The Complete Analytical Solution of the TDOA Localization Method

Petr Hubáček; Jiří Veselý; Jana Olivová

doi:10.14429/dsj.72.16933

Petr Hubáček Department of Communication Technologies, Electronic Warfare and Radars, University of Defence in Brno, Brno - 66210, Czech Republic https://orcid.org/0000-0002-4613-3453
Jiří Veselý Department of Communication Technologies, Electronic Warfare and Radars, University of Defence in Brno, Brno - 66210, Czech Republic https://orcid.org/0000-0002-2867-1354
Jana Olivová Department of Communication Technologies, Electronic Warfare and Radars, University of Defence in Brno, Brno - 66210, Czech Republic https://orcid.org/0000-0003-4873-3070

DOI: https://doi.org/10.14429/dsj.72.16933

Keywords: Time Difference of Arrival, Localization method, Covariance matrix, Target position estimation, Electronic intelligence

Abstract

This article is focused on the analytical solution of a TDOA (Time Difference of Arrival) localization method, including analysis of accuracy and unambiguity of a target position estimation in 2D space. The method is processed under two conditions - sufficiently determined localization system and an overdetermined localization system. It is assumed that the TDOA localization system operates in a LOS (Line of Sight) situation and several time-synchronized sensors are placed arbitrarily across the area. The main contribution of the article is the complete description of the TDOA localization method in analytical form only. It means, this paper shows a geometric representation and an analytical solution of the TDOA localization technique model. In addition, analyses of unambiguity and solvability of the method algorithm are presented, together with accuracy analysis of this TDOA technique in analytical form. Finally, the description of this TDOA method is extended to an overdetermined TDOA system. This makes it possible to determine and subsequently optimize its computational complexity, for example increase its computational speed. It seems that such a description of the TDOA localization technique creates a simple and effective tool for technological implementation of this method into military localization systems.