Robust vision-based estimation of structural parameters using Kalman filtering

This contribution introduces the Generalized Augmented MANifold Differential Algebraic Extended Kalman Filter (GAMANDA-EKF), a novel Kalman filter-based methodology for state- input-parameter estimation for structures modelled as multibody systems described by differential algebraic equations. The proposed Kalman filter allows for exact equality and inequality constraint satisfaction and consistent error covariance propagation, without requiring a reformulation of the system equations. In addition to the enforcement of the equality and inequality constraints on the a-posteriori estimated system state with a constrained optimization approach, the estimation error covariance matrix is projected on the constraint manifold as well. This results in increased robustness and stability. Numerical and experimental validation cases using a slider-crank system, employing camera-based position tracking as reference measurements for the estimation, demonstrate the effectiveness of the proposed approach in estimating parameters such as connection stiffnesses and slider friction forces across diverse dynamic scenarios. Furthermore, this work highlights how the enforcement of inequality constraints mitigates estimation instability resulting from suboptimal filter tuning, providing increased robustness to the estimation process.