How to Describe Spatial Resolution: An Approach Similar to the Central Limit Theorem

Authors

Omar Ochoa, The University of Texas at El PasoFollow
Martine Ceberio, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-2010

Comments

Technical Report: UTEP-CS-10-13

Published in Applied Mathematical Sciences, 2010, Vol. 4, No. 63, pp. 3153-3160.

Abstract

For spatially distributed quantities v(x), there are two main reasons why the measured value is different from the actual value. First, the sensors are imprecise, so the measured value is slightly different from the actual one. Second, sensors have a finite {\it spatial resolution}: they do not simply measure the value at a single point, they are "blurred", i.e., affected by the values of the nearby points as well. It is known that uncertainty can be often described by the Gaussian distribution. This possibility comes from the Central Limit Theorem, according to which the sum of many independent small measurement errors has an approximately Gaussian distribution. In this paper, we show how a similar technique can be applied to spatial resolution: a combination of several independent small blurrings can be described by a Gaussian blurring function.