基于ICA和高阶累积量的AR序列的分解与复原

Decomposition and recovery on AR based on ICA and higher-order cumulant

本文研究由若干个非因果自回归(auto regression,AR)序列叠加产生的多道时间序列的分解与复原问题,首先从序列的独立性出发,利用序列的高阶统计信息,采用独立成分分析(independent component analysis,ICA)中的广义信息最大化(Info- max)算法寻找一可逆矩阵将混合序列进行分离,然后设计了一种基于高阶统计量的自回归模型的辨识算法,算法中将非因果AR系统看成由因果和反因果系统的极联,在每次迭代中先估计反因果AR的阶数和参数,然后再估计因果AR的阶数和参数,由选用的线性方程组保证了参数的唯一可辨识性.最后通过模拟实验验证了此方法的有效性.

The decomposition and recovery on noncausual auto regression （AR） superposition process that are contained in muhivariable time series are researched in this paper. Firstly, because of the independence of the high-or- der statistical information, it separated the mixtures by searching a reversible matrix with the ICA algorithm-extended infomax algorithm. Then designed an adaptive method to identify AR model based on higher-order cumulant. The noncausual AR system form by causal AR and anticausal AR system. In every iteration, it estimated the order and the parameters of anticausal AR, then estimated the order and the parameters of causal AR. Finally, verified the effectiveness and performance of the algorithm by the computer simulation.