Subspace-Based Adaptive GMM Error Modeling for Fault-Aware Pseudorange-Based Positioning in Urban Canyons

Global navigation satellite system (GNSS) positioning is essential for achieving absolute vehicular positioning in urban scenarios; however, it suffers from limited measurement redundancy and substantial faults caused by complex urban environments. In this work, we propose the subspace-based adaptive error modeling and fault detection and exclusion (FDE) method for pseudorange-based GNSS positioning in urban canyons, which integrates the adaptive error modeling into the FDE process and the positioning-solving process. Notably, we divide the pseudorange measurement space into subspaces regarding elevation angle and carrier-to-noise ratio (C/N0), each of which maintains a Gaussian mixture model (GMM) to adaptively characterize measurement error profiles. Results show that the proposed method has the ability to detect environmental changes. In addition, the proposed method outperforms the conventional FDE method with Gaussian assumptions, reducing the mean positioning error by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$16 \,\%$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$9 \,\%$</tex-math></inline-formula> in slightly and medium urbanized datasets, respectively. The impacts of step size (elevation angle and C/N0) and time window of the proposed method are discussed through controlled experiments.