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

TL;DR

This paper provides a geometric analysis of how well the shape and size of a 2D target can be estimated using unknown-location distance sensors, identifying observable parameters and proposing estimation methods.

Contribution

It offers a geometric probability framework to determine parameter observability and introduces methods for estimating convexity and perimeter length of the target.

Findings

Size and perimeter are observable for convex objects.

Convexity becomes observable for general polygon targets.

Parameters related to concave vertices can be observable under certain conditions.

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.