诊断复共线性的特征分析法及其在GEO定轨中的应用  

Characteristics Analysis Approach for Multicollinearity Diagnosis and Its Applications in Orbit Determination of GEO Satellites

作　　者：韩松辉 杜兰[3] 归庆明[2] 顾勇为[2] 马朝忠[2] 

机构地区：[1]信息工程大学地理空间信息学院,河南郑州450052 [2]信息工程大学理学院,河南郑州450001 [3]信息工程大学导航与空天目标工程学院,河南郑州450052

出　　处：《测绘学报》2013年第1期19-26,共8页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(40974009;41174005;41174025);郑州市科技计划攻关项目(0910SGYG21198);中国卫星导航学术年会青年优秀论文获奖者资助课题;信息工程大学博士研究生学位论文创新基金

摘　　要：根据复共线性本质,采用法矩阵元素绝对值的最小值为参照,给出判断"小特征值"的标准。然后利用有关矩阵特征值的Collatz包含定理,对条件数和复共线性之间的关系进行详细讨论,发现条件数大不一定存在复共线性。然后分析不存在复共线性时,条件数大对最小二乘估计(LS估计)的影响情况。判断出具体的复共线性关系后,基于有偏估计思想提出相应的双k型岭估计克服病态性的影响。最后给出线性模型和GEO定轨的仿真算例,验证改进的特征分析法、相应的双k型岭估计和本文推导的其他结论的有效性和正确性。Based on the multicollinearity nature,the standard to judge small eigenvalues is given by using the minimum absolute value of elements of normal matrix.Then,the relationship between the condition number and multicollinearity is discussed in detail through the Collatz contain theorem which is a theorem about matrix eigenvalues,and the result that large condition number is not necessarily the existence of multicollinearity is found.Next,the influence of the big condition number on LS estimator is analyzed when there does not exist multicollinearity.Determine the specific multicollinearity,the corresponding double k type ridge estimator is proposed to overcome the multicollinearity based on the thought of biased estimator.Finally,simulation cases of linear model and GEO orbit determination are given to verify the validity and correctness of the improved characteristics analysis approach,the corresponding double k type ridge estimator and the other derived conclusions.

关 键 词：复共线性 特征分析法 条件数 双k型岭估计 GEO定轨 

分 类 号：P207[天文地球—测绘科学与技术]