close to the optimal performance.

[0101] In summary, the K distribution clutter parameter estimation method based on the GBDT model proposed in the application can obtain the best comprehensive estimation performance in different clutter environments.

Claims

1. A method for estimating K-distribution clutter parameters based on the GBDT model, characterized in that, Includes the following steps: (1) Obtaining sea clutter sequences: Assume the radar receives N sea clutter sequences, denoted as The sea clutter sequence is moduloed to obtain the sea clutter amplitude sequence. ; (2) Feature extraction: Based on the sea clutter amplitude sequence in step (1), calculate the l-th order sample moments. Extract four moment ratios to form moment features. Sort the sea clutter amplitude sequence from smallest to largest, and calculate the p-th order sample quantile. Extract the ratios of 9 quantiles to form quantile features. ; (3) Constructing the feature vector: Combine the moment feature and quantile feature from step (2) to construct a 13-dimensional feature vector. = T represents transpose; (4) Estimating shape parameters: Set the number of decision trees M=500, the depth of each decision tree D=7, cascade all decision trees to build the GBDT model; simulate to generate K-distribution clutter sequences under different shape parameters; set the shape parameter v to traverse the range of 0.1 to 20 with a step size of 0.1; for a given The value generates N=10000 sequences that follow a K distribution, and the feature vector is calculated according to step (3) to obtain one sample, denoted as { Considering the non-Gaussian intensity of clutter under small shape parameters, when v ≤ 1.5, each shape parameter generates 8000 samples; when v > 1.6, each shape parameter generates 150 samples; finally, all samples are combined into a training dataset. ; will the The GBDT model is trained and learned from the input, and the optimal parameters of GBDT are obtained through iterative updates. ; the feature vector in step (3) As input, it enters the GBDT model with optimal parameters, and outputs an estimate of the shape parameters. , ; To obtain the optimal parameters for GBDT; (5) Estimating the scaling parameter: Based on the probability density function of the K-distribution, calculate the cumulative probability density function of the K-distribution: in, Let v represent the amplitude variable of sea clutter, v be the shape parameter, and b be the scale parameter. For gamma function, It is a modified Bessel function of the second kind of order v; make Substitute Obtain a specific shape parameter quantile values : The estimated shape parameters in step (4) Bring into In this process, specific quantiles are obtained, and the estimated values ​​of the scaling parameters are determined as follows: ; For specific The estimated value; (6) Calculate the KSD value: Combine the sea clutter amplitude sequence and the obtained parameter estimates to calculate the Kolmogorov-Smirnov distance, i.e., KSD, to measure the accuracy of the parameter estimates.

2. The method for estimating K-distribution clutter parameters based on the GBDT model according to claim 1, characterized in that, The specific steps (1) are as follows: (1.1) Assume that the radar receives N sea clutter sequences, denoted as The sequence was then modeled as a composite Gaussian model. (1.2) Calculate the sea clutter amplitude sequence based on the sea clutter sequence. ,in Let represent the modulus of a complex number; according to the composite Gaussian model, the sea clutter amplitude sequence follows a K-distribution, and its probability density function is: in, Let v represent the amplitude variable of sea clutter, v be the shape parameter, and b be the scale parameter. For gamma function, for The second-order modified Bessel function.

3. The method for estimating K-distribution clutter parameters based on the GBDT model according to claim 1, characterized in that, Step (2) specifically involves: (2.1) Based on the i-th sea clutter amplitude sequence in step (1) Calculate the l-th order sample moments : As the number of sea clutter sequence samples N approaches infinity, the sample moments approach the theoretical moments; then, four moment ratios are extracted to form the moment characteristics. : in, , , , , These represent the 0.5th moment, the 1st moment, the 2nd moment, the 3rd moment, and the 4th moment, respectively. (2.2) Sort the sea clutter amplitude sequence from smallest to largest in step (1) and re-record it as follows: Calculate the p-th sample quantile : Where [] indicates taking the integer part; N represents The number of samples is [number]; as N approaches infinity, the sample quantiles approach the theoretical quantiles; then, the ratios of the nine quantiles are extracted to form quantile features. : This proves that the moment ratio and quantile ratio are independent of the scale parameter and are only related to the shape parameter.

4. The method for estimating K-distribution clutter parameters based on the GBDT model according to claim 1, characterized in that, Step (3) specifically involves: Based on the features extracted in step (2), the joint moment features, and the quantile features, a 13-dimensional feature vector is constructed: = Where T represents transpose.

5. The method for estimating K-distribution clutter parameters based on the GBDT model according to claim 1, characterized in that, The specific steps (6) are as follows: By combining the sea clutter amplitude sequence and the obtained parameter estimates, the Kolmogorov-Smirnov distance, i.e., KSD, is calculated: in, The KSD value represents the true cumulative distribution function, which can be replaced by the empirical cumulative distribution function; the smaller the KSD value, the higher the accuracy of the parameter estimation.

6. A computer storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements a method for estimating K-distribution clutter parameters based on a GBDT model as described in any one of claims 1-5.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements a K-distribution clutter parameter estimation method based on the GBDT model as described in any one of claims 1-5.

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