Overbounds of heavy-tailed measurement errors are essential to meet stringent navigation requirements in integrity monitoring applications. This paper proposes to leverage the bounding sharpness of the Cauchy distribution in the core and the Overbounds of heavy-tailed measurement errors are essential for meeting stringent navigation requirements in integrity-monitoring applications. This paper proposes to leverage the bounding sharpness of the Cauchy distribution in the core and the Gaussian distribution in the tails to tightly bound heavy-tailedglobal navigation satellite system measurement errors. We develop a procedure to determine the overbounding parameters for both symmetric unimodal (SU)and non-symmetric unimodal (NSU) heavy-tailed errors and prove that the over-bounding property is preserved through convolution. Experiment results on both simulated and real-world data sets reveal that our method can sharply boundheavy-tailed errors in both the core and tail regions. In the position domain, the proposed method reduces the average vertical protection level by 15% for SU heavy-tailed errors compared with the single-cumulative-density-function Gaussian overbound and by 21%-47% for NSU heavy-tailed errors compared with the navigation discrete envelope and two-step Gaussian overbounds.

翻译：在完好性监测应用中，重尾型测量误差的过界处理是满足严苛导航需求的关键。本文提出利用柯西分布在核心区域的紧凑界性质以及高斯分布在尾部的紧凑界性质，对全球导航卫星系统重尾型测量误差进行紧密过界。我们建立了一套适用于对称单峰（SU）和非对称单峰（NSU）重尾误差的过界参数确定流程，并证明了该过界特性在卷积运算中保持成立。基于仿真与真实数据集的实验结果表明，本方法能够在核心区与尾部同时实现重尾误差的紧凑过界。在位置域中，对于SU重尾误差，所提方法相比单累积分布函数高斯过界法将平均垂直保护级降低15%；对于NSU重尾误差，相比导航离散包络法和两步高斯过界法，该指标降低21%至47%。