Filtrage particulaire sur groupes de Lie : application à la navigation
Clément Chahbazian · HAL (Le Centre pour la Communication Scientifique Directe) · 2023
Bayesian estimation is an important discipline in many scientific and technical domains. It is based on Bayes' theorem, which allows to associate an observation with an a priori knowledge about an event or a parameter. However, this theorem cannot be solved analytically in the case of strong non-linearities. Thus, many methods were developed to address this problem numerically. Among them, particle filters represent probability densities with a cloud of particles. This allows to solve strongly nonlinear problems with a generic approach. However, particle filters present several challenges, such as the resampling step, the resolution of high-dimensional problems, and the computational load. Moreover, studies on estimation algorithms in Lie groups demonstrated the interest of these approaches in many aspects. Indeed, representing the estimation variables on Lie groups allows the use of algebraic and geometric properties of these spaces and leads to a natural handling of uncertainties. Thus, filters on Lie groups show improved accuracy and robustness compared to conventional approaches. This thesis focuses on the new field of particle filtering on Lie groups. It establishes a class of particle filters solving Bayes' theorem on Lie groups by focusing on different aspects of these algorithms, such as the resampling step, the particle representation, and the lower error bound. Furthermore, the proposed methods are applied to the navigation of autonomous systems that need robust algorithms to estimate their state (position, velocity, attitude) in order to perform their control and guidance. An inertial measurement unit (IMU) is usually used to complete the navigation function. However, these sensors drift and need to be frequently updated with aiding sensor measurements, which requires a navigation filter for data fusion. Thus, the algorithms presented in this thesis are tested on challenging navigation scenarios, and demonstrated a significant gain in accuracy and robustness compared to conventional methods.