A Stochastic Modeling Approach for Phase Transition-Induced Errors in GBAS under Ionospheric Scintillation

Abstract

Ionospheric scintillation can introduce diffractive phase transitions that corrupt carrier-smoothed pseudoranges in Ground-Based Augmentation Systems (GBAS), introducing unmodeled errors that are not accounted for in existing GBAS standards. Current GBAS error models assume negligible carrier phase noise contributions. However, phase transitions during scintillation propagate through carrier smoothing filters as step-like biases, potentially degrading system integrity. This paper employs physics-based scintillation simulation to generate controlled error samples and develops a novel stochastic modeling method to derive sigma overbounds for phase transition-induced errors under scintillation conditions. We apply a two-component power-law phase screen model to generate extensive scintillation data under controlled conditions across comprehensive parameter spaces. To address the discrete characteristics of phase transition-induced errors, we propose a stochastic modeling approach that represents phase transitions as Skellam-distributed point processes. This enables analytical derivation of sigma overbounds that statistically extrapolate to rare-event probability levels required for aviation integrity. The proposed approach overcomes the finite sample constraints of empirical CDF overbounding by providing more conservative bounds through statistical extrapolation. Results reveal that ionosphere-free (IFree) and divergence-free (DFree) smoothing modes employed in dual-frequency GBAS architectures amplify phase transition-induced errors. IFree errors approximately 3.5 times larger than L1 single-frequency mode, while the DFree smoothing exhibits 7 times amplification. Phase transition-induced errors increase with longer smoothing time constants, with 600-second smoothing resulting in approximately 2.4 times larger errors than 100-second smoothing. This work proposes a methodology to derive sigma overbounds for phase transition-induced errors that may need to be incorporated into GBAS protection level calculations. The derived parameters enable more comprehensive integrity assessment for aviation operations under scintillation. Although partial mitigation may be achievable through the exclusion processes of existing GBAS integrity monitors or scintillation-dedicated monitors, a thorough investigation into their effectiveness against phase transition-induced errors is required.