An introduction to symmetry-preserving observers. Application to a multi-sensor data fusion tutorial example

Abstract

An observer is a filter that provides an estimation of the state of a dynamical system from several sensors imperfect measurements. In this paper, we focus on nonlinear systems that possess symmetries. We show that the recent theory of symmetry-preserving observers allows to automatically build sensible candidate nonlinear observers from observers designed around only one particular equilibrium point. These observers behave then well around a continuum of equilibrium points. We apply the proposed methodology to design such an observer to the problem of inertial and position sensors fusion, and we illustrate the good performance of these symmetry-preserving estimators through simulation and experimental results.