Alpha稳定分布噪声下时变Hurst指数估计方法研究  

Time-varying Hurst exponent estimation in Alpha stable distribution noise environment

作　　者：盛虎 荣红佳 SHENG Hu;RONG Hongjia(School of Electrical and Information Engineering,Dalian Jiaotong University,Dalian 116028,China)

机构地区：[1]大连交通大学电气信息工程学院

出　　处：《电视技术》2019年第7期7-10,15,共5页Video Engineering

基　　金：辽宁省博士启动基金(20170520215);辽宁省教育厅自然科学研究项目(JDL2019014)

摘　　要：为了分析脉冲噪声环境下时间序列时变Hurst指数估计算法的可靠性,对Alpha稳定分布噪声下仿真随机序列的Hurst指数进行分析。本研究应用功率谱快速傅里叶变换方法仿真合成具有局部自相似特性的分数阶高斯随机序列,并叠加特征指数为1.5的Alpha稳定分布噪声,分别采用基于滑动矩形窗函数和基于滑动布莱克曼窗函数的残差方差算法分析。分析结果表明两种算法都可以有效估计时间序列时变Hurst指数,基于矩形窗函数的残差方差估计法的估计结果相对更加准确,但对脉冲噪声比较敏感;基于布莱克曼窗函数的残差方差估计法虽然准确性稍差,但是对脉冲噪声的鲁棒性更好。In order to analyze the reliability of Hurst exponential estimation algorithm for time-varying time series in impulsive noise environment, the Hurst exponent of simulated random sequence under Alpha stable distribution noise is analyzed. In this study, fractional Gauss random sequences with local self-similarity are simulated and synthesized by power spectrum fast Fourier transform method, and Alpha stable distribution noise with characteristic exponent of 1.5 is superimposed. Residual variance algorithms based on sliding rectangular window function and sliding Blackman window function are used to analyze respectively. The results show that the Hurst exponent of time-varying time series can be estimated effectively by both algorithms. The estimation results of the residual variance estimation method based on rectangular window function are relatively more accurate, but it is more sensitive to impulse noise. The residual variance estimation method based on Blackman window function is less accurate, but it has better robustness to impulse noise.

关 键 词：时变Hurst指数 ALPHA稳定分布噪声 滑动窗函数 

分 类 号：TN911.7[电子电信—通信与信息系统]