Robust Linearly Constrained Square-Root Cubature Kalman Filter for Mismatched Nonlinear Dynamic Systems

This letter addresses the robust state estimation problem for mismatched nonlinear dynamic systems. In this context, we are interested in nonlinear filters able to provide consistent estimates while mitigating the impact of possible modeling errors. We focus on the cubature Kalman filter (CKF) and its square-root form (SCKF), being the most promising nonlinear Gaussian filters, the latter providing improved numerical stability. We leverage on the recently introduced linearly constraint Kalman filter, and derive its sigma-point-based counterparts, the linearly constrained CKF (LC-CKF) and SCKF (LC-SCKF). Such formulation can be exploited, using the correct constraints, to mitigate a large number of model misspecifications. To assess the validity of this approach, we consider an illustrative vehicle navigation problem. Results are provided to support the discussion and show the good performance of the new filters with respect to the state-of-the-art, which are robust to different types of mismatches between the assumed dynamic system model and the true one.