技术领域technical field
本发明属于雷达信号处理领域，具体涉及一种雨杂波建模方法，可用于毫米波段雷达在降雨环境下的目标检测。The invention belongs to the field of radar signal processing, and in particular relates to a rain clutter modeling method, which can be used for target detection of millimeter-wave radar in a rainy environment.
背景技术Background technique
在利用雷达检测和识别恶劣天气条件下的车辆、飞机等目标时，雷达接收到的回波信号不但包含目标的散射信号，还会包含雨、雪、雾等动杂波。在毫米波段，雨杂波的后向散射回波功率较强，且具有多普勒偏移和多普勒带宽，无论是沿着距离维还是多普勒通道进行目标检测，雨杂波的存在都会严重影响检测性能。对雨杂波精确建模，有助于采用匹配于杂波特性的自适应检测算法，提升雷达在降雨环境下的目标检测性能。When using radar to detect and identify targets such as vehicles and airplanes under severe weather conditions, the echo signal received by the radar not only includes the scattered signal of the target, but also includes dynamic clutter such as rain, snow, fog, etc. In the millimeter wave band, the backscattered echo power of rain clutter is strong, and it has Doppler shift and Doppler bandwidth. No matter whether the target detection is carried out along the range dimension or the Doppler channel, the existence of rain clutter will seriously affect the detection performance. Accurate modeling of rain clutter helps to adopt an adaptive detection algorithm that matches the characteristics of clutter to improve the target detection performance of radar in a rainy environment.
早期雨杂波的统计建模主要采用瑞利分布，随着雷达分辨率的提高，雨杂波具有更强的非高斯性，与瑞利分布的偏差较大。对数正态分布模型和韦布尔分布模型能够描述高分辨率雷达雨杂波的幅度分布，但这两种模型只能拟合单一脉冲，无法描述雨杂波的时空相关性。刘瑞平，沈福民在火控雷达技术,2005(01):43-46)发表的论文中公开了一种用零记忆非线性ZNML仿真雨杂波的方法。其首先生成相关的高斯分布随机序列，之后通过非线性变换将相关高斯随机序列转换为相关对数正态随机序列，生成的仿真数据幅度特性与毫米波段的实测雨杂波接近。但该方法由于需要根据杂波功率谱特性设计线性滤波器，相关特性的转换与幅度概率密度函数的转换同步完成，其杂波的幅度和相关性不能独立控制，因此只适用于单脉冲的雨杂波仿真，无法用于描述多脉冲雷达接收到的雨杂波。The statistical modeling of early rain clutter mainly adopts the Rayleigh distribution. With the improvement of radar resolution, the rain clutter has a stronger non-Gaussian property and a larger deviation from the Rayleigh distribution. The lognormal distribution model and Weibull distribution model can describe the amplitude distribution of high-resolution radar rain clutter, but these two models can only fit a single pulse, and cannot describe the temporal and spatial correlation of rain clutter. Liu Ruiping and Shen Fumin disclosed a method for simulating rain clutter with zero-memory nonlinear ZNML in a paper published in Fire Control Radar Technology, 2005(01):43-46). It first generates a correlated Gaussian distribution random sequence, and then converts the correlated Gaussian random sequence into a correlated lognormal random sequence through nonlinear transformation. The amplitude characteristics of the generated simulated data are close to the measured rain clutter in the millimeter wave band. However, since this method needs to design a linear filter according to the characteristics of the clutter power spectrum, the conversion of the correlation characteristics and the conversion of the amplitude probability density function are completed simultaneously, and the amplitude and correlation of the clutter cannot be controlled independently, so it is only suitable for single-pulse rain Clutter simulation cannot be used to describe the rain clutter received by multi-pulse radar.
针对对数正态分布模型和韦布尔分布模型无法描述杂波脉间相关性的缺点，在海杂波建模领域，复合高斯模型CGM被提出，该模型对X波段雷达的高分辨率海杂波有很好的拟合效果，并且充分考虑了杂波的时空相关性，适用于多脉冲雷达的海杂波建模。该模型将杂波建模为纹理分量和散斑分量的乘积，散斑分量服从复高斯分布，而纹理分量可服从不同的分布类型。近年来，研究人员提出了多种纹理分布，以及相应的复合高斯模型。其中，常用的纹理分布有四种，伽马Gamma分布、逆伽马分布、逆高斯分布、对数正态分布，这些纹理分布分别产生了K分布模型、广义帕累托Pareto分布模型、逆高斯纹理复合高斯IG-CG模型和对数正态纹理复合高斯CG-LNT模型。但目前对于复合高斯模型的应用主要集中在海杂波领域，并发展出多种最优和近最优相干检测算法，还没有应用在雨杂波建模上。Aiming at the disadvantage that the lognormal distribution model and the Weibull distribution model cannot describe the inter-pulse correlation of clutter, in the field of sea clutter modeling, the composite Gaussian model CGM is proposed, which is suitable for the high-resolution sea clutter of X-band radar. The wave has a good fitting effect, and fully considers the time-space correlation of clutter, which is suitable for sea clutter modeling of multi-pulse radar. In this model, the clutter is modeled as the product of the texture component and the speckle component, the speckle component obeys a complex Gaussian distribution, and the texture component can obey different distribution types. In recent years, researchers have proposed a variety of texture distributions, and corresponding composite Gaussian models. Among them, there are four commonly used texture distributions, gamma Gamma distribution, inverse gamma distribution, inverse Gaussian distribution, and lognormal distribution. These texture distributions generate the K distribution model, the generalized Pareto Pareto distribution model, and the inverse Gaussian Texture composite Gaussian IG-CG model and lognormal texture composite Gaussian CG-LNT model. However, the current application of the composite Gaussian model is mainly concentrated in the field of sea clutter, and a variety of optimal and near-optimal coherent detection algorithms have been developed, which have not been applied to rain clutter modeling.
发明内容Contents of the invention
本发明的目的在于针对上述已有的雨杂波建模方法的不足，提出一种基于双参数复合高斯模型的雨杂波建模方法，以准确描述毫米波段雨杂波的幅度分布特性，实现对毫米波雷达接收到的多脉冲雨杂波建模。The purpose of the present invention is to address the shortcomings of the above existing rain clutter modeling methods, and propose a rain clutter modeling method based on a two-parameter composite Gaussian model, to accurately describe the amplitude distribution characteristics of rain clutter in the millimeter wave band, and to realize Modeling multi-pulse rain clutter received by mmWave radar.
为实现上述目的，本发明的技术方案如下：To achieve the above object, the technical scheme of the present invention is as follows:
(1)利用复合高斯模型中的四种双参数模型，分别构建基于K分布的毫米波段雨杂波幅度分布模型KRM、基于广义Pareto分布的毫米波段雨杂波幅度分布模型GPRM、基于IGCG分布的毫米波段雨杂波幅度分布模型IGRM和基于CGLN分布的毫米波段雨杂波幅度分布模型LNRM；(1) Using the four dual-parameter models in the composite Gaussian model, construct the millimeter-wave band rain clutter amplitude distribution model KRM based on the K distribution, the millimeter-wave band rain clutter amplitude distribution model GPRM based on the generalized Pareto distribution, and the millimeter-wave band rain clutter amplitude distribution model based on the IGCG distribution. The millimeter-wave band rain clutter amplitude distribution model IGRM and the millimeter-wave band rain clutter amplitude distribution model LNRM based on CGLN distribution;
(2)利用任一雨杂波模型累积分布函数和数据集X经验累积分布函数之间的KS距离KSD(X；·)和任一雨杂波模型概率密度函数和数据集X经验概率密度函数之间的KL散度KLD(X；·)构建最优幅度分布模型选择测度：(2) Using the KS distance KSD(X; ) between the cumulative distribution function of any rain clutter model and the empirical cumulative distribution function of data set X and the probability density function of any rain clutter model and the empirical probability density function of data set X The KL divergence between KLD(X; ) builds the optimal magnitude distribution model selection measure:
其中，ModelBest(X)表示雨杂波数据集X的最优幅度分布模型，表示使括号内数值最小时的毫米波段雨杂波幅度分布模型，Among them, ModelBest (X) represents the optimal amplitude distribution model of the rain clutter data set X, Indicates the rain clutter amplitude distribution model in the millimeter wave band when the values in the brackets are minimized,
(3)用上述四个毫米波段雨杂波幅度分布模型分别拟合一组实测雨杂波数据集X，得到每个模型拟合数据集X的概率密度函数和标准累积分布函数，通过最优幅度分布模型选择测度评价各模型拟合的效果，选出对该数据集拟合性能最优的模型，作为最终的毫米波段雨杂波幅度分布模型。(3) Fit a set of measured rain clutter data sets X with the above four millimeter-wave band rain clutter amplitude distribution models, and obtain the probability density function and standard cumulative distribution function of each model-fitting data set X. The amplitude distribution model selection measure evaluates the fitting effect of each model, and selects the model with the best fitting performance for the data set as the final millimeter-wave band rain clutter amplitude distribution model.
本发明与现有技术相比具有如下优点：Compared with the prior art, the present invention has the following advantages:
第一，本发明由于利用双参数复合高斯模型构建毫米波段雨杂波幅度分布模型，并将雨杂波序列描述为纹理分量和服从复高斯分布的散斑分量的乘积，纹理分量体现了雨杂波的非高斯性，散斑分量体现了雨杂波的脉间相关性，因此所提毫米波段雨杂波幅度分布模型能准确描述毫米波雷达接收到的多脉冲雨杂波的幅度分布特性，可实现毫米波雷达在降雨环境下的恒虚警检测。First, the present invention utilizes a two-parameter composite Gaussian model to construct a rain clutter amplitude distribution model in the millimeter wave band, and describes the rain clutter sequence as the product of a texture component and a speckle component subject to a complex Gaussian distribution. The texture component embodies the rain clutter Due to the non-Gaussian nature of waves, the speckle component reflects the pulse-to-pulse correlation of rain clutter, so the proposed millimeter-wave band rain clutter amplitude distribution model can accurately describe the amplitude distribution characteristics of multi-pulse rain clutter received by millimeter-wave radar. It can realize the constant false alarm detection of the millimeter wave radar in the rain environment.
第二，本发明由于构建了最优幅度分布模型选择测度，且提出的四个毫米波段雨杂波幅度分布模型分别适用于不同的降雨强度，可使雷达在小雨、中雨或大雨等各种环境下接收到一组雨杂波数据时，确定该组数据对应的拟合性能最优的毫米波段雨杂波幅度分布模型，从而提高各种降雨强度下的目标检测性能。Second, because the present invention constructs the optimal amplitude distribution model to select the measurement, and the proposed four millimeter-wave band rain clutter amplitude distribution models are respectively applicable to different rainfall intensities, the radar can be used in light rain, moderate rain or heavy rain, etc. When a set of rain clutter data is received in the environment, the millimeter-wave band rain clutter amplitude distribution model with the best fitting performance corresponding to the set of data is determined, so as to improve the target detection performance under various rainfall intensities.
附图说明Description of drawings
图1为本发明的实现流程图；Fig. 1 is the realization flowchart of the present invention;
图2为实测雨杂波幅度的经验概率密度与本发明基于K分布的毫米波段雨杂波幅度分布模型KRM的拟合概率密度的变化曲线对比图；Fig. 2 is the variation curve comparison figure of the empirical probability density of measured rain clutter amplitude and the fitting probability density of the present invention based on K distribution millimeter wave band rain clutter amplitude distribution model KRM;
图3为实测雨杂波幅度的经验概率密度与本发明基于广义Pareto分布的毫米波段雨杂波幅度分布模型GPRM的拟合概率密度的变化曲线对比图；Fig. 3 is the variation curve comparison diagram of the empirical probability density of measured rain clutter amplitude and the fitting probability density of the present invention based on the millimeter wave band rain clutter amplitude distribution model GPRM of generalized Pareto distribution;
图4为实测雨杂波幅度的经验概率密度与本发明基于IGCG分布的毫米波段雨杂波幅度分布模型IGRM的拟合概率密度的变化曲线对比图；Fig. 4 is the variation curve comparison chart of the empirical probability density of measured rain clutter amplitude and the fitting probability density of the present invention based on IGCG distribution millimeter wave band rain clutter amplitude distribution model IGRM;
图5为实测雨杂波幅度的经验概率密度与本发明基于CGLN分布的毫米波段雨杂波幅度分布模型LNRM的拟合概率密度的变化曲线对比图。Fig. 5 is a comparison chart of the variation curve of the empirical probability density of the measured rain clutter amplitude and the fitted probability density of the CGLN distribution-based rain clutter amplitude distribution model LNRM of the present invention.
具体实施方式Detailed ways
以下结合附图对本发明的实施例和效果作进一步详细描述。Embodiments and effects of the present invention will be further described in detail below in conjunction with the accompanying drawings.
参照图1，本实例的实现步骤如下：Referring to Figure 1, the implementation steps of this example are as follows:
步骤1，利用复合高斯模型中的四个双参数模型，构建毫米波段雨杂波幅度的四个分布模型。Step 1. Using four dual-parameter models in the compound Gaussian model, four distribution models of rain clutter amplitude in the millimeter wave band are constructed.
(1.1)用复合高斯模型中的K分布模型的形式表示基于K分布的毫米波段雨杂波幅度分布模型KRM，以表示零星小雨背景下毫米波段雨杂波的幅度分布特性，其概率密度函数PDF(r；KRM)表示如下：(1.1) Express the millimeter-wave band rain clutter amplitude distribution model KRM based on the K-distribution in the form of the K distribution model in the composite Gaussian model to represent the amplitude distribution characteristics of the millimeter-wave band rain clutter under the background of sporadic light rain, and its probability density function PDF (r; KRM) is expressed as follows:
其中，Γ()为伽马函数，为阶数为1/λK的第二类修正Bessel函数，r表示雨杂波的幅度序列，b表示雨杂波的平均功率，λK表示零星小雨背景下雨杂波的非高斯性，λK越大表示雨杂波的非高斯性越强；Among them, Γ() is the gamma function, is the modified Bessel function of the second kind with order 1/λK , r represents the amplitude sequence of rain clutter, b represents the average power of rain clutter, λK represents the non-Gaussian nature of rain clutter in sporadic light rain background, λ The largerthe K , the stronger the non-Gaussian nature of the rain clutter;
(1.2)用复合高斯模型中的广义Pareto分布模型的形式表示基于广义Pareto分布的毫米波段雨杂波幅度分布模型GPRM，以表示大雨和暴雨背景下毫米波段雨杂波的幅度分布特性，其概率密度函数PDF(r；GPRM)表示如下：(1.2) In the form of the generalized Pareto distribution model in the composite Gaussian model, the millimeter-wave band rain clutter amplitude distribution model GPRM based on the generalized Pareto distribution is used to represent the amplitude distribution characteristics of the millimeter-wave band rain clutter under the background of heavy rain and heavy rain, and its probability The density function PDF(r; GPRM) is expressed as follows:
其中，r表示雨杂波的幅度序列，b表示雨杂波的平均功率；λp表示大雨和暴雨背景下雨杂波的非高斯性，λp越大表示雨杂波的非高斯性越强；Among them, r represents the amplitude sequence of rain clutter, b represents the average power of rain clutter; λp represents the non-Gaussian property of rain clutter under the background of heavy rain and heavy rain, and the larger λp represents the stronger non-Gaussian property of rain clutter ;
(1.3)用复合高斯模型中的逆高斯纹理复合高斯模型IG-CG的形式表示基于IGCG分布的毫米波段雨杂波幅度分布模型IGRM，以表示中雨背景下毫米波段雨杂波的幅度分布特性，其概率密度函数PDF(r；IGRM)表示如下：(1.3) Express the millimeter-wave rain clutter amplitude distribution model IGRM based on the IGCG distribution in the form of the inverse Gaussian texture composite Gaussian model IG-CG in the composite Gaussian model, so as to represent the amplitude distribution characteristics of millimeter-wave rain clutter under the background of moderate rain , its probability density function PDF(r; IGRM) is expressed as follows:
其中，是中间变量，r表示雨杂波的幅度序列，b表示雨杂波的平均功率；λI表示中雨背景下雨杂波的非高斯性，λI越大表示雨杂波的非高斯性越强；in, isan intermediate variable, r represents theamplitude sequence of rain clutter, b represents the average power of rain clutter; powerful;
(1.4)用复合高斯模型中的对数正态纹理复合高斯模型CG-LNT的形式表示CGLN分布的毫米波段雨杂波幅度分布模型LNRM，以表示小雨背景下毫米波段雨杂波的幅度分布特性，其概率密度函数PDF(r；LNRM)表示如下：(1.4) The log-normal texture composite Gaussian model CG-LNT in the composite Gaussian model is used to express the millimeter-wave band rain clutter amplitude distribution model LNRM of the CGLN distribution, so as to represent the amplitude distribution characteristics of the millimeter-wave band rain clutter under the background of light rain , its probability density function PDF(r; LNRM) is expressed as follows:
其中，τ表示独立同分布的正随机序列，服从双参数的对数正态分布r表示雨杂波的幅度序列，b表示雨杂波的平均功率；λL表示小雨背景下雨杂波的非高斯性，λL越大表示雨杂波的非高斯性越强。Among them, τ represents an independent and identically distributed positive random sequence, which obeys the lognormal distribution of two parameters r represents the amplitude sequence of rain clutter, b represents the average power of rain clutter; λL represents the non-Gaussian nature of rain clutter under light rain background, and the larger λL represents the stronger non-Gaussian property of rain clutter.
步骤2，用毫米波段雨杂波幅度分布模型拟合实测雨杂波数据集X。Step 2: Fit the measured rain clutter data set X with the rain clutter amplitude distribution model in the millimeter wave band.
本步骤是用步骤1中构建的四个毫米波段雨杂波幅度分布模型分别拟合一组实测雨杂波数据集X，得到每个模型拟合数据集X的概率密度函数和标准累积分布函数，具体实现如下：This step is to use the four millimeter-wave band rain clutter amplitude distribution models constructed in step 1 to fit a set of measured rain clutter data sets X respectively, and obtain the probability density function and standard cumulative distribution function of each model fitting data set X , the specific implementation is as follows:
(2.1)将数据集X的所有数据取模后按升序排列得到雨杂波幅度序列r；(2.1) Arrange all the data of data set X in ascending order after taking the modulus to obtain the rain clutter amplitude sequence r;
(2.2)用基于K分布的雨杂波幅度分布模型KRM拟合雨杂波数据集X；(2.2) Fit the rain clutter data set X with the rain clutter amplitude distribution model KRM based on the K distribution;
(2.2.1)对雨杂波幅度序列r进行K分布的双分位点参数估计，得到基于K分布的雨杂波幅度分布模型KRM的尺度参数估计值和形状参数估计值/>(2.2.1) Estimate the biquantile point parameters of the K distribution for the rain clutter amplitude sequence r, and obtain the estimated value of the scale parameter of the rain clutter amplitude distribution model KRM based on the K distribution and shape parameter estimates />
(2.2.2)将和/>带入所述基于K分布的毫米波段雨杂波幅度分布模型KRM的概率密度函数PDF(r；KRM)，得到该模型拟合雨杂波数据集X的概率密度函数(2.2.2) will and /> Bring in the probability density function PDF(r; KRM) of the millimeter-wave band rain clutter amplitude distribution model KRM based on the K distribution, and obtain the probability density function of the model fitting rain clutter data set X
(2.2.3)对中的雨杂波幅度序列r进行积分，得到该模型拟合雨杂波数据集X的标准累积分布函数/>(2.2.3) yes Integrate the rain clutter amplitude sequence r in the model to obtain the standard cumulative distribution function of the model fitting the rain clutter data set X />
其中，Γ()为伽马函数，K1/λ()为阶数为1/λ的第二类修正Bessel函数，r表示雨杂波的幅度序列，为尺度参数估计值，表示数据集X中雨杂波的平均功率；/>为形状参数估计值，表示数据集X中雨杂波的非高斯性，/>越大表示雨杂波的非高斯性越强。Among them, Γ() is the gamma function, K1/λ () is the second kind of modified Bessel function with order 1/λ, r represents the amplitude sequence of rain clutter, is the estimated value of the scale parameter, which represents the average power of the rain clutter in the data set X; /> is the estimated value of the shape parameter, representing the non-Gaussian nature of the rain clutter in the data set X, /> The larger the value, the stronger the non-Gaussian nature of the rain clutter.
(2.3)用基于广义Pareto分布的雨杂波幅度分布模型GPRM拟合雨杂波数据集X：(2.3) Fit the rain clutter data set X with the rain clutter amplitude distribution model GPRM based on the generalized Pareto distribution:
(2.3.1)对雨杂波幅度序列r进行广义Pareto分布的双分位点参数估计，得到基于广义Pareto分布的雨杂波幅度分布模型GPRM的尺度参数估计值和形状参数估计值/>(2.3.1) Estimate the biquantile point parameters of the generalized Pareto distribution for the rain clutter amplitude sequence r, and obtain the estimated value of the scale parameter of the rain clutter amplitude distribution model GPRM based on the generalized Pareto distribution and shape parameter estimates />
(2.3.2)将和/>带入所述基于广义Pareto分布的毫米波段雨杂波幅度分布模型GPRM的概率密度函数PDF(r；GPRM)，得到该模型拟合雨杂波数据集X的概率密度函数(2.3.2) will and /> Bring in the probability density function PDF(r; GPRM) of the millimeter-wave band rain clutter amplitude distribution model GPRM based on the generalized Pareto distribution, and obtain the probability density function of the model fitting rain clutter data set X
(2.3.3)对中的雨杂波幅度序列r进行积分，得到该模型拟合雨杂波数据集X的标准累积分布函数/>(2.3.3) yes Integrate the rain clutter amplitude sequence r in the model to obtain the standard cumulative distribution function of the model fitting the rain clutter data set X />
其中，r表示雨杂波的幅度序列，为尺度参数估计值，表示数据集X中雨杂波的平均功率；/>为形状参数估计值，表示数据集X中雨杂波的非高斯性，/>越大表示雨杂波的非高斯性越强。where r represents the magnitude sequence of the rain clutter, is the estimated value of the scale parameter, which represents the average power of the rain clutter in the data set X; /> is the estimated value of the shape parameter, representing the non-Gaussian nature of the rain clutter in the data set X, /> The larger the value, the stronger the non-Gaussian nature of the rain clutter.
(2.4)用基于IGCG分布的雨杂波幅度分布模型IGRM拟合雨杂波数据集X：(2.4) Fit the rain clutter data set X with the rain clutter amplitude distribution model IGRM based on the IGCG distribution:
(2.4.1)对雨杂波幅度序列r进行IGCG分布的双分位点参数估计，得到基于IGCG分布的毫米波段雨杂波幅度分布模型IGRM的尺度参数估计值和形状参数估计值/>(2.4.1) Estimate the biquantile point parameters of the IGCG distribution for the rain clutter amplitude sequence r, and obtain the estimated value of the scale parameter of the rain clutter amplitude distribution model IGRM based on the IGCG distribution and shape parameter estimates />
(2.4.2)将和/>带入所述基于IGCG分布的毫米波段雨杂波幅度分布模型IGRM的概率密度函数PDF(r；IGRM)，得到该模型拟合雨杂波数据集X的概率密度函数(2.4.2) will and /> Bring in the probability density function PDF(r; IGRM) of the millimeter-wave band rain clutter amplitude distribution model IGRM based on the IGCG distribution, and obtain the probability density function of the model fitting rain clutter data set X
(2.4.3)对中的雨杂波幅度序列r进行积分，得到该模型拟合雨杂波数据集X的标准累积分布函数/>(2.4.3) yes Integrate the rain clutter amplitude sequence r in the model to obtain the standard cumulative distribution function of the model fitting the rain clutter data set X />
其中，r表示雨杂波的幅度序列，为尺度参数估计值，表示数据集X中雨杂波的平均功率；/>为形状参数估计值，表示数据集X中雨杂波的非高斯性，/>越大表示雨杂波的非高斯性越强。where r represents the magnitude sequence of the rain clutter, is the estimated value of the scale parameter, which represents the average power of the rain clutter in the data set X; /> is the estimated value of the shape parameter, representing the non-Gaussian nature of the rain clutter in the data set X, /> The larger the value, the stronger the non-Gaussian nature of the rain clutter.
(2.5)用基于CGLN分布的雨杂波幅度分布模型LNRM拟合雨杂波数据集X：(2.5) Fit the rain clutter data set X with the rain clutter amplitude distribution model LNRM based on the CGLN distribution:
(2.5.1)对雨杂波幅度序列r进行CGLN分布的双分位点参数估计，得到基于CGLN分布的毫米波段雨杂波幅度分布模型LNRM的尺度参数估计值和形状参数估计值/>(2.5.1) Estimate the biquantile point parameters of the CGLN distribution for the rain clutter amplitude sequence r, and obtain the estimated value of the scale parameter of the rain clutter amplitude distribution model LNRM based on the CGLN distribution and shape parameter estimates />
(2.5.2)将和/>带入所述基于CGLN分布的毫米波段雨杂波幅度分布模型LNRM的概率密度函数PDF(r；LNRM)，得到该模型拟合雨杂波数据集X的概率密度函数(2.5.2) will and /> Bring in the probability density function PDF(r; LNRM) of the millimeter-wave band rain clutter amplitude distribution model LNRM based on the CGLN distribution, and obtain the probability density function of the model fitting rain clutter data set X
(2.5.3)对中的雨杂波幅度序列r进行积分，得到该模型拟合雨杂波数据集X的标准累积分布函数/>(2.5.3) yes Integrate the rain clutter amplitude sequence r in the model to obtain the standard cumulative distribution function of the model fitting the rain clutter data set X />
其中，τ表示独立同分布随机序列，服从对数正态分布r表示雨杂波的幅度序列，/>为尺度参数估计值，表示数据集X中雨杂波的平均功率；/>为形状参数估计值，表示数据集X中雨杂波的非高斯性，/>越大表示雨杂波的非高斯性越强。Among them, τ represents an independent and identically distributed random sequence, which obeys the lognormal distribution r represents the magnitude sequence of rain clutter, /> is the estimated value of the scale parameter, which represents the average power of the rain clutter in the data set X; /> is the estimated value of the shape parameter, representing the non-Gaussian nature of the rain clutter in the data set X, /> The larger the value, the stronger the non-Gaussian nature of the rain clutter.
步骤3，分别计算四个毫米波段雨杂波幅度分布模型的KS距离和KL散度。Step 3. Calculate the KS distance and KL divergence of the four mm-wave band rain clutter amplitude distribution models respectively.
(3.1)根据步骤(2.1)得到雨杂波幅度序列r；(3.1) Obtain the rain clutter amplitude sequence r according to step (2.1);
(3.2)分别生成雨杂波幅度序列r的经验概率密度函数EPDF(r；X)和经验累积分布函数ECDF(r；X)：(3.2) Generate the empirical probability density function EPDF(r; X) and the empirical cumulative distribution function ECDF(r; X) of the rain clutter amplitude sequence r respectively:
r(n)表示升序排列的雨杂波幅度序列r的第n个元素，N表示序列r的元素数量； r(n) represents the nth element of the rain clutter amplitude sequence r arranged in ascending order, and N represents the number of elements of the sequence r;
(3.3)分别计算四个毫米波段雨杂波幅度分布模型的KS距离：KSD(X；KRM)、KSD(X；GPRM)、KSD(X；IGRM)、KSD(X；LNRM)，将任一模型的KS距离表示为KSD(X；·)，其计算公式表示如下：(3.3) Calculate the KS distances of the four millimeter-wave band rain clutter amplitude distribution models: KSD(X; KRM), KSD(X; GPRM), KSD(X; IGRM), KSD(X; LNRM), and any The KS distance of the model is expressed as KSD(X; ), and its calculation formula is expressed as follows:
其中，r(n)表示雨杂波幅度序列的第n个元素，ECDF(r(n)；X)表示数据集X的经验累积分布函数，表示雨杂波模型拟合数据集X时利用双分位点估计得到的尺度参数和形状参数，/>表示任一雨杂波模型利用参数估计值/>得到的标准累积分布函数；Wherein, r(n) represents the nth element of the rain clutter magnitude sequence, ECDF (r(n) ; X) represents the empirical cumulative distribution function of data set X, Indicates the scale parameter and shape parameter obtained by using the biquantile point estimation when the rain clutter model is fitted to the data set X, /> represents any rain clutter model using parameter estimates /> The resulting standard cumulative distribution function;
(3.4)分别计算四个模型毫米波段雨杂波幅度分布模型的KL散度：KLD(X；KRM)、KLD(X；GPRM)、KLD(X；IGRM)、KLD(X；LNRM)，将任一模型的KL散度表示为KLD(X；·)，其计算公式表示如下：(3.4) Calculate the KL divergence of the four models of millimeter-wave band rain clutter amplitude distribution models: KLD(X; KRM), KLD(X; GPRM), KLD(X; IGRM), KLD(X; LNRM), and The KL divergence of any model is expressed as KLD(X; ), and its calculation formula is expressed as follows:
其中，EPDF(r(n)；X)表示数据集X的经验概率密度函数，表示任一雨杂波模型利用参数估计值/>得到的概率密度函数。Wherein, EPDF (r(n) ; X) represents the empirical probability density function of data set X, represents any rain clutter model using parameter estimates /> The resulting probability density function.
步骤4，选择对雨杂波数据集X拟合性能最优的毫米波段雨杂波幅度分布模型。Step 4. Select the rain clutter amplitude distribution model with the best fitting performance on the rain clutter dataset X.
(4.1)利用任一毫米波段雨杂波幅度分布模型的KS距离KSD(X；·)和KL散度KLD(X；·)构建最优幅度分布模型选择测度：(4.1) Use the KS distance KSD(X; ) and KL divergence KLD(X; ) of any millimeter-wave band rain clutter amplitude distribution model to construct the optimal amplitude distribution model selection measure:
其中，ModelBest(X)表示雨杂波数据集X的最优幅度分布模型，表示使括号内数值最小时的毫米波段雨杂波幅度分布模型；Among them, ModelBest (X) represents the optimal amplitude distribution model of the rain clutter data set X, Indicates the rain clutter amplitude distribution model in the millimeter wave band when the values in brackets are minimized;
(4.2)将步骤(3.3)得到的四个KS距离和(3.4)得到的四个KL散度带入所述最优幅度分布模型选择测度ModelBest(X)，得到对该雨杂波数据集X拟合性能最优的模型，作为最终的毫米波段雨杂波幅度分布模型，完成对雨杂波模型的构建。(4.2) Bring the four KS distances that step (3.3) obtains and the four KL divergences that (3.4) obtain into the optimal amplitude distribution model selection measure ModelBest (X), obtain the rain clutter data set The model with the best fitting performance of X is used as the final millimeter-wave band rain clutter amplitude distribution model to complete the construction of the rain clutter model.
毫米波雷达在降雨环境下检测目标时，会在接收目标反射信号的同时接收到强烈的雨杂波，雨杂波的存在会干扰目标检测。利用本发明的毫米波段雨杂波幅度分布模型，可对雷达接收到的雨杂波进行拟合，得到雨杂波的非高斯特性和平均功率特性，以使用门限随雨杂波特性自适应变化的恒虚警检测器，提升降雨环境下的目标检测性能。When the millimeter-wave radar detects the target in the rainy environment, it will receive strong rain clutter while receiving the reflected signal of the target. The existence of rain clutter will interfere with the target detection. Using the rain clutter amplitude distribution model in the millimeter wave band of the present invention, the rain clutter received by the radar can be fitted, and the non-Gaussian and average power characteristics of the rain clutter can be obtained, so that the threshold can be adaptively adapted to the rain clutter characteristics. Changed constant false alarm detector to improve target detection performance in rainy environment.
本发明的效果可通过以下实验结果作进一步说明：Effect of the present invention can be further illustrated by the following experimental results:
一.实验数据：1. Experimental data:
设置毫米波雷达的载频为26.9GHz，脉冲重复频率为16000赫兹，距离分辨率1.22米，距离单元数为1024，脉冲数为160。将雷达置于楼顶，其波束指向半空。Set the carrier frequency of the millimeter-wave radar to 26.9GHz, the pulse repetition frequency to 16000 Hz, the distance resolution to 1.22 meters, the number of distance units to 1024, and the number of pulses to 160. Place the radar on the roof with its beam pointing at mid-air.
利用该毫米波雷达采集降雨强度为中到大雨的雨杂波数据，该数据近区1-300距离单元内均存在强烈的雨杂波。The millimeter-wave radar is used to collect rain clutter data with rainfall intensity ranging from moderate to heavy rain, and there are strong rain clutters in the 1-300 distance cells in the near area of the data.
二.实验内容：2. Experiment content:
从上述毫米波雷达采集的实测雨杂波数据中截取1-30距离单元内的所有脉冲作为雨杂波数据集1，该数据集中的雨杂波幅度分布特性相同。利用本发明构建的四个毫米波段雨杂波幅度分布模型分别拟合雨杂波数据集1得到概率密度曲线，并于数据集1的经验概率密度曲线进行比较，以观察四个模型的拟合效果，其中：From the measured rain clutter data collected by the above-mentioned millimeter-wave radar, all the pulses in the 1-30 range unit are intercepted as the rain clutter data set 1, and the amplitude distribution characteristics of the rain clutter in this data set are the same. Utilize the four millimeter-wave band rain clutter amplitude distribution models constructed by the present invention to respectively fit the rain clutter data set 1 to obtain a probability density curve, and compare it with the empirical probability density curve of data set 1 to observe the fitting of the four models effect, where:
基于K分布的毫米波段雨杂波幅度分布模型KRM的拟合效果如图2，The fitting effect of the rain clutter amplitude distribution model KRM based on the K distribution in the millimeter wave band is shown in Figure 2.
基于广义Pareto分布的毫米波段雨杂波幅度分布模型GPRM的拟合效果如图3，The fitting effect of the rain clutter amplitude distribution model GPRM based on the generalized Pareto distribution in the millimeter wave band is shown in Figure 3.
基于IGCG分布的毫米波段雨杂波幅度分布模型IGRM的拟合效果如图4，The fitting effect of the rain clutter amplitude distribution model IGRM based on the IGCG distribution in the millimeter wave band is shown in Figure 4.
基于CGLN分布的毫米波段雨杂波幅度分布模型LNRM的拟合效果如图5。The fitting effect of the rain clutter amplitude distribution model LNRM based on the CGLN distribution in the millimeter wave band is shown in Figure 5.
图中横轴表示雨杂波幅度，纵轴表示雨杂波幅度的概率密度，实线表示数据集1中雨杂波数据的经验概率密度曲线，虚线表示采用本发明的雨杂波模型拟合数据集1的概率密度曲线。In the figure, the horizontal axis represents the rain clutter amplitude, the vertical axis represents the probability density of the rain clutter amplitude, the solid line represents the empirical probability density curve of the rain clutter data in data set 1, and the dotted line represents the rain clutter model fitting of the present invention Probability density curve for Dataset 1.
由图2和图5可见，KRM和LNRM的概率密度曲线与经验概率密度曲线偏差较大，说明这两个模型拟合效果较差。It can be seen from Figure 2 and Figure 5 that the probability density curves of KRM and LNRM deviate greatly from the empirical probability density curves, indicating that the fitting effect of these two models is poor.
由图4可见，IGRM的概率密度曲线与经验概率密度曲线偏差较小，说明该模型的拟合效果较好；It can be seen from Figure 4 that the probability density curve of IGRM has a small deviation from the empirical probability density curve, indicating that the fitting effect of the model is better;
由图3可见，GPRM的概率密度曲线与经验概率密度曲线偏差极小，是四张图中最小的，说明该模型对数据集1的拟合效果最好。It can be seen from Figure 3 that the deviation between the probability density curve of GPRM and the empirical probability density curve is extremely small, which is the smallest among the four figures, indicating that the model has the best fitting effect on data set 1.
利用本发明构建的最优幅度分布模型选择测度，计算得到四个模型的测度数值分别是：KRM为0.0380，GPRM为0.0207，IGRM为0.0222，LNRM为0.0384，数值越小说明拟合效果越好。通过该测度选择出的拟合性能最优的模型为GPRM，该结果与通过图2、3、4、5判断出的最优模型相符。因此，对数据集1，其最终的毫米波段雨杂波幅度分布模型选定为基于广义Pareto分布的毫米波段雨杂波幅度分布模型GPRM。Using the optimal amplitude distribution model constructed by the present invention to select the measurement, the calculated measurement values of the four models are: KRM is 0.0380, GPRM is 0.0207, IGRM is 0.0222, and LNRM is 0.0384. The smaller the value, the better the fitting effect. The model with the best fitting performance selected by this measure is GPRM, and this result is consistent with the optimal model judged from Figures 2, 3, 4, and 5. Therefore, for Dataset 1, the final millimeter-wave rain clutter amplitude distribution model is selected as the millimeter-wave rain clutter amplitude distribution model GPRM based on the generalized Pareto distribution.
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