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The challenge of estimating the position, velocity and orientation in space in a precise and reliable way, at any time, with and without reception of satellite signals, is the core subject of this dissertation. To this end, the use of Bayesian filters which fuse outputs from autonomous inertial navigation with satellite positioning is a well-accepted and largely proven approach. The quality of integrated systems is mainly driven by the errors affecting the inertial sensors. This research intends to improve the navigation accuracy of INS/GNSS by proposing and investigating novel approaches at two levels. First, a new estimation framework is developed that allows to model complex composite stochastic processes. We consolidate the proposed estimator on a theoretical basis and validate it through simulations and experiments. Results show the ability of our method to estimate models for which other conventional approaches (e.g. Allan variance and likelihood-based estimators) fail, thereby supporting the challenging stage of navigation filter design. Second, we investigate filter designs accounting for inertial sensor redundancy at observation and state levels. The benefits brought by such filters in terms of navigation accuracy and adaptive modeling of sensor noise are discussed in the context of experiments. For that purpose, a redundant MEMS-based inertial navigation system was designed and operated on a vehicle. Compared to classical single-IMU based filters, we found a significant bounding of the position, velocity and attitude error when operating redundant inertial systems. Contrary to single-IMU/GNSS systems, the redundant configuration is able to self-evaluate the level of system noise and thus to catch the effects of the dynamics. The improved performance and robustness is attractive for many applications requiring reliable and accurate trajectory determination.