Cauchy-Gaussian Overbound for Heavy-tailed GNSS Measurement Errors

TL;DR

This paper introduces a method using Cauchy-Gaussian bounds to accurately model heavy-tailed GNSS measurement errors, improving navigation integrity by reducing protection levels.

Contribution

It develops a novel procedure for overbounding heavy-tailed errors with proven preservation under convolution, enhancing error bounding accuracy in GNSS applications.

Findings

Reduces vertical protection level by 15% for symmetric errors.

Reduces protection level by 21% to 47% for asymmetric errors.

Sharp bounds are effective on both simulated and real datasets.

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 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.