Method for estimating sea clutter parameters based on sample tritile CG-NG distribution

Abstract

The application discloses a sea clutter parameter estimation method based on sample three-quantile CG-NG distribution. The specific steps of the application are as follows: firstly, a CG-NG distribution cumulative distribution function is constructed, and a shape parameter-cumulative probability-quantile point table is constructed; secondly, first and second cumulative probability values are determined, and the estimation values of the first and second quantile points are obtained from the sea clutter sample, and the estimation value of the shape parameter is calculated; finally, the third cumulative probability value is calculated, and the estimation value of the scale parameter is obtained. Compared with the existing parameter estimation method, the application has stronger anti-exceptional sample capability, smaller estimation error and faster estimation speed.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and more specifically relates to a method for estimating sea clutter parameters based on a sample three-point CG-NG distribution (Compound-Gaussian with Nakagami distributed texture) in the field of radar parameter estimation technology. This invention can be used by high-resolution radar to estimate parameters against a sea clutter background under medium to large skidding angles, and the estimated parameters can be used for target detection against this background. Background Technology

[0002] Parameter estimation has always been a core issue in radar target detection. For high-resolution radars with small grazing angles, the amplitude distribution of sea clutter exhibits a long tail and strong non-Gaussianity. Existing models such as the K-distribution amplitude model, the generalized Pareto amplitude model, the inverse Gaussian texture composite Gaussian model, and the log-normal texture composite Gaussian model can achieve good fitting accuracy for sea clutter amplitudes. However, as the grazing angle increases, the non-Gaussianity of the sea clutter amplitude distribution under high-resolution radar weakens, while its Gaussianity strengthens. Currently, the main parameter estimation methods for sea clutter models include the method of moments, the zlog(z) estimation method, and the maximum likelihood estimation method.

[0003] Balleri A et al., in their paper "Maximum likelihood estimation for compound-gaussian clutter with inverse gamma texture" (IEEE Transactions on Aerospace & Electronic Systems, 2007, 43(2):775-779), disclosed a method for estimating sea clutter parameters using the maximum likelihood estimation of a generalized Pareto sea clutter amplitude model. This method first obtains the joint probability density function of the samples, takes its logarithm, and then calculates the partial derivatives with respect to the shape and scale parameters to obtain their estimation expressions. This method achieves high estimation accuracy. However, a drawback remains: because this method uses maximum likelihood estimation of sea clutter parameters, numerical methods are often required, resulting in a large computational load and slow sea clutter parameter estimation speed, making it unsuitable for practical engineering applications.

[0004] Xi'an University of Electronic Science and Technology disclosed a method for estimating K-distributed sea clutter parameters based on dual fractional moments in its patent application, "A Method for Estimating K-Distributed Sea Clutter Parameters Based on Dual Fractional Moments" (Application No. CN201811563827.8, Publication No. CN 109541566 A). This method first obtains a table of fractional order to shape parameter for estimating K-distributed sea clutter fractional moments. Then, it calculates the first estimate of the shape parameters of the radar's sea surface echo data using 1st-2nd-3rd order sample moments. Next, it consults the fractional order to shape parameter table to obtain the optimal fractional moment estimator under ideal conditions. Finally, it calculates the second estimate of the shape parameters of the radar's sea surface echo data. Although this method is relatively fast, it still has shortcomings. Actual sea clutter data contains a small number of high-power anomalies, mainly from small islands and ships, which affect the sample moments, leading to large errors in sea clutter parameter estimation. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the existing technology by providing a sea clutter parameter estimation method based on the CG-NG distribution of sample ternary sites, which solves the problems of slow estimation speed and lack of robustness in the existing technology.

[0006] The specific approach to achieving the objective of this invention is as follows: Based on the characteristics of sample quantiles being less affected by outliers and the speed of table lookup, this invention first constructs a shape parameter-cumulative probability-quantile lookup table. Then, based on the ratio of the estimated values ​​of the first and second quantiles, the estimated value of the shape parameter is obtained by looking up the lookup table. Finally, the estimated value of the scale parameter is calculated based on the third cumulative probability value. The estimated parameters can be used for target detection against sea clutter backgrounds.

[0007] The specific steps to achieve the objective of this invention are as follows:

[0008] Step 1: Integrate the clutter amplitude r in the probability density function of the CG-NG distribution, and set the scale parameter b to 1 to obtain the cumulative distribution function of the CG-NG distribution as follows:

[0009]

[0010] Where F(·) represents the cumulative distribution function of the CG-NG distribution, v represents the shape parameter in the CG-NG distribution, r represents the clutter amplitude in the CG-NG distribution, exp represents the logarithmic operation with the natural constant e as the base, Γ(·) represents the gamma function, and τ represents a random variable that follows the Nakagmai distribution.

[0011] Step 2, construct a shape parameter-cumulative probability-quantile reference table:

[0012] By inverting the cumulative distribution function of the CG-NG distribution, a table of shape parameters, cumulative probabilities, and quantiles is obtained.

[0013] Step 3: Generate an increasing sequence of sea clutter amplitudes;

[0014] Step 4: Determine the estimated values ​​of the first and second quantiles based on the determined first and second cumulative probability values ​​α and β;

[0015] Step 5: Calculate the estimated shape parameters based on the ratio of the estimated values ​​of the two quantiles.

[0016] Step 6, based on the estimated values ​​of the shape parameters Calculate the third cumulative probability value ξ;

[0017] Step 7: Calculate the estimated values ​​of the scaling parameters.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] First, because the present invention establishes a shape parameter-cumulative probability-quantile table and calculates the ratio of the estimated values ​​of the first and second quantiles, the estimated value of the shape parameter can be quickly obtained by looking up the table. This overcomes the shortcomings of the existing technology, such as large computational load, slow estimation speed, and difficulty in meeting the real-time data processing needs in engineering applications. As a result, the present invention is faster and takes less time when estimating parameters of CG-NG distributed sea clutter.

[0020] Secondly, since this invention uses the quantiles of sea clutter samples to estimate sea clutter parameters, it overcomes the shortcomings of existing technologies where the numerical values ​​of sample moments change significantly when there are outliers in the sea clutter samples, resulting in larger parameter estimation errors. This makes the estimation error of this invention lower and more stable when performing parameter estimation. Attached Figure Description

[0021] Figure 1 This is a flowchart of the present invention;

[0022] Figure 2 shows the results of the simulation experiment. Figure 2(a) is a comparison of the shape parameters relative to the root mean square error in the simulation experiment using the present invention, and Figure 2(b) is a comparison of the scale parameters relative to the root mean square error in the simulation experiment using the present invention. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0024] Reference Figure 1 The implementation steps of the embodiments of the present invention will be further described below.

[0025] Step 1: Integrate the clutter amplitude r in the probability density function of the CG-NG distribution, and set the scale parameter b to 1 to obtain the cumulative distribution function of the CG-NG distribution as follows:

[0026]

[0027] Where F(·) represents the cumulative distribution function of the CG-NG distribution, v represents the shape parameter of the CG-NG distribution, r represents the clutter amplitude of the CG-NG distribution, exp represents the logarithmic operation with the natural constant e as the base, Γ(·) represents the gamma function, and τ represents a random variable that follows the Nakagmai distribution.

[0028] The probability density function of the CG-NG distribution is as follows:

[0029]

[0030] Where f(·) represents the probability density function of the CG-NG distribution, and b represents the scale parameter in the CG-NG distribution.

[0031] Step 2: Construct a shape parameter-cumulative probability-quantile reference table.

[0032] By inverting the cumulative distribution function of the CG-NG distribution, a table of shape parameters, cumulative probabilities, and quantiles is obtained.

[0033] The steps for obtaining the shape parameter-cumulative probability-quantile lookup table by inverting the cumulative distribution function of the CG-NG distribution are as follows:

[0034] The first step is to select an unselected value every 0.01 intervals within the shape parameter range of [0.05, 10], and use the value of the selected element as the shape parameter value v in the CG-NG distribution;

[0035] The second step is to select an unselected value every 0.01 intervals within the cumulative probability interval [0.1, 0.99], and use the value of the selected element as the cumulative probability value γ.

[0036] The third step is to invert the cumulative distribution function of the CG-NG distribution, and then substitute the selected shape parameter value v and the cumulative probability value γ into the following formula to calculate the value as the corresponding quantile value r. γ .

[0037] r γ =F -1 (γ;v)

[0038] Among them, F -1 (·) represents the inverse function of F(·).

[0039] The fourth step is to determine whether all elements in the cumulative probability interval have been selected. If so, proceed to the fifth step; otherwise, proceed to the second step.

[0040] Fifth step: Determine if all elements in the shape parameter range have been selected. If yes, proceed to sixth step; otherwise, proceed to first step.

[0041] Step 6: Compile a shape parameter-cumulative probability-quantile lookup table for all shape parameters and the corresponding quantiles of cumulative probabilities.

[0042] Step 3: Generate an increasing sequence of sea clutter amplitudes.

[0043] The generation of the sea clutter amplitude increasing sequence refers to generating a sea clutter sequence that follows a CG-NG distribution using Matlab software, taking the modulus of the sea clutter sequence and arranging it in ascending order to obtain the sea clutter amplitude increasing sequence.

[0044] Step 4: Determine the estimated values ​​of the first and second quantiles based on the determined first and second cumulative probability values ​​α and β.

[0045] The steps for determining the estimated values ​​of the first and second quantiles based on the determined first and second cumulative probability values ​​α and β are as follows:

[0046] The first step is to select a value from the interval [0.5, 0.99] as the second cumulative probability value β. In this embodiment of the invention, β = 0.85 is selected, and α = -0.3574β 2 +0.6472β-0.09682, determine the first cumulative probability value α.

[0047] The second step is to extract the first wave from the increasing amplitude sequence of sea clutter. The sea clutter amplitude is used as the estimate for the first quantile. The first of the sea clutter amplitude increasing sequence The sea clutter amplitude was used as an estimate of the second quantile. Where N represents the length of the increasing sea clutter amplitude sequence, This indicates the floor function.

[0048] Step 5: Calculate the estimated shape parameters based on the ratio of the estimated values ​​of the two quantiles.

[0049] The estimated shape parameter is calculated based on the ratio of the estimated values ​​of the two quantiles. This refers to finding the shape parameter-cumulative probability-quantile reference table that matches... The two corresponding quantiles r α and r β The ratio r β / r α , will r β / r α The shape parameter value corresponding to the ratio is used as an estimate of the shape parameter of the CG-NG distribution.

[0050] Step 6, based on the estimated values ​​of the shape parameters Calculate the third cumulative probability value ξ.

[0051] The estimated value based on shape parameters Calculating the third cumulative probability value ξ means that, from The third cumulative probability value ξ is obtained.

[0052] Step 7: Calculate the estimated values ​​of the scaling parameters.

[0053] The steps for calculating the estimated value of the scale parameter are as follows:

[0054] The first step is to use the first wave in the sea clutter amplitude increasing sequence. The clutter amplitude is used as an estimate of the third quantile.

[0055] The second step is to use the shape parameter-cumulative probability-quantile lookup table to find the estimated value of the shape parameter. The quantile r corresponding to the third cumulative probability ξ ξ .

[0056] The third step is... Obtain the estimated value of the scaling parameter.

[0057] The effects of the present invention will be further described below with reference to simulation experiments.

[0058] 1. Simulation conditions:

[0059] The simulation experiment of this invention was run on an Intel(R) Core i7-6700 CPU@3.40GHz, a 64-bit Windows operating system, and the simulation software used was Matlab R2022a.

[0060] 2. Simulation content and result analysis:

[0061] The simulation experiment employed the 2nd-4th order moment estimation method, the 1st-2nd order moment estimation method, the zlog(z) estimation method, and the numerical maximum likelihood estimation method of the present invention and existing technologies to conduct simulation experiments for each shape parameter. Each simulation generated 10,000 samples with the same parameters that followed the CG-NG distribution, with the proportion of anomalous samples being 2%. The ratio of the power of the anomalous samples to the average power of the sea clutter was a random number between 10 and 100. The parameter estimation was performed, and the simulation and estimation experiments were repeated 10,000 times to obtain the estimated values ​​of 10,000 shape parameters. The relative root mean square error was calculated, and the relative root mean square error comparison curve was plotted, as shown in Figure 2.

[0062] The four existing technologies used in the simulation experiment are:

[0063] Existing technologies 1 and 2 refer to the second-to-fourth order moment estimation method and the first-to-second order moment estimation method proposed by Han Y et al. in their paper "Low-order moment-based estimation of shape parameter of CGIG clutter model" (Electronics Letters, 2016, 52(18): 1561-1563).

[0064] The prior art 3 refers to the zlog(z) estimation method for parameters of the log-normal texture complex Gaussian clutter model proposed by I. Chalab et al. in their published paper “Estimators of compound Gaussian clutter with lognormal texture” (Remote Sens. Lett. 10(7)(2019) 709–716).

[0065] The prior art 4 refers to the maximum likelihood estimation method for parameters of the inverse gamma texture complex Gaussian clutter model proposed by Balleri A et al. in their paper “Maximum likelihood estimation for compound-gaussian clutter with inverse gamma texture” (IEEE Transactions on Aerospace & Electronic Systems, 2007, 43(2): 775-779).

[0066] Simulations were performed on CG-NG distributed sea clutter, and a shape parameter-cumulative probability-quantile comparison table was established. Existing estimation methods (2nd-4th order moment estimation, 1st-2nd order moment estimation, zlog(z) estimation, and numerical maximum likelihood estimation) were compared with this invention. The simulation experiment of this invention was conducted with a sample size of 10,000. The shape and scale parameters of CG-NG distributed sea clutter were estimated using the method of this invention and existing estimation methods, respectively, and the relative root mean square error comparison curves are shown in Figure 2.

[0067] In Figure 2(a), the horizontal axis represents the shape parameter values ​​of the CG-NG distribution, and the vertical axis represents the relative root mean square error values ​​of the shape parameters of the CG-NG distribution. In Figure 2(a), the curves marked with asterisks represent the relative root mean square error curves of the 2nd to 4th order moment estimation methods, the dashed lines represent the relative root mean square error curves of the 1st to 2nd order moment estimation methods, the dotted lines represent the relative root mean square error curves of the zlog(z) estimation method, the dashed lines represent the relative root mean square error curves of the numerical maximum likelihood estimation method, and the solid lines represent the relative root mean square error curves of the present invention.

[0068] In Figure 2(b), the horizontal axis represents the shape parameter values ​​of the CG-NG distribution, and the vertical axis represents the relative root mean square error values ​​of the scale parameter of the CG-NG distribution. The dashed lines in Figure 2(b) represent the relative root mean square error curves of the 2nd-4th moment estimation method, the 1st-2nd moment estimation method, and the zlog(z) estimation method. All three methods use the second moment of the sample to estimate the scale parameter. The dotted lines represent the relative root mean square error curve of the numerical maximum likelihood estimation method, and the solid lines represent the relative root mean square error curve of the present invention.

[0069] As shown in Figure 2, with a sample size of 10,000 and containing 2% outliers, the relative root mean square error (RMSE) of the shape and scale parameters of the CG-NG distribution estimated by this invention is significantly smaller than that of the existing 2nd-4th moment estimation method, 1st-2nd moment estimation method, zlog(z) estimation method, and maximum likelihood estimation method, demonstrating high estimation accuracy. This proves that the estimation results of this invention are more stable than those of existing sea clutter parameter estimation methods.

Claims

1. A method for estimating sea clutter parameters based on the CG-NG distribution of sample ternary sites, characterized in that: A shape parameter-cumulative probability-quantile lookup table is constructed. Based on the ratio of the estimated values ​​of the first and second quantiles, the estimated value of the shape parameter is obtained by looking up the lookup table. The estimated value of the scale parameter is calculated based on the third cumulative probability value. The steps of this method include the following: Step 1: Calculate the clutter amplitude in the probability density function of the CG-NG distribution. Perform integration and convert the scale parameter Setting it to 1 yields the following cumulative distribution function for the CG-NG distribution: ， in, The cumulative distribution function of the CG-NG distribution is represented. This represents the shape parameter in the CG-NG distribution. This represents the clutter amplitude in the CG-NG distribution. This represents the logarithmic operation with base e. Represents the gamma function. Let represent a random variable that follows a Nakagmai distribution; Step 2, construct a shape parameter-cumulative probability-quantile reference table: By inverting the cumulative distribution function of the CG-NG distribution, a table of shape parameters, cumulative probabilities, and quantiles is obtained. Step 3: Generate an increasing sequence of sea clutter amplitudes; Step 4, based on the determined first and second cumulative probability values and The steps to determine the estimated values ​​of the first and second quantiles are as follows: The first step is to select a value from the interval [0.5, 0.99] as the second cumulative probability value. ,Depend on Determine the first cumulative probability value ; The second step is to extract the first wave from the increasing amplitude sequence of sea clutter. The clutter amplitude is used as an estimate of the first quantile. The first of the sea clutter amplitude increasing sequence The clutter amplitude is used as an estimate of the second quantile. ,in, Indicates the length of the increasing amplitude sequence of sea clutter. This indicates a round-down operation; Step 5: Calculate the estimated shape parameters based on the ratio of the estimated values ​​of the two quantiles. ; Step 6, based on the estimated values ​​of the shape parameters Calculate the third cumulative probability value : ; Step 7: Calculate the estimated values ​​of the scaling parameters. .

2. The method for estimating sea clutter parameters based on the CG-NG distribution of sample ternary sites according to claim 1, characterized in that, The probability density function of the CG-NG distribution mentioned in step 1 is as follows: ， in, This represents the probability density function of the CG-NG distribution. This represents the scale parameter in the CG-NG distribution.

3. The method for estimating sea clutter parameters based on the CG-NG distribution of sample ternary sites according to claim 1, characterized in that, The steps in step 2 to obtain the shape parameter-cumulative probability-quantile reference table by inverting the cumulative distribution function of the CG-NG distribution are as follows: The first step is to select an unselected value every 0.01 intervals within the shape parameter range of [0.05, 10], and use the selected value as the shape parameter value in the CG-NG distribution; The second step is to select an unselected value every 0.01 intervals within the cumulative probability interval [0.1, 0.99], and use the value of the selected element as the cumulative probability value. The third step is to take the inverse function of the cumulative distribution function of the CG-NG distribution, substitute the selected shape parameter value and cumulative probability value into the inverse function, and use the calculated value as the corresponding quantile value. The fourth step is to determine whether all elements in the cumulative probability interval have been selected. If so, proceed to the fifth step; otherwise, proceed to the second step. Fifth step: Determine if all elements in the shape parameter range have been selected. If yes, proceed to sixth step; otherwise, proceed to first step. Step 6: Compile a shape parameter-cumulative probability-quantile lookup table by matching all shape parameters with the quantiles corresponding to the cumulative probabilities.

4. The method for estimating sea clutter parameters based on the CG-NG distribution of sample ternary sites according to claim 1, characterized in that, The generation of the sea clutter amplitude increasing sequence in step 3 refers to generating a sea clutter sequence that follows a CG-NG distribution using Matlab software, taking the modulus of the sea clutter sequence and arranging it in ascending order to obtain the sea clutter amplitude increasing sequence.

5. The method for estimating sea clutter parameters based on the CG-NG distribution of sample ternary sites according to claim 1, characterized in that, Step 5 describes calculating the estimated shape parameters based on the ratio of the estimated values ​​of the two quantiles. This refers to finding the shape parameter-cumulative probability-quantile reference table that matches... The two corresponding quantiles and ratio ,Will The shape parameter value corresponding to the ratio is used as an estimate of the shape parameter of the CG-NG distribution. .

6. The method for estimating sea clutter parameters based on the CG-NG distribution of sample ternary sites according to claim 1, characterized in that, The estimated value of the scale parameter is calculated in step 7. The steps are as follows: The first step is to use the first wave in the sea clutter amplitude increasing sequence. The clutter amplitude is used as an estimate of the third quantile. ; The second step is to use the shape parameter-cumulative probability-quantile lookup table to find the estimated value of the shape parameter. and the third cumulative probability corresponding quantiles ; The third step is... The estimated values ​​of the scaling parameters are obtained. .

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