The Invariant Unscented Kalman Filter

Jean-Philippe Condomines (1) , Cédric Seren (2) , Gautier Hattenberger (3)

1 DRONES - ENAC - Programme transverse Drones
2 ONERA - The French Aerospace Lab [Toulouse]
3 ENAC - Ecole Nationale de l'Aviation Civile

This article proposes a novel approach for nonlinear state estimation. It combines both invariant observers theory and unscented filtering principles whitout requiring any compatibility condition such as proposed in the -IUKF algorithm. The resulting algorithm, named IUKF (Invariant Unscented Kalman Filter), relies on a geometrical-based constructive method for designing filters dedicated to nonlinear state estimation problems while preserving the physical invariances and systems symmetries. Within an invariant framework, this algorithm suggests a systematic approach to determine all the symmetry- preserving terms without requiring any linearization and highlighting remarkable invariant properties. As a result, the estimated covariance matrices of the IUKF converge to quasi-constant values due to the symmetry-preserving property provided by the invariant framework. This result enables the development of less conservative robust control strategies. The designed IUKF method has been successfully applied to some relevant practical problems such as the estimation of attitude for aerial vehicles using low-cost sensors reference systems. Typical experimental results using a Parrot quadrotor are provided in this paper

Domaines: Traitement du signal et de l'image [eess.SP]

Jean-Philippe Condomines, Cédric Seren, Gautier Hattenberger. The Invariant Unscented Kalman Filter. CDC 2017, 56th IEEE Conference on Decision and Control, Dec 2017, Melbourne, Australia. ⟨hal-01509893⟩