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.

中文翻译：

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对 GBAS I 类操作中电离层影响导致的未检测距离误差的闭式分析

电离层异常可能会导致地基增强系统 (GBAS) 用户出现较大的差分距离误差。为了减轻这些完整性威胁，GBAS 地面设施必须限制潜在可用卫星几何结构的最坏情况电离层引起的位置误差。这种缓解方法要求我们计算受假设电离层前沿影响的每颗卫星的最坏情况范围误差。本文提出了一种基于模拟的方法，用于推导出未检测到的电离层引起的距离误差的闭式表达式。根据电离层前沿的运动定义了两种类型的电离层撞击情景。推导出码载波平滑滤波器和码载波发散监视器的输出的显式表达式，以减少电离层撞击模拟的计算负载。应用穷举搜索算法来生成所有可能的电离层撞击条件中最差的未检测到的距离误差。最后，将限制最大电离层距离误差的闭式表达式确定为梯度大小和电离层前沿相对速度的线性函数。