Geometric Analysis of Observability of Target Object Shape Using Location-Unknown Distance Sensors
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.
Cite
@article{arxiv.1707.06128,
title = {Geometric Analysis of Observability of Target Object Shape Using Location-Unknown Distance Sensors},
author = {Hiroshi Saito and Hirotada Honda},
journal= {arXiv preprint arXiv:1707.06128},
year = {2017}
}
Comments
under submission