On sound ranging in some non-proper metric spaces

Abstract

We consider the sound ranging, or source localization, problem --- find the unknown source-point from known moments when the spherical wave of linearly, with time, increasing radius reaches known sensor-points --- in some non-proper metric spaces (closed ball is not always compact). Under certain conditions we approximate the solution to arbitrary precision by the iterative processes with and without a stopping criterion. We also consider this problem in normed spaces with a strictly convex norm when the sensors are dense on the unit sphere. Appended is the implementation of the approximation algorithm in Julia language.