Statistical estimation of locations of lightning events

In this paper, a statistical approach to the retrieval of lightning locations is proposed for the first time. This novel approach views the errors of the time measurements as random variables rather than unknown numbers. The unknown location ( x , y , z ) as well as the standard deviation σ of the errors are treated as unknown parameters of a statistical model and are estimated using the maximum likelihood estimation (MLE) technique. On the basis of Monte Carlo simulations these statistical estimators are compared with the least squares estimators (LSE), as well as the solutions of the system of linear equations proposed by Koshak and Solakiewicz [1996]. Although the method is general, the Lightning Detection and Ranging (LDAR) system currently used at the Kennedy Space Center is chosen as a model for simulations. Simulations show that the MLE always gives better precision than the LSE technique. Also, it is demonstrated that if the time measurements are fairly accurate and a thunderstorm takes place in the neighborhood of the measuring sites (the distance is less than 80 km), the MLE significantly improves the accuracy of the solutions of the system of linear equations.