Stochastic Modeling and Quantification of Multipath Error in Static Gnss Observations Using Rtklib
Year: 2026
Type: article
Abstract: 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.
Authors: Ossai, E. N., Alohan, N.O., Nwodo, G.O., Eze, I. R.
Institution: University of Benin
Language: English
Subfield: Aerospace Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7170154881
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