Robust GNSS Positioning via Variational Bayesian Factor Graph Optimization With Dirichlet Process Mixture Models

Factor Graph Optimization (FGO) is widely used in global navigation satellite system (GNSS) positioning; however, its performance degrades severely under non-Gaussian noise induced by non-line-of-sight (NLOS) propagation and multipath interference. Conventional FGO methods rely on Gaussian assumptions, which cannot capture heavy-tailed, skewed, and multimodal noise characteristics. Existing probabilistic methods suffer from several limitations, including the lack of a unified framework for Bayesian hierarchical or infinite-mixture modeling and the neglect of heterogeneous noise and temporal correlations in abnormal GNSS measurements. To overcome these issues, this paper proposes a robust variational FGO approach for GNSS positioning that combines Dirichlet Process Mixture Models (DPMM) with variational Bayesian (VB) inference. A nonparametric infinite-mixture noise model adaptively learns the actual noise distribution without relying on predefined mixing distributions. Heterogeneous noise is explicitly characterized by mapping DPMM components to distinct satellites and measurements, while temporal constraints are introduced to capture the persistent NLOS and multipath effects. A deeply coupled VB-FGO framework facilitates joint iterative estimation of GNSS states and latent noise variables via closed-form updates compatible with state-of-the-art solvers. Experimental results obtained using both simulation data and the open-source UrbanNav dataset demonstrate that the proposed method outperforms existing robust Kalman filter and FGO-based methods in positioning accuracy under complex non-Gaussian noise conditions, thereby providing an effective framework for robust GNSS positioning in complex scenarios.