Algorithme d'adaptation du filtre de Kalman aux variations soudaines de bruit

This research targets the case of Kalman filtering as applied to linear time-invariant systems having unknown process noise covariance and measurement noise covariance matrices and addresses the problem represented by the incomplete a priori knowledge of these two filter initialization parameters. The goal of this research is to determine in realtime both the process covariance matrix and the noise covariance matrix in the context of adaptive Kalman filtering.;The thesis begins with a description of the problem under consideration (the design of a Kalman filter that is able to adapt to sudden noise variations) followed by a typical application (INS-GPS integrated navigation system) and by a statistical analysis of publications related to adaptive Kalman filtering. Next, the thesis presents the current architectures of the adaptive Kalman filtering: the innovation adaptive estimator (IAE) and the multiple model adaptive estimator (MMAE). It briefly presents their formulation, their behavior, and the limit of their performances.;The thesis continues with the architectural synthesis of the evolutionary adaptive Kalman filter. The steps involved in the solution of the problem under consideration is also presented: an analysis of Kalman filtering and sub-optimal filtering methods, a comparison of current adaptive Kalman and sub-optimal filtering methods, the emergence of evolutionary adaptive Kalman filter as an enrichment of sub-optimal filtering with the help of biological-inspired computational intelligence methods, and the step-by-step architectural synthesis of the evolutionary adaptive Kalman filter. Next, the thesis describes all the aspects related to MATLAB/Simulink modeling and simulation: the performance criterion represented by the Cramer-Rae Lower Bound, the step-by-step modeling of the evolutionary adaptive Kalman filter, and the simulation results that confirm the viability of this approach.;The thesis ends with the conclusion and the references. The appendices (the mathematical model of a 6DoF Inertial Measurement Unit, the experimental setup, the Simulink diagrams/MATLAB programs that constitute the evolutionary adaptive Kalman filter, plus the simulation results) are regrouped in a separate document.;The resultant filter, called evolutionary adaptive Kalman filter, is able to adapt to sudden noise variations and constitutes a hybrid solution for adaptive Kalman filtering based on metaheuristic algorithms. MATLAB/Simulink simulation using several processes and covariance matrices plus comparison with other filters was selected as validation method. The Cramer-Rae Lower Bound (CRLB) was used as performance criterion.