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Smoothing algorithms for navigation, localisation and mapping based on high-grade inertial sensors. (Algorithmes de lissage pour la navigation, la localisation et la cartographie, basés sur des capteurs inertiels haute qualité)

Mobile systems need to locate themselves ever more accurately, and in ever more complex situations. This is in particular true for autonomous systems, for which controlling the position error is a critical safety issue. To this end, they are endowed with various sensors, the data of which are fused to obtain an estimate of the vehicle’s location, either globally (with the GPS for instance), or locally, with respect to its surroundings (with cameras for instance). This thesis investigates algorithms for localisation by sensor fusion, namely filtering and especially smoothing, when the mobile is equipped with high-grade inertial sensors. The first part deals with the nonlinear consequences of the use of high-grade inertial sensors, and demonstrates how the nonlinear structure of both filtering and smoothing algorithms may be improved by leveraging the invariant filtering framework. The second part deals with the problems incurred by the linear solvers that are used at each step of nonlinear smoothing algorithms as a result of having highly precise sensors. It introduces a novel least-squares linear solver that solves the issues.