测量平差中不适定问题解的统一表达与选权拟合法

将测量平差中常见的几种数学模型分析比较,发现它们的解可以统一表达,形式上,都可以由吉洪诺夫正则化原理导出.在拟稳平差思想的启迪下,作者提出选权拟合法解不适定问题的思路.作者强调,解不适定问题应根据具体问题对参数作具体分析,找出合理的权阵或参数约束矩阵,利用统一的解式,可以得到符合客观实际的结果.最后介绍两个新解法算例.

Uniform Expression of Solutions of Ill-posed Problems in Surveying Adjustment and the Fitting Method by Selection of the Parameter Weights

By analysis and comparison of several mathematical models in surveying adjustment, it could be found that their solution expressions may be unified in form. The unified formula of these solutions could be derived based on the principle of Tikhonov regularization.Due to the inspiration of Quasi-Stable adjustment, the new idea is put forward by author of the paper to solve ill-posed problems, that is named "fitting method by selection of the parameter weights".It is emphasized that a specific analysis of the parameters should be performed based on the specific situation when an ill-posed problem is considered to be solved. The results in accord with objective practice will be obtained by using the uniform formula of the solutions as a reasonable weight matrix or restricted condition about the unknown parameters is constructed. In the final section of the paper, two examples are introduced to illustrate the effect of the new method.