Iterative truncation moment estimation method for K-distribution sea clutter amplitude model parameters

Abstract

The invention discloses an iterative truncation moment estimation method for K-distribution sea clutter amplitude model parameters, which comprises the following steps of: sorting samples according to an ascending order, eliminating a part of high-value samples containing abnormal values by setting a threshold value, and calculating a theoretical value of a K-distribution truncation moment based on truncation distribution of a K-distribution model so as to estimate the K-distribution sea clutter amplitude model parameters. And a theoretical value and a sample truncation moment estimation value are combined, and a parameter estimation value is obtained through iteration. According to the method, robust and high-performance estimation of parameters can be realized by deleting high-value samples and using all samples lower than a threshold value.

Description

Technical Field

[0001] This invention belongs to the field of electrical digital data processing technology, specifically, it relates to an iterative truncation moment estimation method for parameters of a K-distribution sea clutter amplitude model. Background Technology

[0002] Accurate description and modeling of sea clutter characteristics are crucial for achieving marine radar target detection and maintaining a constant false alarm rate (CFAR). The K-distribution model is one of the effective models for describing high-resolution sea clutter and is widely used in sea surface target detection. In the context of K-distribution sea clutter, researchers have proposed optimal OKD detection methods and near-optimal and computationally feasible α-AMF detection methods. To adapt to environmental changes and maintain CFAR, the detection threshold of these methods is determined by the cumulative pulse count, false alarm rate, and the shape and scale parameters of the K-distribution model. Therefore, accurate estimation of its parameters is a crucial prerequisite for the practical application of the K-distribution model in target detection. Furthermore, the accuracy of parameter estimation has a significant impact on the detection performance and CFAR characteristics of the detection method.

[0003] The two-parameter K-distribution is the most studied sea clutter model, and its parameter estimation methods have been extensively developed. Moment-based estimation methods, including the Method of Integer Moment (MoIM), the Method of Fractional Moment (MoFM), and the Method of Logarithmic Moment (MoLM), are easy to implement but have low estimation performance. Maximum Likelihood (ML) estimation of K-distribution parameters can achieve higher estimation performance, but it lacks an analytical expression and has high computational complexity. It is worth noting that sea clutter parameter estimation needs to be performed in non-ideal real-world environments, where anomalous samples inevitably exist from non-cooperative targets, islands, reefs, and fixed offshore platforms. Unfortunately, moment estimation and maximum likelihood estimation are sensitive to anomalous samples, leading to a degraded estimation performance. Based on the robustness of data sample quantiles to anomalous samples, Yu Han et al. proposed a robust Tri-Percentile (TriP) estimation method for anomalous samples. The ternary locus estimation method is equivalent to using three specific points to interpolate on the cumulative distribution function (CDF) curve of the K distribution to estimate parameters. This method only utilizes three ternary locus samples, and a large number of other available samples are not effectively utilized, thus limiting the accuracy of parameter estimation.

[0004] The information disclosed in this background section is only intended to enhance the understanding of the background technology of this application, and therefore may include prior art that is not known to those skilled in the art. Summary of the Invention

[0005] This invention proposes an iterative truncation moment estimation method and its control method for parameters of a K-distribution sea clutter amplitude model. By using truncation moment information for parameter estimation, the method can effectively reduce the impact of high-power outliers in the original data on parameter estimation performance, thereby solving the technical problem of low target detection accuracy in sea clutter background.

[0006] To achieve the above-mentioned invention / design objectives, the present invention adopts the following technical solution:

[0007] An iterative cutoff moment estimation method for parameters of a K-distribution sea clutter amplitude model, the method comprising:

[0008] Input sea clutter data ;

[0009] The modulus values ​​of the sea clutter data are used to obtain the sea clutter amplitude sequence. ;

[0010] Sort the sea clutter amplitude sequence in ascending order to obtain the sea clutter data amplitude increasing sequence. ;

[0011] The inverse shape parameter estimates are obtained using the integer moment of inference (MoIM) parameter estimation method. and scale parameter estimates ;

[0012] Cut-off distribution ;

[0013] Where f(x) and F(x) represent the probability density function PDF and cumulative distribution function CDF of the random variable x, respectively, a=0, b=r ω , b represents the quantile of ω in the K distribution;

[0014] p-th cutoff moment of the K-distribution for:

[0015] ;

[0016] Among them, K q (•) denotes a modified Bessel function of the second kind with order q; It is a generalized hypergeometric function of order m or n; It is the Gamma function; , Let μ be the shape parameter of the sea clutter, and μ be the scale parameter of the sea clutter.

[0017] p-th order cutoff moment of a sample with cutoff ratio ω and the ω quantile of the sample for:

[0018] ;

[0019] in, Represents the integer closest to N×ω;

[0020] make ,but

[0021]

[0022] function Related to the inverse shape parameter λ, we define a ratio class statistic:

[0023] ; It is a monotonic function of λ;

[0024] The inverse shape parameter λ, scale parameter μ, and cutoff ratio ω of the K-distribution model are estimated using an iterative method, letting... The iterative process is as follows:

[0025] S1. Use the estimated integer moments (MoIM) as initial values:

[0026] ;

[0027] S2. Iteratively update the cutoff ratio ω, inverse shape parameter λ, and scale parameter μ:

[0028] S3. Statistically process the sea clutter data to obtain the true cumulative distribution function (CDF) results. The iteration results and Substituting the cumulative distribution function (CDF) into the K-distribution model, we obtain the CDF fitting result of the K-distribution model. The logarithmic Kolmogorov-Smirnov distance (LoKSD) was used as the iteration termination condition.

[0029] ;

[0030] Where δ is a pre-set positive real number;

[0031] The iteration terminates when the above equation holds true, and the result is output. Otherwise, let k = k + 1 and go to step S2 to continue the iteration.

[0032] The iterative cutoff moment estimation method for the parameters of the K-distribution sea clutter amplitude model, as described above, includes the p-th order raw moment of the K-distribution. and their corresponding sample moments for:

[0033] ;

[0034] .

[0035] The iterative cutoff moment estimation method for the parameters of the K-distribution sea clutter amplitude model, as described above, and the amplitude probability density function PDF of the K-distribution sea clutter model. and cumulative distribution function CDF The method for determining it is as follows:

[0036] .

[0037] In the iterative truncation moment estimation method for the parameters of the K-distribution sea clutter amplitude model described above, δ is a pre-set positive real number less than a set value.

[0038] Compared with existing technologies, the advantages and positive effects of this invention are as follows: The iterative cutoff moment estimation method for parameters of the K-distribution sea clutter amplitude model first sorts the samples in ascending order, then excludes some high-value samples containing outliers by setting a threshold, and then calculates the theoretical value of the K-distribution cutoff moment based on the cutoff distribution of the K-distribution model. The theoretical value and the sample cutoff moment estimates are then combined to iteratively obtain the parameter estimates. This method achieves robust and high-performance parameter estimation by deleting high-value samples and using all samples below the threshold.

[0039] Other features and advantages of the present invention will become clearer after reading the detailed embodiments of the invention in conjunction with the accompanying drawings. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart of the iterative cutoff moment estimation method for the parameters of the K-distribution sea clutter amplitude model in a specific embodiment of the present invention.

[0042] Figure 2 This is a performance comparison chart of parameter estimation methods in the absence of outliers.

[0043] Figure 3This is a performance comparison of parameter estimation methods when outliers exist. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] In the description of this invention, it should be understood that the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0046] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances. In the description of embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0047] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature.

[0048] In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0049] The K-distribution is a commonly used amplitude model to describe high-resolution sea clutter, and its parameter estimation is crucial in adaptive target detection. Non-sea surface scattered echoes from ships, reefs, fixed platforms, etc., are characterized by high power and are known as outliers. These outliers can significantly negatively impact the accuracy of K-distribution model parameter estimation. To address this issue, an Iterative Method of Truncated Moment (IMoTM) is proposed to estimate the parameters of the K-distribution sea clutter model. This method utilizes truncation moment information for parameter estimation, effectively reducing the impact of high-power outliers in the original data on parameter estimation performance, thereby improving the accuracy of target detection against sea clutter backgrounds.

[0050] Explanation of the K-distribution sea clutter model:

[0051] The composite Gaussian model can well describe the characteristics of sea clutter. It can be described as the product of a slowly varying nonnegative texture component τ and a rapidly varying complex Gaussian speckle component u.

[0052] (1)

[0053] Where c represents sea clutter. When the texture component τ of the sea clutter follows a Gamma distribution, the amplitude r of the sea clutter follows a K distribution.

[0054] The probability density function (PDF) of the texture component τ is as follows.

[0055] (2)

[0056] in, Let Gamma be the function, and μ be the scale parameter of sea clutter. The shape parameters of the sea clutter are given.

[0057] Shape parameters The shape parameter is used to describe the non-Gaussianity of sea clutter; the smaller the shape parameter, the stronger the non-Gaussianity. To improve the discriminative power of the function, the reciprocal form of the shape parameter is used. .

[0058] Therefore, the probability density function PDF of the amplitude r of the K-distribution sea clutter model is... and cumulative distribution function CDF The method for determining it is as follows:

[0059] (3)

[0060] in, K represents the amplitude of sea clutter.q (•) denotes a modified Bessel function of the second kind with order q.

[0061] When shape parameters When the inverse shape parameter λ approaches infinity, or approaches 0, the K-distribution clutter amplitude model degenerates into a Rayleigh distribution, and the corresponding sea clutter approaches a complex Gaussian distribution.

[0062] According to equation (3), the p-th order raw moment of the K distribution and their corresponding sample moments for:

[0063] (4)

[0064] in, and Representing the p-th order raw moment and sample moment respectively, r n This represents the amplitude sample of the sea clutter data, where N is the number of samples.

[0065] The parameter estimation method for integer moments (MoIM) is as follows:

[0066] (5)

[0067] Although moment-based estimation methods are relatively simple in form, they are suitable for situations where there are sufficient clutter samples and the data does not contain outliers. Using higher-order sample moments can lead to increased estimation errors when the sample size is insufficient.

[0068] Therefore, an iterative method of truncated moment (IMoTM) estimation for parameters of the K-distribution sea clutter amplitude model is proposed. The following section combines... Figure 1 The estimation method will be explained in detail:

[0069] Input sea clutter data .

[0070] The modulus values ​​of the sea clutter data are used to obtain the sea clutter amplitude sequence. .

[0071] Sort the sea clutter amplitude sequence in ascending order to obtain the sea clutter data amplitude increasing sequence. .

[0072] The inverse shape parameter estimates are obtained using the integer moment of inference (MoIM) parameter estimation method. and scale parameter estimates .

[0073] The truncated distribution is a conditional distribution obtained by restricting the domain of the probability density function, and its definition is as follows.

[0074] (8)

[0075] Here, f(x) and F(x) represent the probability density function PDF and cumulative distribution function CDF of the random variable x, respectively.

[0076] In sea clutter, anomalous samples specifically refer to samples with high power; therefore, samples with power greater than the threshold b are deleted.

[0077] a=0, b=r ω , b represents the quantile of ω in the K distribution.

[0078] Therefore, the p-th order cutoff moment of the K distribution for:

[0079] (9)

[0080] in, It is a generalized hypergeometric function of order m or n.

[0081] p-th order cutoff moment of a sample with cutoff ratio ω and the ω quantile of the sample for:

[0082] (10)

[0083] in, Represents the integer closest to N×ω.

[0084] make ,but

[0085] (11)

[0086] function It is only related to the inverse shape parameter λ. Define ratio class statistics:

[0087] (12)

[0088] It is a monotonic function of λ, and its inverse function is... It exists. Although the inverse function does not have an analytical expression, the inverse shape parameter λ can be estimated by looking up a table. Since the inverse shape parameter λ, the scale parameter μ, and the cutoff ratio ω are all unknown, and formula (11) contains hypergeometric functions, the closed-form solution of the three unknowns cannot be obtained when solving the simultaneous equations. Therefore, the inverse shape parameter λ, the scale parameter μ, and the cutoff ratio ω of the K-distribution model are estimated by an iterative method. Let The iterative process is as follows:

[0089] S1. Initialization. Use the estimate of the integer moment of infinity (MoIM) as the initial value, i.e.

[0090] (13) S2. Iteratively update the cutoff ratio ω, inverse shape parameter λ, and scale parameter μ:

[0091] (14) S3, Iteration termination condition:

[0092] The true cumulative distribution function (CDF) results were obtained by statistically processing the sea clutter data. The iteration results and Substituting the values ​​into the cumulative distribution function (CDF) of the K-distribution, we can obtain the results of fitting the cumulative distribution function CDF to the K-distribution model. The logarithmic Kolmogorov-Smirnov distance (LoKSD) was used as the iteration termination condition.

[0093] (15)

[0094] Where δ is a pre-set positive real number. δ is a pre-set positive real number less than the set value, and δ is a very small positive real number.

[0095] The iteration terminates when equation (15) holds, and the result is output. Otherwise, let k = k + 1 and go to step S2 to continue the iteration.

[0096] The estimation performance of the proposed IMoTM method was tested using simulated sea clutter data and compared with the MoIM, ML and TriP estimation methods.

[0097] K-distribution sea clutter can be simulated using the following formula:

[0098] (16)

[0099] in, The scale parameter is μ and the shape parameter is μ. The Gamma distribution, This represents a complex Gaussian distribution with a mean of 0 and a variance of 1. The upper quantile of the TriP method is set to β = 0.95, and the lower quantile is set to α = 0.17. In the experiment, the sample size was N = 10000; the shape parameter ranged from 1 to 10 with an interval of 1; and the scale parameter was fixed at 1. The shape and scale parameters of the K-distribution simulated sea clutter data were estimated using the MoIM, ML, TriP, and proposed IMoTM methods, respectively. The relative root mean square error (RMSE) of the estimated shape and scale parameters was calculated after T = 1000 independent trials.

[0100] (17)

[0101] in, These represent the estimated values ​​of the shape and scale parameters for each experiment, respectively.

[0102] The first experiment explores the estimation performance of MoIM, ML, TriP, and the proposed IMoTM method in the absence of outliers. The estimation results for shape and scale parameters are as follows: Figure 2 As shown, overall, as the shape parameter increases, the RRMSE of the shape parameter gradually increases, while the RRMSE of the scale parameter gradually decreases. When the shape parameter is large, the K-distribution model approaches the Rayleigh distribution, at which point the shape parameter estimation errors of all methods are very large. This is because the shape parameter depends on the tail, and a smaller shape parameter implies a longer tail. On the other hand, for the scale parameter, which characterizes clutter power, estimation becomes more difficult as the tail increases, leading to increased errors. In the method comparison, the ML method is generally the best because it has the smallest RRMSE for both the shape and scale parameters. The IMoTM estimation method's estimation performance is slightly lower than that of the ML method. Under the current experimental conditions, the TriP method is relatively moderate, with the estimation accuracy of both parameters lagging behind the ML and IMoTM methods. Compared to the other three methods, the MoIM method has the worst shape parameter estimation performance, but its scale parameter estimation performance is comparable to that of the ML and IMoTM methods.

[0103] In the second experiment, outliers were considered. In each experiment, 5% of the sea clutter samples were randomly selected and replaced with outlier samples. The amplitude of the selected samples was multiplied by a factor of γ, following a uniform distribution within the interval [5, 10]. Other parameter settings were the same as in the first experiment. The RRMSE curves for parameter estimation using the four methods are shown below. Figure 3As shown. When the data sample contains outliers, the advantages of the ML method disappear, and robust estimation methods (including the IMoTM method and the TriP method) take their place. The proposed IMoTM method has the smallest RRMSE for both shape and scale parameters; the TriP method follows closely behind. The estimation accuracy of the TriP method is lower than that of the IMoTM method proposed in this patent. This is because the TriP method only utilizes three quantile samples, and a large number of other available samples are not effectively utilized, thus limiting the accuracy of parameter estimation. In contrast, the proposed IMoTM method utilizes samples below the threshold r. ω The proposed IMoTM method is applicable to parameter estimation of K-distribution sea clutter models and radar detection in real-world marine scenarios. However, the ML and MoIM methods, which are sensitive to outliers, clearly fail, with their RRMSE being significantly higher than that of robust estimation methods. Therefore, the proposed IMoTM method can be applied to parameter estimation of K-distribution sea clutter models and radar detection in practical marine scenarios.

[0104] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions claimed by the present invention.

Claims

1. An iterative cutoff moment estimation method for parameters of a K-distribution sea clutter amplitude model, characterized in that, The method includes: Input sea clutter data ; The modulus values ​​of the sea clutter data are used to obtain the sea clutter amplitude sequence. ; Sort the sea clutter amplitude sequence in ascending order to obtain the sea clutter data amplitude increasing sequence. ; The inverse shape parameter estimates are obtained using the integer-order moment parameter estimation method. and scale parameter estimates ; Determine the p-th cutoff moment of the K-distribution The p-th order cutoff moment of the sample with cutoff ratio ω and the ω quantile of the sample ; ,in, , Let ω be the shape parameter of the sea clutter, and μ be the scale parameter of the sea clutter; determine ω, Functions related to the inverse shape parameter λ Determine ratio statistics , It is a monotonic function of λ; The inverse shape parameter λ, scale parameter μ, and cutoff ratio ω of the K-distribution model are estimated using an iterative method, letting... The iterative process is as follows: S1. Use the estimation results of the integer order moment parameter estimation method as the initial value; S2. Iteratively update the cutoff ratio ω, inverse shape parameter λ, and scale parameter μ; S3. Statistically process the sea clutter data to obtain the true cumulative distribution function (CDF) results. Substituting the iteration results into the cumulative distribution function (CDF) of the K-distribution model, we obtain the CDF fitting result of the K-distribution model. The logarithmic KS distance is used as the iteration termination condition. When the iteration termination condition is met, the iteration terminates and the result is output; otherwise, the iteration continues in step S2.

2. The iterative cutoff moment estimation method for the parameters of the K-distribution sea clutter amplitude model according to claim 1, characterized in that, Cut-off distribution ; Where f(x) and F(x) represent the probability density function PDF and cumulative distribution function CDF of the random variable x, respectively, a=0, b=r ω , b represents the quantile of ω in the K distribution; p-th cutoff moment of the K-distribution for: ； Among them, K q (•) denotes a modified Bessel function of the second kind with order q; It is a generalized hypergeometric function of order m or n; It is the Gamma function; ； in, Represents the integer closest to N×ω; hour, ； function Related to the inverse shape parameter λ, we define a ratio class statistic: ; It is a monotonic function of λ; In step S2, ; The iteration termination condition is: ; Where δ is a pre-set positive real number.

3. The iterative cutoff moment estimation method for the parameters of the K-distribution sea clutter amplitude model according to claim 2, characterized in that, The amplitude probability density function (PDF) of the K-distribution sea clutter model and cumulative distribution function CDF The method for determining it is as follows: 。 4. The iterative cutoff moment estimation method for the parameters of the K-distribution sea clutter amplitude model according to claim 2, characterized in that, δ is a pre-set positive real number that is less than the set value.

5. The iterative cutoff moment estimation method for the parameters of the K-distribution sea clutter amplitude model according to claim 1, characterized in that, p-th order raw moment of the K distribution and their corresponding sample moments for: ； 。

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