摘要
本文首先给出一种从观测量中适当抽取若干样本获得线性模型中参数的稳健初始估计的新方法,其中心思想是寻求在一切线性估计中对辨识单个异常值性能优良的估计,该估计消除了杠杆点,对辨识任何位置上的异常值具有几乎同等的效率。在获得了稳健初始估计后,文中提出在递推估计过程中利用t-分布检验统计量逐个辨识线性模型中的所有异常值,最终求得线性模型中参数的极大似然估计。该方法适用于单站对空中飞行目标的一次跟踪数据处理,当数据可用一阶或二阶多项式线性模型描述时,其崩溃点δ~*=33％。该方法同时适用于低阶的稳健线性回归。
A new method of obtaining the robust initial estimation of the parameters in the linear model using several points drawn appropriately from the samples is presented in the paper.The key idea of it lies in the search for the linear estimator with excellent performance of identifying single outlier among the observations.The linear estimator is free from the average points and able to identify the outlier at any location with nearly equal efficien-cy.After obtaining the robust initial estimation the method is adopted that it identifies outliers in the linear model stepwise using t-distribution statistics in the process of recursive estimation,and a maximal likelihood estimation of the parameters in the linear model is finally obtained.The new method is suitable for engineering application as it needs less computation.The breakdown point of the robust method for the linear model of the polynomial of degree one or two is ε*=33%.
出处
《控制理论与应用》
EI
CAS
CSCD
北大核心
1992年第2期141-147,共7页
Control Theory & Applications
基金
国家自然科学基金
关键词
稳健估计
线性模型
robust estimation
average points
breakdown point
