On sound ranging in proper metric spaces

TL;DR

This paper investigates the problem of source localization in proper metric spaces, including finite-dimensional normed spaces, proposing an iterative approximation method with arbitrary precision.

Contribution

It extends sound ranging techniques to proper metric spaces and introduces an iterative process for precise source localization.

Findings

Effective iterative approximation method for source localization

Applicable to proper metric and finite-dimensional normed spaces

Achieves arbitrary precision in localization

Abstract

We consider the sound ranging, or source localization, problem - find the source-point from the moments when the wave-sphere of linearly, with time, increasing radius reaches the sensor-points - in the proper metric spaces (any closed ball is compact) and, in particular, in the finite-dimensional normed spaces. We approximate the solution to arbitrary precision by the iterative process with the stopping criterion.