基于杂波拖尾分布的雷达无人机检测性能分析

doi:10.12305/j.issn.1001-506X.2024.01.13

摘要/Abstract

摘要：

固定翼无人机(unmanned aerial vehicle, UAV)给雷达低空监视提出了严峻挑战。分析雷达对固定翼UAV的检测性能, 可为雷达UAV检测能力评估和技术升级提供重要参考。本文结合雷达探测低空固定翼UAV外场实测数据, 首先分析了低空固定翼UAV雷达接收信号幅度统计分布, 采用多项式对杂波拖尾导致的虚警概率进行拟合建模; 然后, 根据虚警概率分布得到雷达检测门限; 进而根据UAV回波+杂波幅度分布理论推导得到雷达检测概率; 最后, 将理论分析性能与传统性能分析结果、雷达实际检测性能进行对比。结果表明, 采用多项式对杂波拖尾导致的虚警概率进行单独建模, 由此获得的雷达检测门限精度更高, 从而使雷达UAV检测性能分析结果较传统性能分析结果更准确。

关键词: 雷达检测, 杂波拖尾, 无人机, 性能分析, 虚警概率

Abstract:

Detection of the fixed-wing unmanned aerial vehicle (UAV) is an important issue for low-altitude radar surveillance. Analyzing the radar detection performance for fixed-wing UAV provides important reference for the evaluation and technical upgrade of radar UAV detection capability. In this paper, based on the experimental data of radar detection of low-altitude fixed-wing UAV, the statistical distribution of fixed-wing UAV radar received signal amplitude is analyzed at first. Then the false alarm probability caused by the clutter tail is modeled by polynomial. Then, according to the distribution of the tail of false alarm probability and the distribution of amplitude of UAV echo plus clutter, the detection threshold and radar detection performance are obtained by theoretical derivation. Finally, the theoretical radar detection performance is compared with traditional performance analysis results and actual radar detection performance. The comparison results show that radar detection threshold owns higher accuracy by using the polynomial to fit the tail of the false alarm probability, which makes the prediction of radar UAV detection performance has higher accuracy than the traditional methods.

Key words: radar detection, clutter tail, unmanned aerial vehicle (UAV), performance analysis, false alarm probability

中图分类号:

TN95

杨勇, 王雪松. 基于杂波拖尾分布的雷达无人机检测性能分析[J]. 系统工程与电子技术, 2023, 46(1): 113-120.

Yong YANG, Xuesong WANG. Analysis of radar detection performance for UAV based on clutter tail distribution[J]. Systems Engineering and Electronics, 2023, 46(1): 113-120.

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分布	概率密度函数	关键参数估计
瑞利分布	$ f(x)=\frac{x}{\sigma^2} \mathrm{e}^{-\frac{x^2}{2 \sigma^2}}$	$ \hat{\sigma}^2=\frac{1}{2} m(2)$
对数正态分布	$f(x)=\frac{1}{\sqrt{2 \pi \alpha^2 x^2}} \mathrm{e}^{-\frac{(\ln x-\ln \mu)^2}{2 \alpha^2}} $	$\hat{\alpha}^2=\ln \left[m(2) / m^2(1)\right], \mu=m(1) / \mathrm{e}^{\hat{\sigma}^2 / 2} $
韦布尔分布	$f(x)=\frac{c}{b^c} x^{c-1} e^{-}\left(\frac{x}{b}\right)^{c} $	$\hat{c}=\operatorname{interp}\left[\varOmega, c, m(2) / m^2(1)\right], \hat{b}=\frac{m(1)}{\varGamma\left(\frac{1}{\hat{c}}+1\right)} $
伽马分布	$ f(x)=\frac{x^{\gamma-1}}{\varGamma(\gamma) \beta^\gamma} \mathrm{e}^{-\frac{x}{\beta}}$	$ \hat{\beta}=\frac{m(2)-m^2(1)}{m(1)}, \hat{\gamma}=\frac{m(1)}{\hat{\beta}}$
K分布	$f(x)=\frac{2}{\chi \varGamma(\varsigma)}\left(\frac{x}{2 \chi}\right)^{\varsigma} K_{\varsigma-1}\left(\frac{x}{\chi}\right) $	$ \begin{array}{l}\;\;\;\;\;\;\;\varsigma=\operatorname{interp}\left(x_0, y_0, x_d\right), \chi=\sqrt{\frac{m(2)}{4 \zeta^2}} \\y_0=[0.1, 100], x_0=\frac{\varGamma\left(y_0+1\right) \varGamma\left(y_0\right)}{\varGamma^2\left(y_0+\frac{1}{2}\right) \varGamma^2\left(\frac{3}{2}\right)}\end{array}$

分布	N=50		N=100		N=500
分布	拟合度	最大拟合误差	拟合度	最大拟合误差	拟合度	最大拟合误差
瑞利分布	0.51	0.16	0.34	0.13	3e-7	0.18
对数正态分布	0.24	0.2	0.02	0.21	1e-10	0.22
韦布尔分布	0.99	0.06	0.79	0.09	3e-7	0.18
伽马分布	0.68	0.14	0.34	0.13	3e-7	0.18
K分布	0.95	0.1	0.79	0.09	3e-7	0.18

分布	N=50		N=100		N=500
分布	拟合度	最大拟合误差	拟合度	最大拟合误差	拟合度	最大拟合误差
瑞利分布	0.68	0.14	0.14	0.16	5.4e-14	0.25
对数正态分布	0.84	0.12	0.14	0.16	5.4e-14	0.25
韦布尔分布	0.99	0.08	0.68	0.1	5.4e-14	0.25
伽马分布	0.95	0.1	0.56	0.11	5.4e-14	0.25
K分布	0.99	0.08	0.68	0.1	5.4e-14	0.25

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