Parameter-state estimation for mechanical systems with small model errors

Abstract

The performance of algorithms for parameter-state estimation, often expressed within a Bayesian filtering context, can be hindered by the need to recompute the parametric system matrices at each parameter iteration step. This work aims to alleviate the associated computational burden by expressing model errors that stem from parametric uncertainties, as additive parametric terms in the state and observation equations. For this purpose errors in the eigenstructure of a parametrized mechanical system are propagated to the physical parameters and eventually modelled as additive terms by means of perturbation analysis. A state observer is derived under the assumption that the change between the current and a true model parameter is deterministic and known. An estimate of the possible parameter discrepancy is obtained by minimizing the value of a change detection test applied on a Kalman filter innovation sequence.