用混沌振子和Kalman滤波检测强分形噪声中的弱信号
Weak Signal Detection of Strong Fractional Noise Using Chaos Oscillator and Kalman Filtering
作者：苏理云(四川大学 数学学院, 四川 成都 610064)；马洪(四川大学 数学学院, 四川 成都 610064)；唐世福(四川大学 数学学院, 四川 成都 610064)
Author：(School of Mathematics, Sichuan Univ., Chengdu 610064, China)；(School of Mathematics, Sichuan Univ., Chengdu 610064, China)；(School of Mathematics, Sichuan Univ., Chengdu 610064, China)
收稿日期：2006-04-26 年卷（期）页码：2007,39(3):149-154
期刊名称：工程科学与技术
Journal Name：Advanced Engineering Sciences
关键字：分形噪声；Duffing振子；微弱信号检测；Kalman滤波
Key words：fractional noise; Duffing oscillator; weak signal detection; Kalman filter
基金项目：国家自然科学基金资助项目(10571127);教育部博士点基金资助项目(20040610004)
中文摘要
针对强分形噪声中微弱信号难于检测这一问题，提出了小波域多尺度模糊自适应Kalman滤波和Duffing振子相结合的方法。先对淹没在强分形噪声中的信号进行多尺度小波变换，根据分形噪声信号小波系数的平稳性，建立状态方程和观测方程，用模糊自适应Kalman滤波，对每一尺度估计出分形信号，然后将估计信号与观测信号作差得误差信号，把误差信号送入Duffing振子，利用Duffing振子对噪声的免疫性，来检测微弱信号。也给出了Duffing振子的免疫性一种新的统计解释。仿真实验结果表明：该方法能在低信噪比和低信干比下有效地检测出淹没在强分形噪声中的微弱谐波信号。
英文摘要
Weak signal detection of strong fractional noise was proposed using Duffing oscillator and fuzzy adaptive Kalman filter. A dynamic system was formulated based on the orthonormal wavelet decomposition coefficients of fractional noise. The noisy error signal was added into Duffing chaotic oscillator, and based on the motion transition of a chaotic system, new schemes of detecting weak sinusoidal signal berried in strong fractional noise were put forward. A new statistical understanding of immunity to noise of Duffing systems was also presented. Simulation results demonstrated the effectiveness of the proposed algorithm.
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