Using symbolic computation to solve algebraic Riccati equations arising in invariant filtering
Utilisation de méthodes symboliques pour la résolution d'équations algébriques de Riccati apparaissant en filtrage invariant
Abstract
This paper proposes a new step in the development of invariant observers. In the past, this theory led to impressive simplifications of the error equations encountered in estimation problems, especially those related to navigation. This was used to reduce computation load or derive new theoretical properties. Here, we leverage this advantage to obtain closed-form solutions of the underlying algebraic Riccati equations through advanced symbolic computation methods.