A conformal prediction-based probabilistic weighting method for GNSS NLOS mitigation in urban canyons

Abstract

In urban canyon environments, global navigation satellite system (GNSS) signals frequently suffer from building blockage and reflection, generating non-line-of-sight (NLOS) errors that significantly degrade positioning accuracy. Traditional elevation-angle and carrier-to-noise ratio (C/N0) weighting methods rely on indirect signal quality indicators, and fail to reliably identify NLOS satellites in dense urban settings; existing machine learning approaches apply classifier-derived LOS probabilities directly to satellite weighting, but these probabilities often lack accuracy in complex occlusion scenarios, allowing some NLOS satellites to retain excessively high weights. To address these limitations, this paper proposes conformal prediction (CP)-single point positioning (SPP), which integrates CP into GNSS satellite weighting. Using a gradient boosting decision tree as the base classifier, we construct a ten-dimensional feature vector from C/N0, elevation angle, pseudorange residuals, and related observables. Conformal p-values are computed for each satellite based on an LOS calibration set—lower values indicating higher NLOS likelihood—and mapped to continuous weights via an exponential function, effectively down-weighting NLOS satellites while preserving LOS satellite weights; all satellites are retained to maintain geometric strength. Evaluated on the Hong Kong UrbanNav dataset with 10% labeled target-domain samples, CP-SPP achieves a horizontal positioning RMSE of 10.74 m and a CEP of 4.77 m, representing improvements of 30.8% and 53.2% over traditional elevation-angle weighting and 14.6% and 27.8% over machine learning probability weighting. The CP framework attains a 97.1% LOS/NLOS prediction-set coverage rate (exceeding the 90% nominal target), with 90.0% of satellites receiving singleton LOS or NLOS prediction sets, demonstrating that CP offers a promising approach for reliable GNSS single-point positioning in complex urban environments.