基于分数维的地形分析在航迹规划中的应用
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摘要
论述了分形、分数维的基本概念,以及分数布朗运动的数学模型.结合实际推导了地形分数维D和方差σ值的求解方法.而后提出了航迹规划选取流程,着重研究了用分数维地形分析方法进行巡航弹航迹规划的算法流程.最后,对两幅地形图进行了实验分析.并指出分数维数D表征了局部地形粗糙的程度,其值越大,地形匹配成功率越大;方差值σ表征了地形起伏的程度,它是选择高程规划航迹的重要条件之一;信息熵表征了在某一具体方向上的地形变化情况,其值越大匹配的成功率往往也越大.
The conceptions of fractal,fractal dimension and the mathematical model of fractional Brownian motion are discussed.The methods of getting the values of fractal dimension D and variance σ are deduced,and then the flow of route planning is put forward,studying mainly the arithmetic flow of the route planning for cruise missiles with fractal dimension terrain analysis.At last,two relief maps are analyzed by experimentations.Fractal dimension D tokens the degree of roughness of part terrain,and if its value is bigger,the terrain matching rate is higher;variance σ shows the degree of terrain gurgitation,and is one of the important qualifications for route planning with elevation;information entropy indicates the terrain variety in a certain direction,and the matching rate will also be higher,if information entropy′s value is bigger.
The conceptions of fractal,fractal dimension and the mathematical model of fractional Brownian motion are discussed.The methods of getting the values of fractal dimension D and variance σ are deduced,and then the flow of route planning is put forward,studying mainly the arithmetic flow of the route planning for cruise missiles with fractal dimension terrain analysis.At last,two relief maps are analyzed by experimentations.Fractal dimension D tokens the degree of roughness of part terrain,and if its value is bigger,the terrain matching rate is higher;variance σ shows the degree of terrain gurgitation,and is one of the important qualifications for route planning with elevation;information entropy indicates the terrain variety in a certain direction,and the matching rate will also be higher,if information entropy′s value is bigger.
引文
[1] 张济忠.分形[M].北京:清华大学出版社,1995.
[2] 高安秀树.分数维[M].沈步明,常子文,译.北京:地震出版社,1994.
[3] BattyM.Thefractalnatureofgeography[J].GeographicalMagazine,1992,(5):32-36.
[4] 赵韶平.军事地理信息处理及其在精确制导武器作战中的应用研究[D].西安:西安高技术研究所,1998.
[5] 毋河海.地图信息的分形描述[J].测绘通报,2001,(2):24-26.
[6] 李栋龙,李群宏.三维Ginzburg-Landau方程的吸引子的分形结构[J].广西大学学报(自然科学版),2003,28(3):218-224.
[2] 高安秀树.分数维[M].沈步明,常子文,译.北京:地震出版社,1994.
[3] BattyM.Thefractalnatureofgeography[J].GeographicalMagazine,1992,(5):32-36.
[4] 赵韶平.军事地理信息处理及其在精确制导武器作战中的应用研究[D].西安:西安高技术研究所,1998.
[5] 毋河海.地图信息的分形描述[J].测绘通报,2001,(2):24-26.
[6] 李栋龙,李群宏.三维Ginzburg-Landau方程的吸引子的分形结构[J].广西大学学报(自然科学版),2003,28(3):218-224.
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