2維線元不確定性ε[sub σ]模型誤差帶幾何特征的代數研究

Abstract

對地理信息系統(GIS)中2維線元不確定性ε[sub σ]模型的誤差帶的幾何特征進行研究。運用函數單調性和極值理論,從理論上證明εσ模型的誤差帶的幾何特征;得到線元誤差帶不僅具有"兩端大、中間小",而且也可能具有"一端大、一端小"的幾何形狀;給出了誤差帶的最小帶寬及其位置;論證了誤差帶的最小誤差帶寬的位置靠近中誤差較小的一端。本研究完善了2維線元不確定性εσ模型,使其更具有嚴密性,同時為GIS空間數據不確定性的研究提供了新的方法。 The geometrical characteristic of error band for 2D linear segment uncertainty ε[sub σ] model has been studied in this paper.The monotony and extremum theory of function are applied to prove the geometrical characteristic of error band for 2D linear segment uncertainty εσ model in theory.The result shows that the error band has the geometrical shape of "larger ends and smaller middle" or "one end larger and the other smaller".The minimum width and its exact position of the error band are calculated too.It is proved that the minimum width position of the error band is near the end with the smaller mean square error.Thus,the paper perfects the 2D linear segment uncertainty εσ model in theory and makes it more scientific,and also provides a new way to study the space data uncertainty in GIS.