半参数回归分析及其在测绘数据处理中的应用

Semiparametic regression and its application in survey data processing

在测量实践和科学研究中,随机因素和确定因素往往是共同存在的。经典测量平差是建立在随机模型基础上的,即认为观测值中仅含有偶然误差,不存在具有确定性的系统误差。而实际上,系统误差的存在是客观的,如果忽略这一点,平差结果将是有偏的。为此,我们希望能在平差模型和平差过程中,对上述两种误差加以区分,以获得最优无偏估计。基于上述目的,本文从最小二乘配置的理论和模型出发,在分析、研究近年来关于统计分析和测量数据处理有关文献的基础上,引入半参数回归分析的概念,并讨论了正则化参数a对解的影响。通过模拟计算得出结论:只要正则化参数取值合适,就能得到令人满意的结果。

Stochastic factors and certain factors often coexist in survey practice and research. Conventional measurement adjustment adopts stochastic model which just treats random error including those in observation and does not treats certain systematic errors. But, in fact, systematic error surely exist in obseration, if it is ignored, the adjusted result would be biased. So we want to distinguish between the two errors including in adjustment model and adjusting procedure so as to obtain the best optional unbiasing estimates. In this paper many of involved reference information on statistic analysis and processing of observe data are analyzed and studied, the semi-parametric regression is adopted, and the effect of regularization parameter upon the solution are discussed. The result shows that if the parameters are proper then the solution will be fully satisfactory.