Wj. Koshak et Rj. Solakiewicz, ON THE RETRIEVAL OF LIGHTNING RADIO-SOURCES FROM TIME-OF-ARRIVAL DATA, JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES, 101(D21), 1996, pp. 26631-26639
We examine the problem of retrieving three-dimensional lightning locat
ions from radio frequency time-of-arrival (TOA) measurements. Arbitrar
y antenna locations are considered. By judiciously differencing measur
ements that are related to the location of the antennas and their exci
tation times, the problem is converted from the initial spherical nonl
inear form to a system of linear equations. In the linear formalism, t
he source location and time-of-occurrence is viewed geometrically as a
n intersection of hyperplanes in the four-dimensional Minkowski space
(x,y,z,t). The linear equations are solved to obtain explicit analytic
expressions for the location and time variables. Retrieval errors are
not interpreted with conventional Geometrical Dilution of Precision (
GDOP) arguments as discussed by Holmes and Reedy [1951], but with more
recent inversion analyses considered by Twomey [1977]. Measurement er
rors are propagated analytically so that the specific effect of these
errors on the solution is clarified, The sensitivity of the solution o
n the number of antennas used, antenna network geometry, source positi
on, and measurement differencing schemes are discussed in terms of the
eigenvalues of the linear system.