Passive location and tracking of radio emitters is of great research value in civilian and defense applications. Among the existing methods, localization based on received signal strength indicator (RSSI) has been widely used due to its advantages in terms of low cost and easy implementation. However, most RSSI-based localization methods rely on the assumption that the emitter has been detected. Moreover, the emitter signal is supposed to propagate with the simplified path-loss model in which the shadow effects caused by obstacles are not considered. As a result, there are still gaps between the aforementioned methods and practical applications. In this paper, we consider the combined path-loss and shadowing model, which has been empirically confirmed in both outdoor and indoor radio propagation environments. Joint detection and tracking of an emitter is proposed by modeling the state of the emitter as Bernoulli random finite set, characterized by an existence probability and a spatial probability density function. Compared to existing studies, this paper works upon more practically appealing signal propagation model, and achieves better performance in real-time emitter detection and tracking. Moreover, the proposed method also provides explicit estimates of the unknown shadowing-related parameters, which can be adopted in further applications such as spectrum cartography and radio map construction. The feasibility of the proposed method is assessed via simulation experiments.