Rejection of parametric model errors in a recursive Kalman filter for virtual sensing applications

The performance of the Kalman filter is often hindered by the discrepancies between a model used to realize the filter and the true model of the data-generating system. While some methods to account for those errors exists, the majority is restricted to Luenberger's observers. The objective of this work is to develop a joint input-state estimation filter where the effect of parametric model errors is rejected from the state and observation equations before the development of the state estimate, and without the explicit knowledge of the error terms. For this purpose, errors in a physical parameter of a parametrized mechanical system are modelled as additive terms in the state and observation equations by means of first-order perturbation analysis. The rejection step is achieved with an injection of a shaped output nullifying the effect of the added terms. An input-state observers are then derived under the assumption that the injected shaped outputs and the system states are uncorrelated. The performance of the proposed approach is illustrated on a numerical data of a spring-mass system.