一种改进的不适定问题奇异值分解法

¹海军工程大学导航工程系,武汉市解放大道717号430033;²海军海洋测绘研究所,天津市友谊路40号300061;³海军大连舰艇学院海测工程系,大连市解放路667号116018

基金项目: 国家863计划资助项目(2006AA06A202,2009AA121405);国家重大海洋勘测专项资助项目(4200301);国家自然科学基金资助项目(41074002)

详细信息

An Improved Singular Values Decomposition Method for Ill-Posed Problem

¹ Department of Navigation Engineering,Naval University of Engineering,717 Jiefang Avenue,Wuhan 430033,China;² Tianjin Institute of Hydrographic Surveying and Charting,40 Youyi Road,Tianjin 300061,China;³ Department of Hydrography and Cartography,Dalian Naval Academy,667 Jiefang Road,Dalian 116018,China

Funds: 国家863计划资助项目(2006AA06A202,2009AA121405);国家重大海洋勘测专项资助项目(4200301);国家自然科学基金资助项目(41074002)

摘要: 综合截断奇异值法和奇异值修正法的特点,提出了一种改进的不适定问题奇异值分解法,先用截断参数将奇异值分为相对较大的奇异值和相对较小的奇异值;再用修正参数对相对较小的奇异值进行修正,以抑制其对观测噪声的放大作用。通过位场延拓中航空重力测量数据向下延拓的仿真实验,验证了改进的奇异值分解法要优于截断奇异值法、奇异值修正法和Tikhonov正则化法。
- 不适定问题 /
- 改进的奇异值分解法 /
- GCV法
Abstract: Based on the characteristics of the truncation singular values method and the modification singular values method,an improved singular values decomposition method is designed.The basic principle of the method is synchronously using the truncation parameter and the modification parameter to deal with the singular values of the coefficient matrix.The simulational results from the downward continuation of the airborne gravity data show that the significant quality advantages of the improved singular values decomposition method.
- ill-posed problem /
- improved singular values decomposition method /
- GCV