Methodological Research on Measuring Distance Uncertainty in Two-Dimensional Space
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摘要: 距离是空间位置的函数，定量、精确地揭示空间位置不确定性向距离不确定性传递的函数关系具有重要的理论与现实意义，是测绘与地理信息领域亟待解决的重大科学问题。本文针对该问题现有解决方案的局限性，在满足与不确定点观测位置对应的实际位置在误差圆内服从完全空间随机分布的前提下，推导了二维空间中一个确定点与一个不确定点间以及两个不确定点间距离不确定性的概率分布函数和对应的概率密度函数，并利用后者研究了点位不确定性向距离不确定性传递的规律，为研究与解决距离不确定性问题开辟了新的途径。结果表明确定点与不确定点间以及两个不确定点间的距离不确定性均服从如下规律：（1）当误差圆半径（对应点位精度）与点间观测距离同时改变时，前者与后者之比与距离不确定性正相关；（2）当误差圆半径保持不变时，距离不确定性与点间观测距离负相关；（3）当点间观测距离保持不变时，距离不确定性与误差圆半径正相关。当误差圆半径与点间观测距离一致时，两个不确定点间距离的不确定性大于确定点和不确定点间距离的不确定性；当该条件不成立时，涉及不确定点数不同的距离不确定性不具可比性。Abstract: Objectives:Distances are functions of spatial positions. Precisely revealing the functional relationship which quantitatively embodies the transmission of uncertainty from spatial positions to their distance, a key scientific problem in need of being solved urgently in Geoinformatics, has important theoretical and practical significance. Methods:Aiming at the limitation of presently available solution of the above mentioned problem, under the premise of that the real position corresponding with the observed position of an uncertain point obeys the complete spatial random distribution within the error circle, this article derived the probability distribution function of distance uncertainty and the corresponding density function between a certain point and an uncertain point and between two uncertain points respectively in two-dimensional space. The latter has been employed to explore the transmission law of point uncertainty to distance uncertainty, opening up a new way for studying and solving the problem of distance uncertainty. Results:The results show that for all cases:(1) When the radius of the error circle (corresponding to the point position accuracy) and the observation distance between points change simultaneously, their ratio has a significant positive correlation with distance uncertainty. (2) When the former remains constant, the distance uncertainty has a significant negative correlation with the latter. (3) When the latter remains constant, the distance uncertainty has a significant positive correlation with the former. Conclusions:As far as distance uncertainty of cases containing an uncertain point and the one of those between two uncertain points are concerned, the latter is obviously greater than the former when the radius of the error circle and the observation distance between points are consistent for both of them. Otherwise they are not comparable.
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Key words:
- Distance /
- Uncertainty /
- Two-dimensional space /
- Point position /
- Measurement methods
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