Parameter Estimation Based on LMI with Bounded Data Uncertainties
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摘要: 对于系数矩阵 A和观测向量b 存在不确定性的情况,本文提出了一种基于线性矩阵不等式(LMI)的参数估计方法,这种方法适用于不确定性的先验界已知的情况.由此而得到的算法计算更为简单,实用并具有一般性.文中给出了计算公式的推导、解的分析,并针对几种特殊的情况进行了讨论.最后给出了仿真结果.Abstract: A class of parameter estimation problem is put forth with bounded data uncertainties, and solved it based on linear matrix inequalities (LMI). The uncertainties are expressed by a priori bounds on perturbations of coefficient matrix and its elements, which covers some situations explored in [3] and [4] and is a more general one. Thus, the proposed method, which based on LMI, is simple, practical, and general. We analyzed the solution, and discussed several special cases, such as selected columns are subject to perturbations. Simulation results give more details of the proposed method.
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[1] Golub G H, Van Loan C F. An analysis of the total least squares problem[J]. SIAM J Numer Anal, 1980, 17:883~893. [2]Huffel S Van, Vandewalle J. The total least squares problem:Computational aspects and analysis[M]. Philadelphia:SIAM,1991. [3]Ghaoui L E, Lebret H. Robust solutions to least-squares problems with uncertain data[J]. SIAM J Matrix Anal Appl, 1997, 10(4):1035~1064. [4]Chandrasekaran S, Golub G H,Gu M, et al. Parameter estimation in the presence of bounded data uncertainties[J]. SIAM J Matrix Anal Appl, 1998,11(4):235~252. -
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