模型的稀疏选择与参数辨识及应用

基于正则化技术的稀疏成分分析方法可同时完成模型选择和参数估计功能。现分别从迭代算法的设计和对应岭估计的构造两方面切入,研究正则化函数的选取及特点,并深入分析其模型参数辨识的机理,说明正则化参数与广义岭估计的最佳岭参数的耦合性。该方法可操作性强,可保证参数迭代的收敛性,对于正则化函数的构造和参数估计的统计特性分析均有规则可循。缺项多项式和制导工具误差系数求解的数值例子表明,该方法具有有效的一体化模型选择和参数估计功能。

Integrated Sparse Model Selection and Parameter Identification with Applications

Regularizationbased Sparse Component Analysis can select sparse model and identify parameter simultaneously.This paper investigates the characters of regularization function from the design of iterative algorithm and construction of corresponding generalized ridge estimate,then analyze the principle of its parameter identification.The coupling between the regularization parameter with best ridge parameter is also demonstrated and explained.A novel regularization function is constructed,then a new principle of model selection is presented with corresponding algorithm of coefficient solution,which can guarantee the convergence of iteration.Finally,a noisy polynomial signal with missing term and an example of solving Guidance Instrumentation Systematic Error coefficients are both processed to get the coefficients by our method.Numeric results demonstrate that our method can identify the missing term and solve the coefficient accurately at the same time.