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The complex and dynamic propagation of oscillations and waves is oftentriggered by sources at unknown locations. Accurate source localization enablesthe elimination of the rotor core in atrial fibrillation (AFib) as an effectivetreatment for such severe cardiac disorder; it also finds potential use inlocating the spreading source in natural disasters such as forest fires andtsunamis. However, existing approaches such as time of arrival (TOA) and timedifference of arrival (TDOA) do not yield accurate localization results sincethey tacitly assume a constant signal propagation speed whereas realisticpropagation is often non-static and heterogeneous. In this paper, we develop anonlinear TDOA (NTDOA) approach which utilizes observational data from variouspositions to jointly learn the propagation speed at different angles anddistances as well as the location of the source itself. Through examples ofsimulating the complex dynamics of electrical signals along the surface of theheart and satellite imagery from forest fires and tsunamis, we show that with asmall handful of measurements, NTDOA, as a data-driven approach, cansuccessfully locate the spreading source, leading also to better forecasting ofthe speed and direction of subsequent propagation.

Data-Driven Nonlinear TDOA for Accurate Source Localization in Complex Signal Dynamics