Efficient synthesis of consistent graphs and their applications in digital signal processing
In speaker localisation one records the time delay of the speech signal from the source to a microphone array. From the recorded signals one calculates the Time Differences of Arrivals (TDOA) between the different microphones, which have the special property that the sum of TDOAs along a set of neighboured microphones has to be zero.
This feature allows to abstract the problem to a graph with a set of nodes and a set of edges, where the TDOA values represent the weights on each directed edge. The task is now to find and compare algorithms for the efficient synthesis of such graphs, given a set of measured weights.