The TDOA system topology optimization from signal source position error estimation point of view

This article is focused on a problem of the error estimation of the radar signal source localization by the TDOA (Time Difference of Arrival) method. More precisely, it is focused on the finding and solving of an analytical equation (error equation) that describes the source position error without any mathematical simplifications and approximations. The solution of this analysis is the covariance matrix. It seems to be the desired error equation. The covariance matrix is powerful tool for solution of next problem, i.e. the main problem of this article. It is the optimization of the geometry adjustment of TDOA system (its receiving stations). The main goal of this optimization is determination of the minimal number of receiving stations and their geographical coordinates on condition of allowed source position error. The correct operation of the optimization algorithm based on the covariance matrix is shown by computer simulation on real data. The main contribution of the article is evaluation of the fully analytical error equation for the TDOA systems and evaluation of the method of optimization their geometry from the signal source localization accuracy viewpoint. Key-Words: TDOA, TOA, signal processing, localization technique, covariance matrix, hyperbolical equation.