﻿ 多特征值分解的稀疏混沌信号盲源分离算法研究
«上一篇
 文章快速检索 高级检索

 智能系统学报  2018, Vol. 13 Issue (5): 843-847  DOI: 10.11992/tis.201703032 0

### 引用本文

ZHOU Shuanghong, WANG Lingling. Research on multi-eigenvalue decomposition blind source separation algorithm for sparse chaotic signals[J]. CAAI Transactions on Intelligent Systems, 2018, 13(5): 843-847. DOI: 10.11992/tis.201703032.

### 文章历史

Research on multi-eigenvalue decomposition blind source separation algorithm for sparse chaotic signals
ZHOU Shuanghong, WANG Lingling
College of Science, Harbin Engineering University, Harbin 150001, China
Abstract: To perform high-precision restructuring of chaotic laser-source signals that are experiencing noise interference, in this paper, we propose a blind-source-separation algorithm based on a phase-space-reconstructed chaotic stream signal. This algorithm first performs a time-delay reconstruction of the phase space of separation signals, and then treats the separation matrix as a parameter to be optimized. Then, it converts the blind source separation into an optimization problem by constructing an objective function in the phase space, and solves the optimal separation matrix using a particle swarm optimization algorithm. It then multiplies the observation data by the optimal separation matrix to reconstruct the source signals. Experimental results show that the algorithm achieves rapid convergence, and its accuracy is obviously superior to the existing independent component analysis method under various noise intensities.
Key words: chaotic signals    blind source separation    phase space    separation matrix    particle swarm optimization    multi-eigenvalue decomposition    minimum mutual information method    maximum likelihood estimation    independent component analysis

1 混沌信号的盲源分离方法

 ${x_i}(t) = \sum\limits_{j = 1}^n {{a_{ij}}{s_j}(t)}$ (1)

 ${{x}}(t) = {{As}}(t) + {{n}}(t)$ (2)

 ${{x}}(t) = {\left[ {{x_1}(t)\,\,\,{x_2}(t) \cdots {x_m}(t)} \right]^{\rm{T}}}$ (3)
 ${{s}}(t) = {\left[ {{s_1}(t)\,\,\,{s_2}(t) \cdots {s_n}(t)} \right]^{\rm{T}}}$ (4)

 Download: 图 1 混沌流信号的盲源分离模型 Fig. 1 Blind source separation model of chaotic stream signal

 $\hat{{ s}}(t) = {{Bx}}(t) = {{BAs}}(t)$ (5)

 ${{BA}} = {{\varLambda P}}$ (6)

2 基于相空间的盲源分离理论分析

 \begin{align}&{{\varsigma }}(t) = {[{{x}}(t)\,\,\,{{x}}(t + 1) \cdots {{x}}(t + d - 1)]^{\rm{T}}}\end{align} (7)

 $V_{\rm{\varsigma }}(t) = {\left\| {{{\varsigma }}(t + 1) - {{\varsigma }}(1)} \right\|^2}$ (8)

 ${P_\sigma }({\rm{\varsigma }}) = \frac{{D(V_{\rm{\varsigma }}(t))}}{{{E^2}(V_{\rm{\varsigma }}(t))}},\;\quad t = 1,2, \cdots ,\sigma$ (9)

 $\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{P_\sigma }({k_1}{{{\varsigma }}_{{1}}}+{k_2}{{{\varsigma }}_{{2}}}) < \max ({P_\sigma }({{{\varsigma }}_{{1}}}),{P_\sigma }({{{\varsigma }}_{{2}}})),\forall {k_1},{k_2} \ne 0\text{。}$

 \left\{ {\begin{aligned}& {\mathop {\max }\limits_{{{B}} \in {R^{n \times n}}} \left\{ {{P_\sigma }({{{\varsigma }}_{\hat{{ s}},1}}) + {P_\sigma }({{{\varsigma }}_{\hat{{ s}},2}})+ \cdots + {P_\sigma }({{{\varsigma }}_{\hat{{ s}},n - 1}})} \right\}\;\;\;} \\ & {E\left[ {\hat{{ s}}(t){{\hat{{ s}}}^{\rm T}}(t)} \right] = {{I}}} \end{aligned}} \right. (10)

3 盲源分离算法的过程

 ${x_i}(t) = {x_i}(t) - E\left[ {{x_i}(t)} \right],\;i = 1,2, \cdots ,n$ (11)

 ${{{B}}_{2 \times 2}} = \left[ {\begin{array}{*{20}{c}} {\cos {\theta _1}}&{ - \sin {\theta _1}} \\ {\sin {\theta _1}}&{\cos {\theta _1}} \end{array}} \right]$ (12)
 \begin{aligned}{{{B}}_{3 \times 3}} =& \left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 0&{\cos {\theta _1}}&{ - \sin {\theta _1}} \\ 0&{\sin {\theta _1}}&{\cos {\theta _1}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\cos {\theta _2}}&0&{ - \sin {\theta _2}} \\ 0&1&0 \\ {\sin {\theta _2}}&0&{\cos {\theta _2}} \end{array}} \right] \cdot \\ & \left[ {\begin{array}{*{20}{c}} {\cos {\theta _3}}&{ - \sin {\theta _3}}&0 \\ {\sin {\theta _3}}&{\cos {\theta _3}}&0 \\ 0&0&1 \end{array}} \right]\end{aligned} (13)

 $\mathop {\max \{ {P_\sigma }({{{\varsigma }}_{{{y}},1}})+{P_\sigma }({{{\varsigma }}_{{{y}},2}})+ \cdots + {P_\sigma }({{{\varsigma }}_{{{y}},n - 1}})\} },{{\theta _i} \in [0,2\text{π} ]}$ (14)

1) 观测信号 ${{x}}(t)$ 去均值；

2) 预白化观测信号 ${{x}}(t)$ ，得 ${{\tilde x}}(t)$

3) 使用 $[0,2{\text{π}}]$ 上均匀分布的随机数初始化每个粒子的初始位置；

4) 对于每个粒子，根据式(11)、(12)、(13)计算分离矩阵B，根据式(3)计算分离信号，根据式(5)实现相位空间重构；根据式(7)~(9)计算适度函数值；

5) 应用粒子群算法优化式(14)直到满足终止条件，记录优化粒子位置θopt

6) 输出重构的源信号 ${{y}}(t)$ =Bopt ${{\tilde x}}(t)$ Bopt为分离矩阵。

4 仿真实验

 \begin{align}{\rm PI} =& \frac{1}{{n(n - 1)}}\sum\limits_{i = 1}^n {\left( {\sum\limits_{j = 1}^n {\frac{{{{\left| {{g_{ij}}} \right|}^2}}}{{{{\max }_k}{{\left| {{g_{ik}}} \right|}^2}}}} } \right)} + \sum\limits_{j = 1}^n {\left( {\sum\limits_{i = 1}^n {\frac{{{{\left| {{g_{ij}}} \right|}^2}}}{{{{\max }_k}{{\left| {{g_{kj}}} \right|}^2}}}} } \right)} \end{align} (15)

 \left\{ {\begin{aligned}& {\frac{{{\rm {d}}{x}}}{{{\rm {d}}{t}}} = - y - z}\\& {\frac{{{\rm {d}}{y}}}{{{\rm {d}}{t}}} = x + {\rm{0}}{\rm{.2}}y}\\& {\frac{{{\rm {d}}{z}}}{{{\rm {d}}{t}}} = 0.2 + z\left( {x - 5} \right)}\end{aligned}} \right. (16)
 \left\{ {\begin{aligned}& {\frac{{{\rm d}{x}}}{{{\rm d}{t}}} = 16(x-y)}\\& {\frac{{{\rm d}{y}}}{{{\rm d}{t}}} =45.92x-y-xz}\\& {\frac{{{\rm d}{z}}}{{{\rm d}{t}}} = xy-4z}\end{aligned}} \right. (17)
 \left\{ {\begin{aligned}& {\frac{{{\rm d}{x}}}{{{\rm d}{t}}} = y}\\& {\frac{{{\rm d}{y}}}{{{\rm d}{t}}} =- 0.5y + x - {x^3} + 0.42\sin t}\\\end{aligned}} \right. (18)
 $x(i + 1) = x(i) + \frac{{0.2x(i - 17)}}{{1 + {x^{10}}(i - 17)}} - 0.1x(i)$ (19)
4.1 混沌流无噪声信号的盲源分离仿真结果

 Download: 图 3 无噪声条件下的收敛条件 Fig. 3 The convergence condition of the algorithm at no noise

4.2 噪声环境下混沌流信号的盲源分离仿真结果

 Download: 图 4 不同盲源分离算法在不同噪声强度下的性能 Fig. 4 The performance of blind source separation algorithm under different noise intensities
5 结束语

 [1] LIN Yancong, YANG Jiachen, LV Zhihan, et al. A self-assessment stereo capture model applicable to the internet of things[J]. Sensors, 2015, 15(8): 20925-20944. DOI:10.3390/s150820925 (0) [2] YAN Gan, LV Yuxiang, WANG Qiyin, et al. Routing algorithm based on delay rate in wireless cognitive radio network[J]. Journal of networks, 2014, 9(4): 948-955. (0) [3] WANG Ke, ZHOU X, LI Tonglin, et al. Optimizing load balancing and data-locality with data-aware scheduling[C]//IEEE International Conference on Big Data. Washington, DC, USA, 2014: 119–128. (0) [4] ZHANG Liguo, HE Binghang, SUN Jianguo, et al. Double image multi-encryption algorithm based on fractional chaotic time series[J]. Journal of computational and theoretical nanoscience, 2015, 12(11): 4980-4986. DOI:10.1166/jctn.2015.4467 (0) [5] SU Tianyun, LV Zhihan, GAO Shan, et al. 3D seabed: 3D modeling and visualization platform for the seabed[C]// Proceedings of 2014 IEEE International Conference on Multimedia and Expo Workshops. Chengdu, China, 2014: 1–6. (0) [6] GENG Yishuang, CHEN Jin, FU Ruijun, et al. Enlighten wearable physiological monitoring systems: on-body RF characteristics based human motion classification using a support vector machine[J]. IEEE transactions on mobile computing, 2016, 15(3): 656-671. DOI:10.1109/TMC.2015.2416186 (0) [7] LV Zhihan, HALAWANI A, FENG Shengzhong, et al. Multimodal hand and foot gesture interaction for handheld devices[J]. ACM transactions on multimedia computing, communications, and applications, 2014, 11(1S): Article No. 10. (0) [8] LIU Guanxiong, GENG Yishuang, PAHLAVAN K, et al. Effects of calibration RFID tags on performance of inertial navigation in indoor Environment[C]//International Conference on Computing, Networking and Communications. Garden Grove, CA, USA, 2015: 196–200. (0) [9] HE Jie, GENG Yishuang, WAN Yadong, et al. A cyber physical test-bed for virtualization of RF access environment for body sensor network[J]. IEEE sensors journal, 2013, 13(10): 3826-3836. DOI:10.1109/JSEN.2013.2271721 (0) [10] HUANG Wenhua, GENG Yishuang. Identification method of attack path based on immune intrusion detection[J]. Journal of networks, 2014, 9(4): 964-971. (0)