基于高阶累积量的Hammerstein模型记忆效应辨识
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摘要
旨在研究存在加性高斯噪声时,Hammerstein模型的记忆效应辨识问题。在输入信号统计量和Hammer-stein模型的无记忆非线性效应均未知的情况下,利用模型输出信号的高阶累积量建立两种线性方程组,并从理论上证明了两种线性方程组均具有唯一解;提出将两个线性方程组结合使用的系数提取方法,其过程不受Hammerstein模型的无记忆非线性模块影响。最后的仿真结果表明,在高斯(有色或无色)噪声存在的情况下,此类辨识方法比直接提取参数法具有更好的数值鲁棒性。
This paper focused on memory effect identification of Hammerstein model in Gaussian noise.When input statistics and nonlinearity of Hammerstein are unknown,by using higher order cumulant of output signal,two sets linear equations were proposed to extract coefficients of linear block with memory.Theoretical derivation shows that those two sets of linear equations have unique solutions.They could be used alternately to identify the memory effect of Hammerstein model,and the identification process is not affected by memory-less nonlinear block.Finally,simulations verify that the new developments have higher performance than direct extraction method.
This paper focused on memory effect identification of Hammerstein model in Gaussian noise.When input statistics and nonlinearity of Hammerstein are unknown,by using higher order cumulant of output signal,two sets linear equations were proposed to extract coefficients of linear block with memory.Theoretical derivation shows that those two sets of linear equations have unique solutions.They could be used alternately to identify the memory effect of Hammerstein model,and the identification process is not affected by memory-less nonlinear block.Finally,simulations verify that the new developments have higher performance than direct extraction method.
引文
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[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,1996:281
[9]Giannakis G B,Mendel J M.Cumulant-based order determina-tion of non-Gaussian ARMA models[J].IEEE Trans.on Acou-si.,Speech,Signal Processing,1990,38:1411-1422
[10]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
[2]邱天爽,张旭秀,李小兵.统计信号处理[M].北京:电子工业出版社,2004:79
[3]Giannakis G B,Mendel J M.Identification of nonminimum phasesystems using higher order statistics[J].IEEE Trans.on Acou-si.,Speech,Signal Processing,1989,37:360-377
[4]Friedlande B,Porat B.Adaptive IIR algorithms based on highorder statistics[J].IEEE Trans.on Acousi.,Speech,Signal Pro-cessing,1989,37:485-485
[5]Tugnait.New results on FIR system identification using higher-order statistics[J].IEEE Trans.on Signal Processing,1991,39:2216-2221
[6]Zhang X D,Zhang Y S.FIR system identification using higherorder cumulants alone[J].IEEE Trans.on Signal Processing,1994,42(10):2854-2858
[7]Kalouptsidis N,Koukoulas P.Blind Identification of Volterra-Hammerstein Systems[J].IEEE trans on signal processing,2005,53:2777-2787
[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,1996:281
[9]Giannakis G B,Mendel J M.Cumulant-based order determina-tion of non-Gaussian ARMA models[J].IEEE Trans.on Acou-si.,Speech,Signal Processing,1990,38:1411-1422
[10]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
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