﻿ 基于神经网络的混沌海杂波背景下信号检测技术
 舰船科学技术  2022, Vol. 44 Issue (24): 149-152    DOI: 10.3404/j.issn.1672-7649.2022.24.031 PDF

1. 广西船联网工程技术研究中心，广西 南宁 530007;
2. 广西职业师范学院，广西 南宁 530007

Signal detection technology based on neural network in chaotic sea clutter background
ZHU Jing-feng1,2
1. Guangxi Ship Networking Engineering Technology Research Center, Nanning 530007, China;
2. Guangxi Vocational Normal University, Nanning 530007, China
Abstract: The neural network technology is studied, and the neural network structure model is emphasized. The neural network model is constructed, and the learning method of neural network is proposed. The change curve of neural network model error with time is given; The chaotic characteristics of sea clutter are analyzed, and the characteristics of chaos theory are emphasized. The chaotic identification technology of sea clutter is analyzed, and the curve of false nearest neighbor ratio versus embedding dimension is given; Finally, the signal detection method in the background of chaotic sea clutter is studied, and the chaotic time series curve is given. This paper studies the signal detection technology in the background of chaotic sea clutter based on neural network, which has a positive role in promoting the development of ship signal detection technology in China.
Key words: neural network     chaotic sea clutter     signal detection
0 引　言

1 神经网络技术 1.1 神经元模型

 图 1 神经元模型 Fig. 1 Neuron model

 ${u_k} = \sum\limits_{i = 1}^m {{w_{ik}}{x_i}} \text{，}$ (1)
 ${y_k} = f\left( {{u_k} + {b_k}} \right)\text{。}$ (2)

 $v = {u_k} + {b_k}\text{。}$ (3)
 $f\left( v \right) = \left\{ {\begin{array}{*{20}{c}} {1,v \geqslant 0}，\\ {0,v \lt 0} 。\end{array}} \right.$ (4)
 ${\text{g}}\left( v \right) = \left\{ {\begin{array}{*{20}{l}} {1,v \geqslant 1}，\\ {v, - 1 \lt v \lt 1}，\\ { - 1,v \leqslant - 1} 。\end{array}} \right.$ (5)
 $h\left( v \right) = \frac{1}{{1 + {e^{ - v}}}}\text{。}$ (6)

1.2 神经网络模型及学习方法

 $radbas\left( {\left\| {dist} \right\|} \right) = {e^{ - {{\left\| {dist} \right\|}^2}}}\text{。}$ (7)

 $y = \sum\limits_{i = 1}^n {{\omega _n}\phi \left( {\left\| {X - {C_i}} \right\|} \right)} \text{。}$ (8)

 $\phi \left( {\left\| {X - {C_i}} \right\|} \right) = \exp \left( { - \frac{{{{\left\| {X - {C_i}} \right\|}^2}}}{{2\delta _i^2}}} \right)\text{。}$ (9)

 图 2 神经网络误差随时间变化 Fig. 2 The error of neural network changes with time
 $y = \sum\limits_{i = 1}^n {{\omega _i}\exp \left( { - \frac{{\left\| {{X_t} - {C_i}} \right\|}}{{2{\sigma ^2}}}} \right)} \text{，}$ (10)
 ${\delta _i} = \frac{{{C_{\max }}}}{{\sqrt {2M} }}\text{，}$ (11)
 ${\omega _i} = \exp \left( { - \frac{M}{{C_{\max }^2}}\left\| {{X_t} - {C_i}} \right\|} \right)\text{，}$ (12)
 ${C_i}\left( {n + 1} \right) = \left\{ {\begin{array}{*{20}{l}} {C_i}\left( n \right) + \eta \left[ {{X_k}\left( n \right) - {C_i}\left( n \right)} \right],&i = i\left( {{X_k}} \right)\text{，} \\ {C_i}\left( n \right),& 0 < \eta < 1 \text{。} \end{array}} \right.$ (13)
2 海杂波混沌特性分析 2.1 混沌理论定义和特征

 $\left\{ {\begin{array}{*{20}{l}} {\mathop {\lim }\limits_{n \to \infty } \sup d\left( {{f^n}\left( x \right),{f^n}\left( y \right)} \right) \gt 0,\forall x,y \in {S_0},x \ne y}，\\ {\mathop {\lim }\limits_{n \to \infty } \inf d\left( {{f^n}\left( x \right),{f^n}\left( y \right)} \right) = 0,\forall x,y \in {S_0}} ，\\ {\mathop {\lim }\limits_{n \to \infty } \sup d\left( {{f^n}\left( x \right),{f^n}\left( p \right)} \right) \gt 0,\forall x \in {S_0},\forall p \in per\left( f \right)} 。\end{array}} \right.$ (14)

2.2 海杂波混沌识别

 $D = \mathop {\lim }\limits_{r \to 0} \frac{{\log {C_n}\left( r \right)}}{{\log r}}\text{，}$ (15)

 ${C_{\text{n}}}\left( r \right) = \frac{1}{{N\left( {N - 1} \right)}}\sum\limits_{i = 1}^N {\sum\limits_{j = 1}^N {H\left( {r - \left\| {{X_i} - {X_j}} \right\|} \right)} } \text{。}$ (16)

 $y\left( i \right) = \frac{1}{{\Delta t}}\left( {In{d_j}\left( i \right)} \right)\text{。}$ (17)

 ${d_j}\left( i \right) = {C_j}{e^{{\lambda _i}\left( {i\Delta t} \right)}}\text{。}$ (18)

 $K = \sum\limits_{{\lambda _i} \gt 0} {{\lambda _i}} \text{。}$ (19)
 图 3 虚假近邻率随嵌入维数的变化曲线 Fig. 3 Curve of false nearest neighbor rate changing with embedding dimension
3 混沌海杂波下的信号检测技术

 $\varepsilon \left( n \right) = x\left( n \right) - \hat x\left( n \right)\text{，}$ (20)
 ${R_\varepsilon } = \frac{1}{N}\sum\limits_{n = 1}^N {{\varepsilon ^2}\left( n \right)} \text{，}$ (21)
 $RMSE = \sqrt {\frac{1}{N}\sum\limits_{n = 1}^N {{{\left( {x\left( n \right) - \hat x\left( n \right)} \right)}^2}} } \text{。}$ (22)

 图 4 混沌时间序列曲线 Fig. 4 Chaotic time series curve
 $\left\{ {\begin{array}{*{20}{l}} {{H_0}:x\left( n \right) = c\left( n \right)}\text{，} \\ {{H_1}:x\left( n \right) = s\left( n \right) + c\left( n \right)} \text{。} \end{array}} \right.$ (23)
4 结　语

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