摘要
研究正则化方法在航空重力测量数据向下延拓问题中的应用。首先对这种不适定问题的线性模型,分析设计阵的复共线性结构与其对参数估计危害之间的关系,利用参数LS估计的信噪比提取各个参数是否受到复共线性严重危害的信息,从而在一定程度上揭示设计阵复共线性结构的特征。然后提出基于信噪比的正则化方法(SNR),以信噪比为依据构造正则化矩阵,以极小化均方误差为目标选取正则化参数。构造正则化矩阵无需利用附加物理或先验信息,这对于在缺乏此类信息的情况下运用正则化方法提供了新的手段。最后进行的数值试验结果表明,提出的新方法(SNR)比普通的正则化方法(OR)在滤噪保真方面表现更佳。
Regularization in airborne gravity downward to the earth surface is studied.First,the relationship between multicollinearity structure in design matrix of ill-posed linear model and its harm to the unknown parameters is analyzed.The information if the unknown parameters suffer the harm is extracted by an index called signal-to-noise ratio,which reveals multicollinearity structure to some extent.Second,regularization based on signal-to-noise ratio（SNR）is put forward.The regularization matrix is constructed according to the ratio.The regularization parameter is selected by minimization the mean squared error of roots to the solution.The regularization matrix constructed in this paper need not use additional physics or priori information,so the algorithm provided in this paper gives a new way of regularization when this kind of information is short of.At last conclusions are drawn from numerical experiments.Compared with ordinary regularization（OR）,SNR is better in noise filtering and information fidelity.
出处
《测绘学报》
EI
CSCD
北大核心
2010年第5期458-464,共7页
Acta Geodaetica et Cartographica Sinica
基金
国家自然科学基金(40974009,40474007)
河南省基础与前沿技术研究计划(082300410240)
郑州市科技计划攻关项目(0910SGYG21198)
关键词
航空重力测量
向下延拓
复共线性
信噪比
正则化方法
滤噪
信息保真度
airborne gravity measurement
downward continuation
multicollinearity
signal-to-noise ratio
regularization algorithm
noise filtering
information fidelity
作者简介
顾勇为（1965-），男，博士生，副教授，研究方向为测量误差理论和数据处理。E—mail：gyw1019@sina．com
