Stochastic Modeling and Quantification of Multipath Error in Static GNSS Observations using rtklib

This study presents the stochastic modeling and quantification of multipath error in static Global Navigation Satellite System (GNSS) observations processed using RTKLIB. Multipath remains a major source of positioning inaccuracy, particularly in obstructed environments. The research statistically characterizes multipath and evaluates its contribution to overall observation uncertainty through a data-driven modeling approach. Static GNSS data were collected under two contrasting conditions: an open-sky environment and a multipath-prone site, using Tersus GNSS receivers. Pseudorange residuals, satellite elevation angles, and carrier-to-noise ratios (C/N₀) were extracted from RTKLIB output files and filtered using a Python-based parser to ensure consistency. The cleaned datasets were then used to develop a stochastic model expressing observation variance as a function of satellite elevation and signal strength. Parameter estimation was carried out using least squares and non-negative least squares (NNLS) regression to ensure physically meaningful variance predictions. Results from the open-sky dataset revealed a baseline variance (σ₀²) of 0.000000 m² and an elevation-dependent coefficient of a₁ = 1.6456, indicating stable and low-noise observations. In contrast, the multipath-prone site exhibited a substantially larger baseline variance (σ₀² = 142.97 m²) and stronger elevation and signal-strength dependency, with coefficients of a₁ = 10.063 and a₂ = 4.79 × 10⁸, reflecting severe distortion caused by signal reflections. Approximately 25% of the pseudorange variance in open-sky conditions was explained by satellite elevation and C/N₀, while slightly lower explanatory power was observed in the multipath environment due to irregular signal reflections. Multipath variances exhibited heavy-tailed distributions, with 95th-percentile values reaching 2,726 m² (approximately 52.2 m) under multipath conditions and 63.6 m² (approximately 8.0 m) in open-sky conditions. Certain satellite PRNs were consistently more affected than others, confirming the directional dependency of multipath effects.