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We geometrically analyze the problem of estimating parameters related to theshape and size of a two-dimensional target object on the plane by usingrandomly distributed distance sensors whose locations are unknown. Based on theanalysis using geometric probability, we discuss the observability of theseparameters: which parameters we can estimate and what conditions are requiredto estimate them. For a convex target object, its size and perimeter length areobservable, and other parameters are not observable. For a general polygontarget object, convexity in addition to its size and perimeter length isobservable. Parameters related to a concave vertex can be observable when someconditions are satisfied. We also propose a method for estimating the convexityof a target object and the perimeter length of the target object.

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