This paper presents a method of nonintrusive load monitoring (NILM) for electrical systems consisting of a fixed and known set of devices. This constraint is inherently met by embedded and mobile power systems, and is also commonly satisfied in industrial settings. The proposed NILM method provides time-accurate profiles of device behavior using only probabilistic device models and system-level measurements. The full method consists of model training, construction of a system-level model, and prediction of device-level energy use. Energy use estimations are determined by maximizing the probability of the predicted behavior given the system-level measurements, and are calculated online at each sampling instant. The method is validated using test data from public databases, and its performance is assessed using standard NILM accuracy metrics. The intended application of the proposed method is to support system status assessments and to provide early indications of potential equipment damage through identification of atypical device behavior.