Error characterisation and overbounding for mission-critical applications
Creators: name: Alghananim, Ma'mon
Publisher: name: Imperial College London
Year: 2022

description: Global Navigation Satellite Systems (GNSS) such as GPS, have been shown to benefit many sectors globally such as transport, health, transport, and emergency services. GNSS provides Positioning, Navigation, Time (PNT) for users worldwide. The development of PNT systems largely assumes that the relevant measurement errors follow a Gaussian distribution, which has a significant impact on PNT performance for mission (e.g. safety) critical applications. The mission critical applications require that PNT integrity is monitored to assure an acceptable level of confidence in positioning and related information provided by a navigation system. Integrity is defined as the ability of a navigation system to provide a timely warning when the system is faulty and should not be used. In addition to determining the distribution that a measurement error belongs to, overbounding that distribution is significant to ensure the highest level of integrity. To date, these two aspects are still to be addressed adequately particularly for complex datasets and scenarios including dynamic operations. This thesis addresses the limitations above and extends the state-of-the-art in GNSS error characterisation, which is mostly currently based on pseudorange residuals using the Gaussian and GEV distributions in static mode. The extension involves both pseudorange and carrier phase residuals in dynamic mode and addition of the Generalised t distribution. Improving carrier phase residuals characterisation, by implementing Gaussian alternative distributions, supports the applications that required high level of accuracy especially mission-critical applications such as autonomous driving, maritime navigation, and robust navigation. In addition, this thesis proposes a novel distribution generated from the GEV and Gaussian distributions to take advantage of both distributions. This distribution, refer as GEV-based Gassusian distribution, provides better bounds than the conventional Gaussian distribution, accordingly, implementing this distribution provides advantages to the system integrity in terms of ensuring the bounding. Furthermore, two novel numerical overbounding assessment methods are proposed for the first time to address the limitation of graphical assessment in evaluating distribution overbounding. These assessments aim to evaluate precisely the distribution overbounding, which can be used to select the candidate probability density function for mission-critical applications. This thesis also proposes a novel overabounding method that ensures overbounding for complex datasets for the first time. This method can ensure the integrity/safety of mission-critical positioning algorithms. This thesis also proposes a novel error distribution derived from the GEV and Generalised t distributions for fast overbounding computation for real-time applications. The results show that the GEV-based Gaussian distribution provides the best bounding of the three distributions (GEV, Gaussian and GEV-based Gaussian), which provides advantages for mission-critical applications integrity/safety. Put differently, implementing GEV-based Gaussian distribution in the positioning algorithm would end up in safer solutions than using Gaussian distribution. The results also show that a higher level of detail can be captured from the proposed novel assessments compared with graphical assessments. Moreover, the proposed overbounding method results can ensure bounding for all location-scale distributions in complex datasets.