Hammerstein模型的记忆效应盲辨识方法
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摘要
针对未知记忆深度的Hammerstein模型,提出一种基于高阶累积量的Hammerstein模型记忆效应盲辨识方法。将Hammerstein模型中对记忆深度的确定转换为对模型输出信号高阶累积量扩展矩阵的求秩问题,给出对角元素乘积(NPODE)方法以确定记忆深度,分别比较该方法与GM直接定阶法、拐点法的鲁棒性。结合提出的记忆深度估计算法,给出线性记忆模块系数的提取方法。理论推导与仿真结果表明,线性记忆模块系数的提取过程不受无记忆非线性效应的影响。
Aiming at the Hammerstein model with unknown memory depth,this paper proposes a blind identification method of memory effect for Hammerstein model based on high cumulant.The memory depth determination is converted into finding the rank of extended matrix constructed by cumulants of system output.In order to yield the rank of cumulant matrix.It proposes Nonlinear Product Of Diagonal Entry(NPODE) method,and simulation verifies its robustness by comparing with GM method and inflexion method.Linear block coefficients extraction method is given,the theoretical derivation and simulation result indicates that the extraction process is not affected by the strength of nonlinearity of Hammerstein model.
Aiming at the Hammerstein model with unknown memory depth,this paper proposes a blind identification method of memory effect for Hammerstein model based on high cumulant.The memory depth determination is converted into finding the rank of extended matrix constructed by cumulants of system output.In order to yield the rank of cumulant matrix.It proposes Nonlinear Product Of Diagonal Entry(NPODE) method,and simulation verifies its robustness by comparing with GM method and inflexion method.Linear block coefficients extraction method is given,the theoretical derivation and simulation result indicates that the extraction process is not affected by the strength of nonlinearity of Hammerstein model.
引文
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[5]王少水,戴永寿.参数化地震子波估计模型定阶方法研究综述[J].地球物理学进展,2009,24(4):1405-1410.
[6]Koukoulas P,Kalouptsidis N.Blind Identification of Second Order Hammerstein Series[J].Signal Processing,2003,83(1):213-234.
[7]Kalouptsidis N,Koukoulas P.Blind Identification of Volterra-Hammerstein Systems[J].IEEE Trans.on Signal Processing,2005,53(8):2777-2787.
[8]张贤达.时间序列分析——高阶统计量方法[M].北京:清华大学出版社,1996.
[9]徐小平,钱富才,王峰.基于改进粒子群算法的Hammerstein模型辨识[J].计算机工程,2008,34(14):200-202.
[2]Cadzow J A.Spectral Estimation:An Over-determined Rational Model Equation Approach[J].Proceedings of the IEEE,1982,70(9):907-938.
[3]Giannakis G,Mendel J M.Cumulant-based Order Determination of Non-Gaussian ARMA Models[J].IEEE Trans.on Acousi.,Speech,Signal Processing,1990,38(5):1411-1422.
[4]Zhang Xianda,Zhang Yuansheng.Singular Value Decomposition Based MA Order Determination of Non-Gaussian ARMA Model[J].IEEE Trans.on Signal Processing,1993,41(8):2657-2664.
[5]王少水,戴永寿.参数化地震子波估计模型定阶方法研究综述[J].地球物理学进展,2009,24(4):1405-1410.
[6]Koukoulas P,Kalouptsidis N.Blind Identification of Second Order Hammerstein Series[J].Signal Processing,2003,83(1):213-234.
[7]Kalouptsidis N,Koukoulas P.Blind Identification of Volterra-Hammerstein Systems[J].IEEE Trans.on Signal Processing,2005,53(8):2777-2787.
[8]张贤达.时间序列分析——高阶统计量方法[M].北京:清华大学出版社,1996.
[9]徐小平,钱富才,王峰.基于改进粒子群算法的Hammerstein模型辨识[J].计算机工程,2008,34(14):200-202.
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