Scalable Bayesian Distributional Regression for GNSS Multipath Error Modeling with Uncertainty Quantification

Abstract Global navigation satellite system (GNSS) positioning relies on accurate stochastic models for measurement errors to provide reliable position estimates and bounds. This paper presents a novel approach for modeling errors in GNSS measurements with Bayesian distributional regression, using variational inference to scale model complexity and data set size beyond typical computational limits. This methodology is applied to an automotive data set for GNSS pseudorange (multipath) errors, targeting a Student’s t-distributed model to realistically characterize heavy-tailed data. The distribution is regressed on signal quality indicators from the GNSS receiver to segment different environmental effects on the measurements. Bayesian penalized tensor product splines are used to model nonlinear relationships based on the signal quality indicators. Detailed analyses of goodness-of-fit diagnostics show that the model is able to fit well to the data, and model uncertainty is quantified such that users may be aware of and compensate for inaccuracies in modeling.