Error Propagation in Space-time Prisms

Harvey J. Miller1, Tetsuo Kobayashi1 and Wailed Othman2
1.Department of Geography University of Utah, Salt Lake City, Utah, USA
2.Theoretical Computer Science Group, Hasselt University, Diepenbeek, Belgium
harvey.miller@geog.utah.edu; tetsuo.kobayashi@geog.utah.edu; wailed.othman@UHasslet.be

Abstract: The space-time prism demarcates all locations in space that a mobile object or person can occupy during an episode of potential or unobserved movement. The prism is a central concept in time geography as a measure of accessibility, and in mobile object databases as a measure of object location possibilities given sampling error. This paper develops an analytical approach to assessing error propagation in space- time prisms and prism-prism intersections. We analyze the geometry of the prisms to derive a core set of geometric problems involving the intersection of circles and ellipses. Analytical error propagation techniques such as the Taylor linearization method based on the first-order partial derivatives are not available since explicit functions describing the intersections and their derivatives are unwieldy. However, since we have implicit functions describing the core geometry, we modify this approach using an implicit function theorem that provides the required first-order partials without the explicit expressions.

Keywords: mobile objects, space-time prism, error propagation, implicit function theorem

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