摘要
This paper discusses the regularization solution of ill posed equation with the help of its spectral decomposition formula. It shows that regularization can filter the influence of the high frequency errors which are very sensitive to the parameters to be estimated, and gives a complete derivation of the spectral decomposition formulae of least squares adjustment, rank deficient adjustment and the regularization solution of ill posed equation. It also shows the equivalence between the trace of the mean squares error and the expectation of the secondnorm of estimated parameter’s total error.
This paper discusses the regularization solution of ill posed equation with the help of its spectral decomposition formula. It shows that regularization can filter the influence of the high frequency errors which are very sensitive to the parameters to be estimated, and gives a complete derivation of the spectral decomposition formulae of least squares adjustment, rank deficient adjustment and the regularization solution of ill posed equation. It also shows the equivalence between the trace of the mean squares error and the expectation of the secondnorm of estimated parameter's total error.
出处
《大地测量与地球动力学》
CSCD
2003年第B12期74-78,共5页
Journal of Geodesy and Geodynamics
基金
SupportedbytheNatrrionalScienceFoundations(4 0234039),OpeningLaboratoryofDynamicalGeodesy ,ChineseAcademyofScience(L21-01)andEducationDevelopmentFoundationofShanghaiCity(0 1JG0 5 0 3 48)
