Data retrieval algorithms for validating the optical transient detector and the lightning imaging sensor

A linear algebraic solution is provided for the problem of retrieving the l ocation and time of occurrence of lightning ground strikes from an Advanced Lightning Direction Finder (ALDF) network. The ALDF network measures field strength, magnetic bearing, and arrival time of lightning radio emissions. Solutions for the plane (i.e., no earth curvature) are provided that imple ment all of these measurements. The accuracy of the retrieval method is tes ted using computer-simulated datasets, and the relative influence of bearin g and arrival time data on the outcome of the final solution is formally de monstrated. The algorithm is sufficiently accurate to validate NASA's Optic al Transient Detector and Lightning Imaging Sensor. A quadratic planar solu tion that is useful when only three arrival time measurements are available is also introduced. The algebra of the quadratic root results are examined in detail to clarify what portions of the analysis region lead to fundamen tal ambiguities in source location. Complex root results are shown to be as sociated with the presence of measurement errors when the lightning source lies near an outer sensor baseline of the ALDF network. For arbitrary nonco llinear network geometries and in the absence of measurement errors, it is shown that the two quadratic roots are equivalent (no source location ambig uity) on the outer sensor baselines. The accuracy of the quadratic planar m ethod is rested with computer-generated datasets, and the results are gener ally better than those obtained from the three-station linear planar method when bearing errors are about 2 degrees.