The application of radio-based positioning systems is ever increasing. In light of the dissemination of the Internet of Things and location-aware communication systems, the demands on localization architectures and amount of possible use cases steadily increases. While traditional radio-based localization is performed by utilizing stationary nodes, whose positions are absolutely referenced, collaborative auto-positioning methods aim to estimate location information without any a-priori knowledge of the node distribution. The usage of auto-positioning decreases the installation efforts of localization systems and therefore allows their market-wide dissemination. Since observations and position information in this scenario are correlated, the uncertainties of all nodes need to be considered. In this paper we propose a discrete Bayesian method based on a multi-dimensional histogram filter to solve the task of robust auto-positioning, allowing to propagate historical positions and estimated position uncertainties, as well as lowering the demands on observation availability when compared to conventional closed-form approaches. The proposed method is validated utilizing different multipath-, outlier and failure-corrupted ranging measurements in a static environment, where we obtain at least 58% higher positioning accuracy compared to a baseline closed-form auto-positioning approach.