Closed-form analysis of undetected range errors due to ionospheric impacts for GBAS category I operations

Abstract

Ionospheric anomalies may cause large differential range errors in Ground-Based Augmentation System (GBAS) users. To mitigate those integrity threats, worst-case ionosphere-induced position errors for potentially usable satellite geometries must be bounded by the GBAS ground facility. This mitigation method requires us to compute the worst-case range error for each satellite affected by a hypothetical ionospheric front. This paper presents a simulation-based method for deriving a closed-form expression of undetected ionosphere-induced range errors. Two types of ionospheric impact scenarios are defined in terms of the motion of an ionospheric front. Explicit expressions for outputs of the code-carrier smoothing filter and the code-carrier divergence monitor are derived to reduce the computational load of ionospheric impact simulations. An exhaustive search algorithm is applied to generate the worst undetected range error among all possible ionospheric impact conditions. Finally, a closed-form expression that bounds the maximum ionospheric range errors is determined as a linear function of the magnitude of gradient and the relative speed of the ionospheric front.