Cauchy-Gaussian Overbound for Heavy-tailed GNSS Measurement Errors

Abstract

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.