New algorithm for footstep localization using seismic sensors in an indoor environment

In this study, we consider the use of seismic sensors for footstep localization in indoor environments. A popular strategy of localization is to use the measured differences in arrival times of source signals at multiple pairs of receivers. In the literature, most algorithms that are based on time differences of arrival (TDOA) assume that the propagation velocity is a constant as a function of the source position, which is valid for air propagation or even for narrow band signals. However a bounded medium such as a concrete slab (encountered in indoor environement) is usually dispersive and damped. In this study, we demonstrate that under such conditions, the concrete slab can be assimilated to a thin plate; considering a Kelvin-Voigt damping model, we introduce the notion of {\em perceived propagation velocity}, which decreases when the source-sensor distance increases. This peculiar behaviour precludes any possibility to rely on existing localization methods in indoor environment. Therefore, a new localization algorithm that is adapted to a damped and dispersive medium is proposed, using only on the sign of the measured TDOA (SO-TDOA). A simulation and some experimental results are included, to define the performance of this SO-TDOA algorithm.