用蒙特卡洛法对附不等式约束的平差问题进行质量评价  

Quality evaluation of adjustment problem with inequality constraints using Monte Carlo method

作　　者：宋路萍 张松林 马强 

机构地区：[1]同济大学测绘与地理信息学院,上海200092 [2]中国地质大学信息工程学院,武汉430074

出　　处：《工程勘察》2018年第1期46-51,共6页Geotechnical Investigation & Surveying

基　　金：国家自然科学基金项目(41174003)

摘　　要：目前对于附不等式约束的平差问题,参数求解已经相对成熟,而质量评价的研究还在发展之中。本文基于蒙特卡洛法,利用概率统计的思想,实现了根据附不等式约束平差参数估值的后验概率密度确定置信区间,并以置信区间作为精度评价指标对不等式约束平差问题进行质量评价。讨论了多峰概率密度出现的条件以及多峰概率密度情况下置信区间的计算方法,给出了多峰概率密度情况下出现分段置信区间的临界置信水平,实现了一个对不等式约束平差问题的质量评价方法。At present, it is relatively mature to solve the adjustment problem with inequality constraints, but the research on the quality description is still under development. In this paper, based on Monte Carlo method and probability statistical theory, confidence regions of inequality constrained least squares problem can be determined according to posterior probability density function. And the confidence region is used as the index to evaluate the quality of inequality constrained adjustment problem. The condition of muhimodal densities is discussed, and in the case of multimodal densities, a method is given to determine the confidence regions. In addition, the critical confidence level is also determined, which can estimate whether it will appear in a piecewise confidence region or not. Thereby a reasonable and objective quality description for inequality constrained least squares problem is fulfilled.

关 键 词：不等式约束平差 质量评价 置信区间 多峰后验概率密度 蒙特卡洛法 

分 类 号：P207.2[天文地球—测绘科学与技术]