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混沌信号协同滤波去噪算法充分利用了混沌信号的自相似结构特征，具有良好的信噪比提升性能.针对该算法的滤波参数优化问题，考虑到最优滤波参数的选取受到信号特征、采样频率和噪声水平的影响，为提高该算法的自适应性使其更符合实际应用需求，基于排列熵提出一种滤波参数自动优化准则.依据不同噪声水平的混沌信号排列熵的不同，首先选取不同滤波参数对含噪混沌信号进行去噪，然后计算各滤波参数对应重构信号的排列熵，最后通过比较各重构信号的排列熵，选取排列熵最小的重构信号对应的滤波参数为最优滤波参数，实现滤波参数的优化.分析了不同信号特征、采样频率和噪声水平情况下滤波参数的选取规律.仿真结果表明，该参数优化准则能在不同条件下对滤波参数进行有效的自动最优化，提高了混沌信号协同滤波去噪算法的自适应性.
[1] L J H, Lu J A, Chen S H 2002 The Analysis and Applications of Chaotic Time Series (Wuhan:Wuhan University Press) pp1-8 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用(武汉:武汉大学出版社)第1–8页]
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[7] Feng J C 2012 Chaotic Signals and Information Processing (Beijing:Tsinghua University Press) pp32-35 (in Chinese) [冯久超 2012 混沌信号与信息处理(北京:清华大学出版社)第32–35页]
[8] Badii R, Broggi G, Derighetti B, Ravani M 1988 Phys. Rev. Lett. 60 979
[9] Cawley R, Hsu G H 1992 Phys. Rev. A 46 3057
[10] Schreiber T, Richter M 1999 Int. J. Bifurcat. Chaos 9 2039
[11] Donoho D L 1995 IEEE Trans. Inf. Theory 41 613
[12] Han M, Liu Y H, Xi J H, Guo W 2007 IEEE Signal Process. Lett. 14 62
[13] Kopsinis Y, McLaughlin S 2009 IEEE Trans. Signal Process. 57 1351
[14] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 050201 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 050201]
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[17] Chen Y, Liu X Y, Wu Z T, Fan Y, Ren Z L, Feng J C 2017 Acta Phys. Sin. 66 210501 (in Chinese) [陈越, 刘雄英, 吴中堂, 范艺, 任子良, 冯久超 2017 物理学报 66 210501]
[18] Dabov K, Foi A, Katkovnik V, Egiazarian K 2007 IEEE Trans. Image Process. 16 2080
[19] Yadav S K, Sinha R, Bora P K 2015 IET Signal Process. 9 88
[20] Hou W, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 2663 (in Chinese) [侯威, 封国林, 董文杰, 李建平 2006 物理学报 55 2663]
[21] Sun K H, He S B, Yin L Z, A D L·Duo L K 2012 Acta Phys. Sin. 61 130507 (in Chinese) [孙克辉, 贺少波, 尹林子, 阿地力·多力坤 2012 物理学报 61 130507]
[22] Yu M Y, Sun K H, Liu W H, He S B 2018 Chaos Solitons Fractals 106 107
[23] Donoho D L, Johnstone I M 1994 Biometrika 81 425
[24] He S B, Sun K H, Wang H H 2016 Physical A 461 812
[25] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[26] Lorenz E N 1963 J. Atmos. Sci. 20 130
[27] Chen G R, Ueta T 1999 Int. J. Bifurcat. Chaos 9 1465
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[1] L J H, Lu J A, Chen S H 2002 The Analysis and Applications of Chaotic Time Series (Wuhan:Wuhan University Press) pp1-8 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用(武汉:武汉大学出版社)第1–8页]
[2] Han M, Xu M L 2013 Acta Phys. Sin. 62 120510 (in Chinese) [韩敏, 许美玲 2013 物理学报 62 120510]
[3] Sun J W, Shen Y, Yin Q, Xu C J 2013 Chaos 23 013140
[4] Li G Z, Zhang B 2017 IEEE Trans. Ind. Electron. 64 2255
[5] Peng G Y, Min F H 2017 Nonlinear Dynam. 90 1607
[6] Urbanowicz K, Hołyst J A 2003 Phys. Rev. E 67 046218
[7] Feng J C 2012 Chaotic Signals and Information Processing (Beijing:Tsinghua University Press) pp32-35 (in Chinese) [冯久超 2012 混沌信号与信息处理(北京:清华大学出版社)第32–35页]
[8] Badii R, Broggi G, Derighetti B, Ravani M 1988 Phys. Rev. Lett. 60 979
[9] Cawley R, Hsu G H 1992 Phys. Rev. A 46 3057
[10] Schreiber T, Richter M 1999 Int. J. Bifurcat. Chaos 9 2039
[11] Donoho D L 1995 IEEE Trans. Inf. Theory 41 613
[12] Han M, Liu Y H, Xi J H, Guo W 2007 IEEE Signal Process. Lett. 14 62
[13] Kopsinis Y, McLaughlin S 2009 IEEE Trans. Signal Process. 57 1351
[14] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 050201 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 050201]
[15] Tung W W, Gao J B, Hu J, Yang L 2011 Phys. Rev. E 83 046210
[16] Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Process. Lett. 17 237
[17] Chen Y, Liu X Y, Wu Z T, Fan Y, Ren Z L, Feng J C 2017 Acta Phys. Sin. 66 210501 (in Chinese) [陈越, 刘雄英, 吴中堂, 范艺, 任子良, 冯久超 2017 物理学报 66 210501]
[18] Dabov K, Foi A, Katkovnik V, Egiazarian K 2007 IEEE Trans. Image Process. 16 2080
[19] Yadav S K, Sinha R, Bora P K 2015 IET Signal Process. 9 88
[20] Hou W, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 2663 (in Chinese) [侯威, 封国林, 董文杰, 李建平 2006 物理学报 55 2663]
[21] Sun K H, He S B, Yin L Z, A D L·Duo L K 2012 Acta Phys. Sin. 61 130507 (in Chinese) [孙克辉, 贺少波, 尹林子, 阿地力·多力坤 2012 物理学报 61 130507]
[22] Yu M Y, Sun K H, Liu W H, He S B 2018 Chaos Solitons Fractals 106 107
[23] Donoho D L, Johnstone I M 1994 Biometrika 81 425
[24] He S B, Sun K H, Wang H H 2016 Physical A 461 812
[25] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[26] Lorenz E N 1963 J. Atmos. Sci. 20 130
[27] Chen G R, Ueta T 1999 Int. J. Bifurcat. Chaos 9 1465
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