Articulated Estimator Random Field and Geometrical Approach Applied in System Identification

Abstract

A new point of view of robust statistics based on a geometrical approach is tackled in this paper. Estimation procedures are carried out from a new robust cost function based on a chaining of elementary convex norms. This chain is randomly articulated in order to treat more efficiently natural outliers in data-set. Estimated parameters are considered as random fields and each of them, named articulated estimator random field (AERF) is a manifold or stratum of a stratified space with Riemannian geometry properties. From a high level excursion set, a probability distribution model Msta is presented and a system model validation geometric criterion (SYMOVAGEC) for system model structures Msys based on Riccian scalar curvatures is proposed. Numerical results are drawn in a context of system identification.