度量LS及正则解质量的信噪差异指标  

Using Index of Signal-to-Noise Difference to Measure Quality of Resolution of LS or Regularization

作　　者：顾勇为[1,2] 归庆明[2] 

机构地区：[1]信息工程大学测绘学院,河南郑州450052 [2]信息工程大学理学院,河南郑州450001

出　　处：《测绘科学技术学报》2010年第4期235-238,共4页Journal of Geomatics Science and Technology

基　　金：国家自然科学基金资助项目(40974009);河南省自然科学基金资助项目(0511010100);郑州市科技计划项目

摘　　要：不适定问题最小二乘(LS)解的质量有时很差,其主要原因之一是设计阵的病态性。正则化方法是克服该缺陷的有效方法,但要以损失一些解的精确性作为代价。不适定问题在LS解质量并不差的情况下,则没有必要采取正则化方法。于是就产生一个决策问题:即何时有必要采取正则化方法。这里提出的信噪差异指标就是一种决策指标。该指标可用于度量LS解和正则解的质量,以及正则化参数的恰当选取。数值试验验证了其有效性。When resolving ill-posed problems with least squares（LS） method,the quality of the solutions are sometimes very poor,which is due to one of the main reasons that design matrix is ill-conditioned.Regularization method is an effective method to overcome this drawback,but it need to pay cost to lose some accuracy.If the quality of LS solution to an ill-posed problem is not bad,it is no need to adopt regularization method.So there comes a decision to be made that when it is necessary to adopt regularization.An index of signal-to-noise difference was put forward to help making this decision.The index can be used to measure the effect of the resolution of LS or regularization,and to select a proper regularization parameter.Some tests have been made to verify the effectiveness.

关 键 词：信噪差异指标 正则化解 正则化参数 测量平差 复共线性 

分 类 号：P207[天文地球—测绘科学与技术]