Most navigation applications nowadays rely heavily on Global Navigation Satellite Systems (GNSSs) and inertial sensors. Both of these systems are known to be complementary, and as such, their... Show moreMost navigation applications nowadays rely heavily on Global Navigation Satellite Systems (GNSSs) and inertial sensors. Both of these systems are known to be complementary, and as such, their outputs are very often combined in an extended Kalman Filter (KF) to provide a continuous navigation solution, resistant to poor satellite geometry, as well as radio frequency interference. Additionally, recent development in safety critical applications (such as aviation) revealed the performance limitations of current algorithms (Advance Receiver Autonomous Integrity Monitoring - ARAIM) to vertical guidance down to 200 feet above the runway (LPV-200). When nominal constellations are depleted, LPV-200 can only sparsely be achieved. Exploiting satellite motion in ARAIM (for instance using a KF) could help alleviate those limitations, but would require adequate modeling of the errors, including the error's time correlation.Power Spectral Density (PSD) bounding is a methodology that provides high integrity, time correlated error models, but this approach is currently limited to stationary errors (which is rarely the case with real data), and has never been applied to navigation errors. More generally, no high integrity, time correlated error models have ever been derived for navigation errors.As a result, in the first part of this thesis, a methodology for high integrity modeling of time correlated errors is introduced. The PSD bounding methodology is extended to both stationary and non-stationary errors. In the second part of this thesis, these methodologies are applied to the 3 main error sources impacting iono-free GNSS measurements (orbit and clock errors, tropospheric errors and multipath), as well as to inertial errors.The methodology introduced in this dissertation provides high integrity time correlated error models and is applicable to any type of applications where high integrity is required (e.g. Differential GNSS - DGNSS, Aircaft Based Augmentation System - ABAS, Ground Based Augmentation System - GBAS, Space Based Augmentation System - SBAS, etc...). Additionally, the error models derived here are not only limited to high integrity applications, but could also be used in applications were the correlation over time of the errors plays an important role (such as any KF integration).In the last part of this dissertation, we focus on a specific safety critical application: aviation, and in particular ARAIM. The dissertation is concluded with an assessment of the performance improvements provided by recursive ARAIM, using those bounding dynamic error models, with respect to those models, used for baseline snapshot ARAIM. Additionally, a sensitivity analysis is performed on each of the error model parameters to assess which of them impacts the KF performance (i.e. covariance) the most. Show less
