Source Identification of Propagating Waves Inside a Network

The localization of short events arising within a network subsequently leading to wave propagation into it, is interest in many applications. This work extend (Caputo et al. , 2019) which demonstrated the identifiability source from two detectors $N$ nodes graph. We show that, rather than source, boundary condition identification also possible and demonstrate generalyzed unicity result. Furthermore, we algorithm proposed an arbitrary number sensors, estimate its complexity depends on sensors notation="LaTeX">$N_{s}$ time dicretisation notation="LaTeX">$N_{t}$ . Increasing increases robustness noise up cut-off being small raction cutt-off detector density for efficiency reduction practical significance. analyze discuss method sensitivity total recording notation="LaTeX">$T_{e}$ sampling frequency, signal ratio. Finally propose pre-sectorisation improve systematic exploration notation="LaTeX">$O(N)$ drop notation="LaTeX">$O(N^{3})$ cost identification. Several tests model real graphs confirm support presented results.