A TDOA-based approach for locating cloud-to-ground lightning strokes, using Taylor series expansion

In this paper, an iterative solution of the time difference of arrival equations for the problem of locating cloud-to-ground (CG) lightning return strokes is presented. It is shown that the problem involves a set of nonlinear hyperbolic equations. To solve the problem, the governing equations are first linearized by expanding them via their first order Taylor series expansion around an initial value. The so-obtained equation set is then solved, using the Gaussian elimination technique. The susceptibility of the solution to a Gaussian time-measurement noise is discussed and its validity is demonstrated by locating a set of predetermined CG lightning return strokes within a geographic area