初值影响下误差分配的微观结构

测量数据处理中,初值对平差结果存在很大的影响,其机理影响设计矩阵的数值特征,进而影响误差的分配结构。本文着力于大地测边控制网的模拟分析,研究初值如何影响误差分配。结果表明,在奇异的网形结构下,初值越靠近真实值,对随机误差的放大作用越大。初值对线性化误差存在影响,在图形最弱方向上,线性化误差影响最大,且误差影响随初值靠近真值而减小。平差结果是随机误差的放大倍率与线性化误差的综合作用的结果,其准确度取决于线性化误差与随机误差的平衡性。

Microcosmic structure of error distribution under the influence of initial values

In observation data processing work,the initial has considerable influence on adjustment resolution,and the numerical characteristics of the design matrix is determined by geometric property of the network and affected by the initial,and the error distribution structure is therefore affected.In this article based on the classical trilateration adjustment,microcosmic structure of error distribution was discussed in detail.Results showed that under the condition of singular network,the closer the initial value is to the true one,the more the random error is magnified.The linearization error was originated from the initial,and particularly the linearization error was most seriously influenced by the initial on the weakest direction in network,and error influence decreasing with the initial closing to the true one.The adjustment resolution was determined by the comprehensive trade-off of magnification of the random error and the linearization error,and the accuracy of the results would depend on the balance of the linearization error and the random error.