Localization via received signal strength (RSS) is often employed in cases where the received signal is fairly weak, either due to distance or due to deliberate covert operation or interference avoidance. However, most research on source localization via RSS implicitly assumes that the background noise is negligible, and that parameters of the transmitter and environment are known. Many commercial chipsets provide per-frame RSS measurements obtained when demodulating the signal, which do not include background noise; however, noise can still cause signal outages. In law enforcement, surveillance, and emergency situations, RSS may be obtained more crudely, such as by energy detection, in which case the RSS will include contributions from the background noise as well. This paper proposes new probabilistic RSS models that account for background noise in both types of RSS measurements. We also derive and evaluate maximum likelihood estimators (MLEs) for these new models, as well as for differential RSS, which has hitherto not been rigorously analyzed in the literature. Several of these MLEs are extended to estimate the transmit power and/or path loss if they are unknown. The new models are justified by extensive measured data.