2维线元不确定性ε_σ模型误差带几何特征的代数研究

Algebraic Research on Geometrical Characteristic of Error Band for 2D Linear Segment Uncertainty ε_σ Model

对地理信息系统(GIS)中2维线元不确定性εσ模型的误差带的几何特征进行研究。运用函数单调性和极值理论,从理论上证明εσ模型的误差带的几何特征;得到线元误差带不仅具有"两端大、中间小",而且也可能具有"一端大、一端小"的几何形状;给出了误差带的最小带宽及其位置;论证了误差带的最小误差带宽的位置靠近中误差较小的一端。本研究完善了2维线元不确定性εσ模型,使其更具有严密性,同时为GIS空间数据不确定性的研究提供了新的方法。

The geometrical characteristic of error band for 2D linear segment uncertainty εσ 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 geometileal 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.