摘要
从观测方程系数矩阵的谱分解着手探讨不适定方程的正则化算法。利用谱分解式阐明了正则化的主要作用是平滑对参数估值比较敏感的观测误差的高频分量 ,完整给出了最小二乘平差、秩亏平差和病态方程正则化解的谱分解公式 。
This paper discusses the regularization solution of ill posed equation with the help of its spectral decomposition formula and elucidates that regularization can smooth the influence of the high frequency errors which are very sensitive to the parameters to be estimated and completely derives out the spectral decomposition formulae of least square adjustment, rank deficient adjustment and the regularization solution of ill posed equation. It also shows the equality between the trace of the mean square error and the second norm of estimated parameter's total error.
出处
《大地测量与地球动力学》
CSCD
2002年第3期10-14,共5页
Journal of Geodesy and Geodynamics
基金
中科院动力大地测量学开放研究实验室基金资助项目
编号 :L2 1-(0 1)
上海市教育发展基金 (0 1JG0 5 0 3 48)资助
