Cramer-Rao bounds for power delay profile fingerprinting based positioning

Power Delay Profile-Fingerprinting (PDP-F) allows to do positioning in multipath and even in NLOS environments. Although many algorithms for position fingerprinting have been developed, analytical investigation in this area is still not matured. In this paper, we derive Cram´er-Rao bounds (CRBs) for location dependent parameters (LDPs) when they are finite and perform local identifiability analysis under different path amplitude assumptions. We show that local identifiability of the position vector can be accomplished if a condition for the pulse shape is satisfied even with one path under the assumption that path amplitude is a genuine function of position (anisotropic path attenuation). On the other hand at least two paths are required to achieve local identifiability for a distance dependent attenuation model (isotropic path attenuation) for path amplitudes. In order to simplify the analysis we assume that pulses from different paths are nonoverlapping. Fisher Information Matrix (FIM) for LDPs and the position vector is derived to prove the statements.