On the CRLB for source localization in a lossy environment

In this work, localization of a source within a lossy medium is considered. By a lossy medium we mean an environment where the signal power decays exponentially with distance. We assume no prior knowledge on the source location, but that the source is heard by nearby sensors when transmitting. The source position shall be estimated based on the power received by these sensors. Under these assumptions, our focus is to determine the Cramer-Rao Lower Bound (CRLB). Thus, we are not studying specific estimators, but rather the (theoretical) performance of an optimal one. We demonstrate that the CRLB greatly depends on the shadowing conditions, and also on the relative positions of the sensors and the source. This spatial variability of the CRLB is used to discuss favorable positioning of the sensors.