Wide-Sense CDF Overbounding for GNSS Integrity

<h3>Abstract</h3> The need for highly reliable positioning in safety-of-life applications has led to the development of global navigation satellite system (GNSS) augmentation systems such as satellite-based augmentation systems and advanced receiver autonomous integrity monitoring. These systems rely on a transfer of integrity from the range to the position domain through concepts such as cumulative distribution function (CDF) overbounding and the more recent two-step overbounding. Here, we propose a new approach, wide-sense CDF overbounding, which offers more flexibility and robustness than existing methods by accommodating biased distributions and relaxing stringent assumptions of symmetry and unimodality while retaining the original simplicity of CDF overbounding. This method combines CDF and paired overbounding, adjusting protection volumes with a formula to compensate for weaker assumptions. We perform numerical analyses using real GNSS data that demonstrate the enhanced flexibility of wide-sense CDF overbounding and show its potential to improve the robustness and performance of GNSS-based safety solutions in various applications.