﻿ 舰船RCS岸基测试与数据处理方法
 舰船科学技术  2016, Vol. 38 Issue (12): 147-150 PDF

Ship RCS shore test and data processing method
LI Yong-xin, YE Zong-min
No. 91404 Unit of PLA, Qinhuangdao 066000, China
Abstract: Aiming at the requirement of the development of weapon equipment, in this paper, the definition of the radar cross section area is defined from two aspects of electromagnetic scattering theory and radar testing, which shows that the concept of RCS is unified in the theory of electromagnetic scattering and the measurement. This paper summarizes the relative comparison method based RCS test, the shore based radar in test ship sea skimming horizontal direction required signal-to-noise radio、acquisition data volume and other requirements. The far field test conditions, specifies the most distant and recent test distance, the accuracy of the ship RCS test results. The methods and application of processing RCS mean、error、probability density and cumulative distribution function are given. Ship shore RCS test method proposed in this paper, to meet the weapons and equipment verification and testing requirements for ship RCS application in the end.
Key words: RCS     far field condition     distance selection     probability density
0 引 言

1 雷达散射截面定义

1.1 电磁散射理论定义

 $\sigma = 4\pi \mathop {\lim }\limits_{R \to \infty } {{{R}}^2}\frac{{{{\left| {{{{E}}^s}} \right|}^2}}}{{{{\left| {{{{E}}^i}} \right|}^2}}} = 4\pi \mathop {\lim }\limits_{R \to \infty } {{{R}}^2}\frac{{{{\left| {{{{H}}^s}} \right|}^2}}}{{{{\left| {{{{H}}^i}} \right|}^2}}}{\text{。}}$ (1)

1.2 雷达测试理论定义

 \begin{aligned} {{{P}}_r} = & \frac{{{{{P}}_t}{{{G}}_t}}}{{{{{L}}_t}}} \cdot \frac{1}{{4\pi {{R}}_t^2{{{L}}_{mt}}}} \cdot \sigma \cdot \frac{1}{{4\pi {{R}}_r^2{{{L}}_{mr}}}} \cdot \frac{{{{{G}}_r}{\lambda ^2}}}{{4\pi {{{L}}_r}}}\\ & \Rightarrow (\text{发射}) \cdot (\text{传播}) \cdot (\text{目标}) \cdot (\text{传播}) \cdot (\text{接收}){\text{。}} \end{aligned} (2)

 $\sigma = 4\pi \cdot \frac{{{{{P}}_r}}}{{{{\rm{A}}_r}/{{R}}_r^2}} \cdot \frac{1}{{\frac{{{{{P}}_t}{{{G}}_t}}}{{4\pi {{R}}_t^2}}}}{\text{。}}$ (3)

2 测试原理

 \begin{aligned} \sigma = & \left( {\frac{{{{{P}}_{ts}}}}{{{{{P}}_t}}}} \right)\left( {\frac{{{{{P}}_r}}}{{{{{P}}_{rs}}}}} \right){\left( {\frac{{{G}}}{{{{{G}}_s}}}} \right)^2}{\left( {\frac{\lambda }{{{\lambda _s}}}} \right)^2}{\left( {\frac{{{R}}}{{{{{R}}_s}}}} \right)^4} \times \\ & {\left( {\frac{{{{{L}}_m}}}{{{{{L}}_{ms}}}}} \right)^2}\left( {\frac{{{{{L}}_t}}}{{{{{L}}_{ts}}}}} \right)\left( {\frac{{{{{L}}_r}}}{{{{{L}}_{rs}}}}} \right)\left( {\frac{{{{{L}}_p}}}{{{{{L}}_{ps}}}}} \right){\sigma _s}{\text{。}} \end{aligned} (4)

 ${{K}} = \frac{{{{(4\pi )}^3}{{{L}}_P}{{{L}}_t}{{{L}}_r}}}{{{{{G}}^2}{\lambda ^2}}} = \frac{{\sigma {{{P}}_t}}}{{{{{P}}_r}{{{R}}^4}{{L}}_m^2}}{\text{。}}$ (5)

 $\sigma = {{K}}{{{P}}_r}{({{R}})^4}{{{L}}_m}^2/{{{P}}_t}{\text{。}}$ (6)
3 RCS 测试要求

3.1 测试所需信噪比

RCS 动态测量过程舰船与背景信号之间的关系如下式：

 ${\sigma _A} + {\sigma _B}-2\sqrt {{\sigma _A} \cdot {\sigma _B}} \leqslant \sigma \leqslant {\sigma _A} + {\sigma _B} + 2\sqrt {{\sigma _A} \cdot {\sigma _B}} {\text{。}}$ (7)

 图 1 雷达散射截面测量误差上下限与信噪比的关系 Fig. 1 The relationship between the radar cross section measurement error and the signal to noise ratio
3.2 远场测量条件

 ${{R}} \geqslant 2\frac{{{{{D}}^2}}}{\lambda }$ (8)

3.3 近场测试

 ${{{R}}_{\min }} = \frac{{720{{D}}}}{{\pi {\varphi _c}}}(1-\frac{{27}}{{\pi {\varphi _c}{{FD}}}}){\text{。}}$ (9)

3.4 测试距离选择

1）最远测试距离

 ${{{R}}_{\text{最远}}}={\rm{4}}{\rm{.12}} \times {\rm{1}}{{\rm{0}}^{\rm{3}}}\sqrt {{H}}{\text{。}}$ (10)

 ${{{R}}_{\text{最近}}} ＞ 1.5{{D}}/\theta{\text{。}}$ (11)

3.5 测量数据样本量要求

 图 2 采集脉个数与均值精度的关系 Fig. 2 Relationship between the number of pulses and the mean accuraly
4 数据处理

4.1 统计方法 4.1.1 算术平均值和标准偏差的计算

1）算术平均值

 $\bar \sigma = \frac{1}{{{N}}}\sum\limits_{i = 1}^n {{\sigma _i}} {\text{。}}$ (12)

2）标准偏差

 ${{STD}} = {\left[ {\frac{{\sum\limits_{i = 1}^N {{{({\sigma _i}-\bar \sigma )}^2}} }}{{{{N}}-1}}} \right]^{\frac{1}{2}}}{\text{。}}$ (13)

4.1.2 概率密度函数和累积分布函数

 ${{P}}({\sigma _0} \leqslant \sigma \leqslant {\sigma _0} + {\text{d}}\sigma ) = \int_{{\sigma _0}}^{{\sigma _0} + d\sigma } {PDF(\sigma ){\rm{d}}\sigma } {\text{，}}$ (14)

 ${{CDF}}(\sigma ) = \int_{-\infty }^\sigma {PDF(\sigma ){\rm{d}}\sigma } {\text{。}}$ (15)
4.1.3 百分概率与中位值

 ${{CDF}}({\sigma _x}) = \int_{-\infty }^{{\sigma _x}} {{{PDF}}(\sigma ){\text{d}}\sigma = x\% } {\text{。}}$ (16)

 $CDF({\sigma _{50}}) = \int_{-\infty }^{{\sigma _{50}}} {PDF(\sigma ){\text{d}}\sigma = 0.5} {\text{。}}$ (17)

4.2 处理方法

1）扇形区间窗口和阀值的确定

2）滑动步长

3）二次采样和移动平均

4）特征值统计

5 结 语

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