State estimation using multibody models and non-linear Kalman filters

Abstract

The aim of this work is to provide a thorough research on the implementation of some non-linear Kalman filters (KF) using multibody (MB) models and to compare their performances in terms of accuracy and computational cost. The filters considered in this study are the extended KF (EKF) in its continuous form, the unscented KF (UKF) and the spherical simplex unscented KF (SSUKF). The MB formulation taken into consideration to convert the differential algebraic equations (DAE) of the MB model into the ordinary differential equations (ODE) required by the filters is a state-space reduction method known as projection matrix-R method. Additionally, both implicit and explicit integration schemes are used to evaluate the impact of explicit integrators over implicit integrators in terms of accuracy, stability and computational cost. However, state estimation through KFs is a closed-loop estimation correcting the model drift according to the difference between the predicted measurement and the actual measurement, what limits the interest in using implicit integrators despite being commonly employed in MB simulations. Performance comparisons of all the aforementioned non-linear observers have been carried out in simulation on a 5-bar linkage. The mechanism parameters have been obtained from an experimental 5-bar linkage and the sensor characteristics from off-the-shelf sensors to reproduce a realistic simulation. The results should highlight useful clues for the choice of the most suitable filters and integration schemes for the aforementioned MB formulation.