In many applications, sensors that map the positions of objects in unknown environments are installed on dynamic platforms. As measurements are relative to the observer's sensors, scene mapping requires accurate knowledge of the observer state. However, in practice, observer reports are subject to positioning errors. Simultaneous localization and mapping addresses the joint estimation problem of observer localization and scene mapping. State-of-the-art approaches typically use visual or optical sensors and therefore rely on static beacons in the environment to anchor the observer estimate. However, many applications involving sensors that are not conventionally used for Simultaneous Localization and Mapping (SLAM) are affected by highly dynamic scenes, such that the static world assumption is invalid. This paper proposes a novel approach for dynamic scenes, called GEneralized Motion (GEM) SLAM. Based on probability hypothesis density filters, the proposed approach probabilistically anchors the observer state by fusing observer information inferred from the scene with reports of the observer motion. This paper derives the general, theoretical framework for GEM-SLAM, and shows that it generalizes existing Probability Hypothesis Density (PHD)-based SLAM algorithms. Simulations for a model-specific realization using range-bearing sensors and multiple moving objects highlight that GEM-SLAM achieves significant improvements over three benchmark algorithms.