A graph-based approach to assist TDOA based localization

In multidimensional source localization based on time difference of arrival (TDOA), it is difficult to identify the direct-path TDOA among all TDOA estimates of one sensor pair and to find the corresponding TDOA values belonging to the same source among different sensor pairs. In this paper, we present a graph based approach to solve this problem. It relies on the concept of consistent graph whose sum of edge weights along all loops is zero. We introduce the concept of consistent graph and reformulate the above TDOA matching task as a synthesis of consistent graphs. We prove the feasibility of a bottom-up synthesis of consistent graphs by using fundamental loops. Finally, we present an efficient synthesis algorithm by exploiting a search in a compatibility-conflict graph. I. TDOA based localization In multidimensional source localization, one is interested to estimate the position of one or multiple sources in space from the temporal measurements of several sensors which sample the time-space wave field induced by the sources [1]. Typically, Ks sources at the positions qk ∈ R 3 transmit the source signals sk(t), 1 ≤ k ≤ Ks which induce the multidimensional wave field x(t, p) at time t and position p ∈ R3. An array of M sensors at the positions p m sample this wave field spatially and collect M sensor signals xm(t) = x(t, pm), 1 ≤ m ≤ M. In an ideal reflection-free environment, the source signal sk(t) arrives at mth sensor after a delay of tmk,0 = ‖pm −qk‖/c where c is the speed of propagation. A real environment causes Qmk additional reflections of sk(t) also arriving at mth sensor . This results in the signal model