﻿ 基于时频域联合滤波的中段群目标信号分离
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 雷达学报  2015  DOI: 10.12000/JR15008 0

### 引用本文 [复制中英文]

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He Si-san, Zhao Hui-ning, Zhang Yong-shun. Signal Separation for Target Group in Midcourse Based on Time-frequency Filtering[J]. Journal of Radars, 2015, x(x): xx-xx. DOI: 10.12000/JR15008.
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### 文章历史

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Signal Separation for Target Group in Midcourse Based on Time-frequency Filtering
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The Aerial Defence and Antimissile Institute, Air Force Engineering University, Xi'an 710051, China
Abstract: To separate the target group siganl in midcourse, a method based on time-frequency filtering is proposed in this paper. Firstly, the micro-motion period of one target is estimated based on the auto correlation method. Then, the signal is divided to several segments based on the estimated period. Also, the strong energy area in time-frequency domain for each segment signal is obtained by S-transform. The intersection of strong energy areas for different period can be seem as the support area of target. So, the signal attribute to one target can be obtained by time-frequency filtering based on the estimated support area. Simulation results verify the effectiveness of the proposed algorithm.
Key words: Ballistic missile     Target group     Signal separation     Time-frequency filtering
1 引言

2 中段群目标微动模型

 ${r_{{\rm{r}}m}}(t) = {x_{{\rm{r}}m}}\cos \left( {{{ω} _{\rm{r}}}t + {{\varphi} _{\rm{r}}}} \right) + {y_{{\rm{r}}m}}\sin \left( {{{ω} _{\rm{r}}}t + {{\varphi} _{\rm{r}}}} \right)$ (1)

 ${r_{{\rm{p}}m}}(t) = {x_{{\rm{p}}m}}\cos {β} (t) + {y_{{\rm{p}}m}}\sin {β} (t)$ (2)

 ${β} (t) = {\rm{acos}}\left( {\cos {\gamma} \cos {{\theta} _{\rm{P}}} \! + \! \sin {\gamma} \sin {{\theta} _{\rm{P}}}\cos ({{w} _{\rm{P}}}t \! + \! {{\varphi} _{\rm{P}}})} \right)$ (3)

 $s(t) = \sum\limits_{n = 1}^N {{s_n}(t)} \hspace{100pt}$ (4)
 ${s_n}(t) = \sum\limits_m^{} {{\sigma _{nm}}\exp \Bigg\{ - {\rm{j}}\frac{{4{π}{f \! _c}}}{{\rm{c}}}{r_{nm}}(t) \Bigg\}}$ (5)
${s_n}(t)$为第n个目标对应回波，${\sigma _{nm}}$为第n个目标上第m个散射中心的散射系数。

3 基于时频域滤波的群目标信号分离

3.1 微动周期估计

 $\hat T = \arg \mathop {\max }\limits_{{T_{\min }} < \tau \le {\rm{Tmax }}} \int {{\rm{s}}({\rm{t}}){{\rm{s}}^{\rm{*}}}({\rm{t + }}\tau ){\rm{dt}}}$ (6)

 $\begin{array}{l} S\left( {\tau ,f} \right) = \int\limits_{ - \infty }^\infty {s\left( t \right)\frac{{\lambda {{\left| f \right|}^p}}}{{\sqrt {2\pi } }}} \exp \left( {\frac{{ - {\lambda ^2}{f^{2p}}{{(\tau - t)}^2}}}{2}} \right)\\ \quad \quad \quad \quad \cdot \exp \left( { - {\rm{j}}2\pi ft} \right){\rm{d}}t \end{array}$ (7)

 $s\left( t \right) = \int_{ - \infty }^\infty {\left\{ {\int_{ - \infty }^\infty {S\left( {\tau ,f} \right){\rm{d}}\tau } } \right\}} \exp \left( {{\rm{j}}2π ft} \right){\rm{d}}f$ (8)

 ${h_x}(t) = \int_{ - \infty }^\infty { \biggr\{ \int_{ - \infty }^\infty {S(\tau ,f)F(\tau ,f){\rm{d}}\tau } \biggr\} } \exp ({\rm{j}}2{\rm{π }}ft){\rm{d}}f$ (9)
 $F(\tau ,f) = \left\{ {\begin{array}{*{20}{c}} \! \! {1,}\ \ {(\tau ,f) \in R}\\ \! \! {0,}\ \ {(\tau ,f) \notin R} \end{array}} \right. \hspace{95pt}$ (10)

 ${s_i}(t') = s(iT + t')\matrix{ {,\;} \cr } 0 \le t' \le T$ (11)

 ${H_{{\rm{t1}}}}(\tau ,f) = \mathop \cap \limits_i {H_{{\rm{d}}i}}(\tau ,f) \hspace{35pt}$ (12)
 ${H_{{\rm{d}}i}}(\tau ,f) = \left\{ {\begin{array}{*{20}{c}} \!\! 1 ,& {{S_i}(\tau ,f) \ge {g_i}}\\ \!\! 0 ,& {{S_i}(\tau ,f) \lt {g_{_i}}} \end{array}} \right.$ (13)

 \begin{aligned} {s_{{\rm{1}}i}}(t') = & \int_{ - \infty }^\infty {\biggr\{ \int_{ - \infty }^\infty \!\!\! {{S_i}(\tau ,f){H_{{\rm{t1}}}}(\tau ,f){\rm{d}}\tau } \biggr\} } \\ & \cdot \exp ({\rm{j}}2π ft){\rm{d}}f \end{aligned} (14)

 ${s_1}\left( t \right) = \left[{{s_{11}}\left( {t'} \right) \ {s_{12}}\left( {t'} \right) \!\!\!\! \quad \cdots } \right]$ (15)
3.3 中段群目标信号分离

(1) 设剩余信号为${s_{{\rm{res}}}}(t) = s(t)$；

(2) 针对${s_{{\rm{res}}}}(t)$，根据式(6)和式(7)估计出进动周期T

(3) 根据估计出的周期T，根据式(11)对$s(t)$进行分段，对每一段信号${s_i}(t')$进行S变换得到${S_i}(\tau ,f)$；

(4) 根据式(13)提取${S_i}(\tau ,f)$的强能量区域${H_{{\rm{d}}i}}(\tau ,f)$；根据式(12)得到目标1在时频面上所对应的支撑域${H_{{\rm{t1}}}}(\tau ,f)$；

(5) 根据式(14)得到目标i在各段对应的信号分量；进一步得到其回波信号${s_1}(t)$；

(6) sres(t)=sres(t)–s1(t)，重复步骤(2)–步骤(5)，直到从${s_{{\rm{res}}}}(t)$中提取的信号能量小于某一门限值。

4 仿真分析

 图 1 群目标回波信号 Fig.1 Radar echo of group target
 图 2 单个目标信号的时频分析结果 Fig.2 Time-frequency spectral of single target

 图 3 基于自相关处理的微动周期估计 Fig.3 Micro-motion period estimation based on autocorrelation processing
 图 4 各段回波信号S变换结果 Fig.4 S transform results of different segment data
 图 5 目标1在时频面上的支撑域 Fig.5 The support domain in time-frequency dimension of target1
 图 6 目标1在1个周期内信号的S变换结果 Fig.6 S transform results of target1’s signal during one period

 图 7 目标2信号分离结果 Fig.7 Signal separation results of target2

5 讨论

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