稀疏原子分解算法在AR模型参数估计中的应用

摘要

Aiming at the problem of AR model order and parameters estimation,a novel algorithm based on sparse representation of atomic decomposition was proposed.Firstly,an over-completed sparse dictionary was constructed according to the characteristic of the autocorrelation coefficient of AR model.Secondly,for noisy signals,this paper used the slack variables to establish a new optimization model for sparsely recovery of the characteristic polynomial roots of AR model.Finally,we converted the parameters estimation problem into the problem of best basis selection which is solved by the modified affine scaling methodology.The experiments show that our algorithm is more effective than the traditional methods in terms of the forecasting precision and robustness.%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.