The method of differentiable functional in a problem of lightning discharge localization and time moment determination

Abstract

In this article, the problem of detection of lightning discharge time and location within the area of the Republic of Kazakhstan is considered. The mathematical model offered in this article is based on a method of timepoints recording by mutually spaced detectors of the network receiving and identifying radio signals, which are generated by cloud to ground lightning discharges (the TOA method − time-of-arrival). According to this method the system of the equations of model is constructed by comparison of distance from a lightning discharge point to stations with the same distance passed by a radio signal taking into account the moment of its records at stations. For solution finding the system of the equations is reducing to continuously differentiable functional with respect to geographical coordinates and the time moment of lightning discharge. The conditions which performing the reached minimum of functional with a practical accuracy provides determination of coordinates and time moment of lightning discharge are considered. The test calculations with estimated accuracy depending on an error of the time moments of lightning discharge detected at the stations are performed.