Research in Graph-based Simultaneous Localization and Mapping has experienced a recent trend towards robust methods. These methods take the combinatorial aspect of data association into account by allowing decisions of the graph topology to be made during optimization. The Generalized Graph Simultaneous Localization and Mapping framework presented in this work can represent ambiguous data on both local and global scales, i.e. it can handle multiple mutually exclusive choices in registration results and potentially erroneous loop closures. This is achieved by augmenting previous work on multimodal distributions with an extended graph structure using hyperedges to encode ambiguous loop closures. The novel representation combines both hyperedges and multimodal Mixture of Gaussian constraints to represent all sources of ambiguity in Simultaneous Localization and Mapping. Furthermore, a discrete optimization stage is introduced between the Simultaneous Localization and Mapping frontend and backend to handle these ambiguities in a unified way utilizing the novel representation of Generalized Graph Simultaneous Localization and Mapping, providing a general approach to handle all forms of outliers. The novel Generalized Prefilter method optimizes among all local and global choices and generates a traditional unimodal unambiguous pose graph for subsequent continuous optimization in the backend. Systematic experiments on synthetic datasets show that the novel representation of the Generalized Graph Simultaneous Localization and Mapping framework with the Generalized Prefilter method, is significantly more robust and faster than other robust state-of-the-art methods. In addition, two experiments with real data are presented to corroborate the results observed with synthetic data. Different general strategies to construct problems from real data, utilizing the full representational power of the Generalized Graph Simultaneous Localization and Mapping framework are also illustrated in these experiments.
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