条件数控制的变量中含有误差模型的正则化算法

Algorithm for regularization of EIV model based on control of condition number

针对病态变量中含有误差模型的正则化问题,该文提出应用矩阵特征值分解分析EIV模型参数估计算法具有的降正则化性质,根据条件数,给出引起其具有降正则化性质的解析式。得到的解析式表明,即使初始模型不呈现病态性,算法的降正则化性质也会导致模型在迭代过程中病态;当初始模型病态时,模型的病态性会更加严重。为顾及这两种情况对参数估值稳定性的影响,根据对模型病态性的适时判断,应用条件数控制EIV模型参数估计流程,建立一种便于程序化设计的迭代算法。结果表明,该算法能够有效降低EIV模型参数估算法的降则化性质对病态模型正则化的扰动。

To solve regularization problem of ill-posed errors-in-variables(EIV)model,this paper proposed that utilization eigenvalue decomposition to analyze descending regularization property of algorithms for errors-in-variables(EIV)model parameters estimation,based on condition number,analytic formula which could explain the reason why algorithms for EIV model had the descending regularization property was given.The analytic formula appeared that although initial model was not ill-posed,the descending regularization property of algorithms may lead model to be ill-posed in process of iteration.Moreover,while initial model was ill-posed,the ill-posed property may become more serious.To take into account that these two factors had influence on stability of parameters estimation,a new iterative algorithm which was suitable for program design was established by judging ill-posed property of model based on condition number.The results demonstrate that this algorithm was able to overcome the disturbance that descending regularization of algorithms for EIV model parameters estimation has on regularization of ill-posed model.