对称α稳定分布特性及其参数估计方法研究
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摘要
对称α稳定分布能较好地描述混响等非高斯对称概率密度序列特征,首先探讨并给出序列非高斯性、对称性判定方法,在此基础上,研究并比较分数低阶矩法和对数矩法两种对称α稳定分布参数估计方法,仿真及实测数据处理结果表明:对数矩法估计性能优于分数低阶矩法。
Symmetrical alpha stable distribution can describe sequence with symmetry and non-Gaussian probability density such as reverberation.The paper first discusses and gives the method of judging symmetry and non-Gaussian property of probability density.Then based on this,two parameter estimation methods for symmetrical alpha stable distribution that are fractional lower-order moment method and logarithmic moment method are studied and compared.Simulation and experimental results show that the logarithmic moment method is preferable to fractional lower-order moment method.
Symmetrical alpha stable distribution can describe sequence with symmetry and non-Gaussian probability density such as reverberation.The paper first discusses and gives the method of judging symmetry and non-Gaussian property of probability density.Then based on this,two parameter estimation methods for symmetrical alpha stable distribution that are fractional lower-order moment method and logarithmic moment method are studied and compared.Simulation and experimental results show that the logarithmic moment method is preferable to fractional lower-order moment method.
引文
[1]邱天爽,张旭秀,李小兵,等.统计信号处理:非高斯信号处理及其应用[M].北京:电子工业出版社,2004,20-100.
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[3]Rupi M,Tsakalides P,Nikias C L,et al.Robust constant modulus array based on fractional lower order statistics[C]//IEEE International Conference on Acoustics,Speech,and Signal Processing,1999,5:2945-2948.
[4]Gonzalez J G,Griffith D W,Arce G R.Zero-order statistics:a signal processing framework for very impulsive processes[J].Processings of the IEEE Signal Processing Workshop on Higher-Order Statistics,1997:254-258.
[5]Kuruoglu E E.Analytical representation for positiveα-stable densities[C]//ICASSP 2003,2003,6:729-732.
[6]Tsihrintzis G A,Nikias C L.Data-adaptive algorithms for signal detection in sub-Gussian impulsive interference[J].IEEE Transactions on Signal Processing,1997,45(7):1873-1878.
[7]Bondenschatz J S,Nikias C L.Symmetric alpha-stable filter theory[C]//IEEE Transactions on Signal Processing,1997,45(9):2301-2306.
[8]Xinyu Ma,Nikias C L.Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics[J].IEEE Transactions on Signal Processing,1996,44(11):2669-2687.
[9]Shao M,Nikias C L.Detection and adaptive estimation of stable processes with fractional lower-order moments[C]//IEEE Sixth SP Workshop on Statistical Signal and Array Processing,1992,94-97.
[10]Manolakis D G,Ingle V K,Kogon S M.Statistical and adaptive signal processing[M].Boston:McGrawHill,2000,40-80.
[11]M.Belge,E.L.Miller.A sliding window RLS-like adaptive algorithm for filtering alpha-stable noise[J].IEEE Signal Processing Letters,2000,7(4):86-89.
[12]Shao M,Nikias C L.Signal detection in impulsive noise based on stable distributions[C]//1993Conference Record of The Twenty-Seventh Asilomar Conference on Signals,Systems and Computers,1993,1:218-222.
[2]Shao M,Nikias C L.Signal processing with fractional lower order moments:stable processes and their applications[J].Proceedings of the IEEE,1993,81(7):986-1010.
[3]Rupi M,Tsakalides P,Nikias C L,et al.Robust constant modulus array based on fractional lower order statistics[C]//IEEE International Conference on Acoustics,Speech,and Signal Processing,1999,5:2945-2948.
[4]Gonzalez J G,Griffith D W,Arce G R.Zero-order statistics:a signal processing framework for very impulsive processes[J].Processings of the IEEE Signal Processing Workshop on Higher-Order Statistics,1997:254-258.
[5]Kuruoglu E E.Analytical representation for positiveα-stable densities[C]//ICASSP 2003,2003,6:729-732.
[6]Tsihrintzis G A,Nikias C L.Data-adaptive algorithms for signal detection in sub-Gussian impulsive interference[J].IEEE Transactions on Signal Processing,1997,45(7):1873-1878.
[7]Bondenschatz J S,Nikias C L.Symmetric alpha-stable filter theory[C]//IEEE Transactions on Signal Processing,1997,45(9):2301-2306.
[8]Xinyu Ma,Nikias C L.Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics[J].IEEE Transactions on Signal Processing,1996,44(11):2669-2687.
[9]Shao M,Nikias C L.Detection and adaptive estimation of stable processes with fractional lower-order moments[C]//IEEE Sixth SP Workshop on Statistical Signal and Array Processing,1992,94-97.
[10]Manolakis D G,Ingle V K,Kogon S M.Statistical and adaptive signal processing[M].Boston:McGrawHill,2000,40-80.
[11]M.Belge,E.L.Miller.A sliding window RLS-like adaptive algorithm for filtering alpha-stable noise[J].IEEE Signal Processing Letters,2000,7(4):86-89.
[12]Shao M,Nikias C L.Signal detection in impulsive noise based on stable distributions[C]//1993Conference Record of The Twenty-Seventh Asilomar Conference on Signals,Systems and Computers,1993,1:218-222.