On Optimal Dimension Reduction in Least-Square System Identification

Fozunbal, Majid

HP Development Company

关键词: Dimension reduction;    echo control;    least-square methods;    manifold learning;    and regularization;   

RP-ID  :  HPL-2008-219

学科分类：计算机科学（综合）

美国|英语

来源: HP Labs

【 摘 要 】

The least-square optimization problem in multi-channel echo control is severely ill-conditioned. Methods to mitigate this problem by decorrelating input signals result in undesired audio distortion. Recently, we demonstrated this approach can be tackled by dimension reduction [1]. In this paper we extend our results by studying the trade-off between the approximation error, i.e. the error of reducing the dimension of the search space, and estimation error, i.e. the error caused by observation noise, as function of the reduction in dimension. Simple expressions are derived to determine the optimal dimension as a function of signal-tonoise ratio and condition number of the normal equations.