摘要
针对传统格网DEM插值数学模型在解算权系数时存在负权现象的问题,提出了解算DEM插值权系数的最大熵模型算法。首先,以熵函数作为目标函数,以参考点数据的0、1、2阶统计矩作为约束条件,并增设非负约束条件,通过最大化熵值来求解格网DEM插值的非负权系数;其次,利用罚函数法,将有约束问题转化为无约束问题,并结合遗传算法的全局最优化特性进行优化解算。在MATLAB平台编程验证算法的正确性、准确性,并与杨赤中法、二次规划法进行了比较。对比显示:最大熵法解得权系数大小比例与点位关系相适应,且其估值精度优于杨赤中法、二次规划法。
This paper carried on the problem to negative-weight in traditional interpolation of gridding DEM,Put forward a new algorithm of maximum entropy model.In the first place,entropy function is added as objective function,and nonnegative,0,1,2 order＇s statistical moment was added as constraint.Nonnegative-weight of interpolation of gridding DEM was solved by Maximum Entropy.Secondly,constraint optimization is transformed to nonconstraint optimization with the help ofthe penalty function method,it was calculated uniting genetic algorithm character of global optimum.The correctness and accuracy of the algorithm were checked in matlab＇s programming,and it was compared with the method of Yang Chizhong interpolation and quadratic program.Comparison shows that the volume and scaling of Maximum Entropy＇s weight was fit to relation of space and its accuracy was superior to The latter two.
出处
《测绘科学》
CSCD
北大核心
2017年第1期25-28,共4页
Science of Surveying and Mapping
基金
国家自然科学基金项目(41161072)
广西空间信息与测绘重点实验室资助课题(桂科能1207115-08)
关键词
杨赤中插值
负权
最大熵法
约束条件
遗传算法
Yang Chizhong interpolation
negative-weight
maximum entropy
constraint condition
genetic algorithm
