Nonlinear state estimation using an invariant unscented Kalman filter

Abstract : In this paper, we proposed a novel approach for nonlinear state estimation, named π-IUKF (Invariant Unscented Kalman Filter), which is based on both invariant filter estimation and UKF theoretical principles. Several research works on nonlinear invariant observers have been led and provide a geometrical-based constructive method for designing filters dedicated to nonlinear state estimation problems while preserving the physical properties and system symmetries. The general invariant observer guarantees a straight-forward form of the nonlinear estimation error dynamics whose properties are remarkable. The developed π-IUKF estimator suggests a systematic approach to determine all the symmetry-preserving correction terms, associated with a nonlinear state-space representation used for prediction, without requiring any linearization of the differential equations. The exploitation of the UKF principles within the invariant framework has required the definition of a compatibility condition on the observation equations. As a first result, the estimated covariance matrices of the π-IUKF converge to constant values due to the symmetry-preserving property provided by the nonlinear invariant estimation theory. The designed π-IUKF method has been successfully applied to some relevant practical problems such as the estimation of Attitude and Heading for aerial vehicles using low-cost AH reference systems (i.e., inertial/magnetic sensors characterized by low performances).
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Jean-Philippe Condomines, Cédric Seren, Gautier Hattenberger. Nonlinear state estimation using an invariant unscented Kalman filter. AIAA GNC 2013, AIAA Guidance, Navigation and Control Conference, Aug 2013, Boston, United States. pp 1-15 ; ISBN : 978-1-62410-224-0, ⟨10.2514/6.2013-4869⟩. ⟨hal-00933568⟩

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