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arXiv · 1707.06128

Geometric Analysis of Observability of Target Object Shape Using Location-Unknown Distance Sensors

Hiroshi Saito·Hirotada Honda
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Abstract

We geometrically analyze the problem of estimating parameters related to the shape and size of a two-dimensional target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis using geometric probability, we discuss the observability of these parameters: which parameters we can estimate and what conditions are required to estimate them. For a convex target object, its size and perimeter length are observable, and other parameters are not observable. For a general polygon target object, convexity in addition to its size and perimeter length is observable. Parameters related to a concave vertex can be observable when some conditions are satisfied. We also propose a method for estimating the convexity of a target object and the perimeter length of the target object.

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Hiroshi Saito, Hirotada Honda. 2017-05-15. Geometric Analysis of Observability of Target Object Shape Using Location-Unknown Distance Sensors. https://arxiv.org/abs/1707.06128

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