On sound ranging in proper metric spaces

  • Sergij V. Goncharov Oles Honchar Dnipro National University
Keywords: Source localization, approximation, algorithm, proper metric space, finite-dimensional, implementation


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 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. Implementation of the proposed method in Julia language is included. 

Author Biography

Sergij V. Goncharov, Oles Honchar Dnipro National University

Faculty of Mechanics and Mathematics