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 Gaussian distribution in the tails to tightly bound heavy-tailed GNSS measurement errors. We develop a procedure to determine the overbounding parameters for both symmetric unimodal (s.u.) and not symmetric unimodal (n.s.u.) heavy-tailed errors and prove that the overbounding property is preserved through convolution. The experiment results on both simulated and real-world datasets reveal that our method can sharply bound heavy-tailed errors at both core and tail regions. In the position domain, the proposed method reduces the average vertical protection level by 15% for s.u. heavy-tailed errors compared to the single-CDF Gaussian overbound, and by 21% to 47% for n.s.u. heavy-tailed errors compared to the Navigation Discrete ENvelope and two-step Gaussian overbounds.

翻译：在完好性监测应用中，重尾测量误差的上界对于满足严格的导航要求至关重要。本文提出利用柯西分布在核心区域的尖锐界特性与高斯分布在尾部的界特性，实现对重尾GNSS测量误差的紧致上界。我们开发了一套适用于对称单峰与非对称单峰重尾误差的上界参数确定流程，并证明了该上界特性在卷积运算中得以保持。在仿真和真实数据集上的实验结果表明，本方法能够在核心区域与尾部区域同时对重尾误差实现尖锐上界。在位置域中，对于对称单峰重尾误差，相较于单CDF高斯上界方法，本方法将垂直保护水平平均降低了15%；对于非对称单峰重尾误差，相较于导航离散包络法与两步高斯上界法，本方法将垂直保护水平平均降低了21%至47%。