观测值残差和未知参数一次范数最小平差

An Adjustment Model of Minimizing the 1--Norm of Residuals and Unknowns

本文首先建立了先后对残差和未知数施加一次范数最小约束的观测值残差和未知数一次范数(以下简称L-X-1范数)最小平差模型 sum from i-1 to m |P_j V_i|+sum from j=1 to m δ|x_j|=min, V=AX-l, 0<δ《P_i,i=1,2,…,n;然后提出了可以较好地解决L^(-1)范数最小解不唯一性的L-L-1范数最小平差的平均极点解;接着讨论了一次范数最小解的精度评定问题;最后将L-X-1范数最小平差用于观测值中含粗差的变形分析,并给出了若干算例。

In this paper, an adjustment model of minimizing the 1-norm of residuals and the1-norm of unknowns (hereafter, simply called the adjustment of minimizing the L-X1-norm) is first established as follows: sum from i=1 to n (p_i|v_i|)+sum from j=1 to m(δ|x_j|)=min, V=AX-l, 0<δ?p_i,i=1,2,…,n.and then the average extreme point of the adjustment of minimizing the L-X 1-norm isdefined to solve the problem of uniqueness of the solution of minimizing the adjustmentof the L 1-norm. After that, the accuracy estimate of the adjustment of minimizing theL-X 1-norm (including the adjustment of minimizing the L 1-norm) is discussed. Fina-lly, the adjustment of minimizing the L-X 1-norm is applied to deformation analysis withmeasurements including gross errors.