Characterization of a subclass of finite-dimensional estimation algebras with maximal rank. Application to filtering
Résumé
Finite-dimensional estimation Lie algebras play a crucial role in the study of finite-dimensional filters for partially observed stochastic process. When the dynamics noise is Gaussian we can characterize the so-called estimation Lie algebras with maximal rank in terms of the observation functions (necessarily affine) and the drift (necessarily a sum of a skew-symmetric linear term and a gradient vector field, with a functional relationship), under the assumption that the estimation algebra has one and only one operator of order greater or equal to two in any of its basis.