A multi observers approach when observability index is higher than the state dimension - a case study -

We address a family of observation problems that would classically require the construction of an embedding, by a different approach which consists in the design of several estimators in parallel. In principle, for a dynamics in dimension n with a scalar output y, each estimator uses the knowledge of only n-1 derivatives of the output, and the further derivatives are used to discriminate at any time among the estimators. Estimators are built here by roots tracking technique. We illustrate our approach on the parameter estimation of a polynomial dynamics. The simulations show that the final estimation jumps from one estimator to another when passing through observability singularities, or when the parameter suddenly changes, preserving a good estimation error.