计算机科学 ›› 2017, Vol. 44 ›› Issue (5): 42-47.doi: 10.11896/j.issn.1002-137X.2017.05.008
姜玉洁,刘国庆,王天荆
JIANG Yu-jie, LIU Guo-qing and WANG Tian-jing
摘要： 针对自回归(Autoregressive,AR)模型阶数和系数的估计问题,提出一种基于稀疏表示的原子分解新算法。首先,根据AR模型自相关函数特征构造一个过完备稀疏字典；其次,针对含噪观测信号,通过引入松弛变量,建立关于AR模型特征根稀疏恢复的优化模型；最后, 将定阶和参数估计问题转化为求解稀疏最优基问题,并提出一种改进的变尺度变换算法来求解该优化问题。实验结果表明,无论是对模拟信号,还是真实的脑电信号,该算法在定阶和系数估计两方面均优于传统估计方法,具有更好的预测精度和鲁棒性。
| [1] XU B,CUI Y,ZHOU G Y,et al.Unsupervised Speckle Level Estimation of SAR Images Using Texture Analysis and AR Model [J].IEICE Transactions on Communications,2014,7(3):691-698. [2] ZHAO N,RICHARD Y F,SUN H J,et al.Interference alignment with delayed channel state information and dynamic AR model channel prediction in wireless networks[J].Wireless Networks,2015,1(4):1227-1242. [3] INOUSSA G,PENG H,WU J.Nonlinear time series modeling and prediction using functional weights wavelet neural network-based state-dependent AR model[J].Neurocomputing,2012,6(1):59-74. [4] CHISCI L,MAVINO A,PERFERI G,et al.Real-time epileptic seizure prediction using AR models and support vector machines [J].IEEE Transactions on Biomedical Engineering,2010,57(5):1124-1132. [5] AKAIKE H.A Bayesian analysis of the minimum AIC procedure[J].Annals of the Institute of Statistical Mathematics,1978,30(1):9-14. [6] KAY S M,MARPLE S L.Spectrum Analysis－a Modern Perspective[J].IEEE Trans on Acoustics,Speech,and Signal Processing,1981,8(4):441-445. [7] BLU T,DRAGOTTI P L,VETTERLI M,et al.Sparse sampling of signal innovations[J].Signal Processing Magazine IEEE,2008,5(2):31-40. [8] CHEN S S,DONOHO D L,SAUNDERS M A.Atomic decomposition by basis pursuit[J].SIAM Review,2001,43(1):129-159. [9] RAO B D,KREUTZ-DELGADO K.An affine scaling methodo-logy for best basis selection[J].IEEE Transactions on Signal Processing,1999,7(1):187-200. [10] 张晓峒.应用数量经济学[M].北京:机械工业出版社,2009:266-287. [11] CHENG H,LIU G Q.A Modified Affine Scaling Methodology for Non-smooth optimization[J].Numerical Mathematics A Journal of Chinese Universities,2006,8(1):20-25.(in Chinese) 程浩,刘国庆.求解一类非光滑优化问题的改进变尺度方法[J].高等学校计算数学学报,2006,8(1):20-25. [12] 解可新,韩健,林友联.最优化方法(修订版)[M].天津:天津大学出版社,2004:114-123. [13] LUENBREGER D G,YE Y Y.Linear and Nonlinear Programming[M].New York:Spinger,2008:201-212. [14] DING J D,LIU G Q.Covergence Analysis of an Affine Scaling Transformation for Best Basis Selection[J].Numerical Mathematics A Journal of Chinese Universities,2011,3(4):289-294.(in Chinese) 丁建东,刘国庆.最优基选择变尺度变换方法收敛性分析[J].高等学校计算数学学报,2011,3(4):289-294. [15] HAGER W W,ZHANG H C.An affine scaling method for optimization problems with polyhedral constraints [J].Comput Optim Appl,2014,59(1):163-183. [16] PANTULA S G,FULLER W A.A Comparison of Unit-RootTest Criteria[J].Journal of Business & Economic Statistics,1994,2(4):449-459. [17] CHEN J L,ISLAM S,BISWAS P.Nonlinear dynamics of hourly ozone concentrations:nonparametric short term prediction[J].Atmospheric Environment,1998,2(11):1839-1848. |
| No related articles found! |
|
||
首页