This work addresses the problem of localizing an impact in a dispersive medium (waveguide) using a network of vibration sensors (accelerometers), distributed at various locations in the waveguide, measuring (and detecting the arrival of) the impact-generated seismic wave. In particular, the last part of this document focuses on the problem of localizing footsteps using underfloor accelerometers. The author believes the outcomes of this work pave the way for realizing real-time indoor occupant tracking using underfloor accelerometers; a system that is tamper-proof and non-intrusive compared to occupant tracking systems that rely on video image processing. A dispersive waveguide (e.g., a floor) causes the impact-generated wave to distort with the traveled distance and renders conventional time of flight localization methods inaccurate. Therefore, this work focuses on laying the foundation of a new alternative approach to impact localization in dispersive waveguides. In this document, localization algorithms, including wave-signal detection and signal processing, are developed utilizing the fact that the generated wave's energy is attenuated with the traveled distance. The proposed localization algorithms were evaluated using simulations and experiments of hammer impacts, in addition to occupant tracking experiments. The experiments were carried out on an instrumented floor section inside a smart building. As will be explained in this document, energy-based localization will turn out to be computationally cheap and more accurate than conventional time of flight techniques. / PHD