The Invariant Unscented Kalman Filter

International audienceThis 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 pape

Reducing Computational Cost in the Invariant Unscented Kalman Filtering For Attitude Estimation

This article proposes a new formulation to derive the invariant unscented Kalman filter (IUKF) algorithm for attitude estimation problem, where both state and sigma-point are considered as a transformation group parametrization of the filter. The detailed IUKF equations are presented in this article. The filter equations relie on the same ideas as the usual Unscented Kalman Filter (UKF), but it uses a geometrically adapted correction term based on an invariant output error. The specific interest of the proposed formulation is that only the invariant state estimation errors between the predicted state and each sigma point must be known to determine the predicted outputs errors. As we have already computed the set of invariant state errors during the prediction step, the computation cost to find the covariance matrix of the invariant state estimation in the update step is greatly reduced

Invariant Observer-Based State Estimation for Micro-Aerial Vehicles in GPS-Denied Indoor Environments Using an RGB-D Camera and MEMS Inertial Sensors

This paper presents a non-linear state observer-based integrated navigation scheme for estimating the attitude, position and velocity of micro aerial vehicles (MAV) operating in GPS-denied indoor environments, using the measurements from low-cost MEMS (micro electro-mechanical systems) inertial sensors and an RGB-D camera. A robust RGB-D visual odometry (VO) approach was developed to estimate the MAV’s relative motion by extracting and matching features captured by the RGB-D camera from the environment. The state observer of the RGB-D visual-aided inertial navigation was then designed based on the invariant observer theory for systems possessing symmetries. The motion estimates from the RGB-D VO were fused with inertial and magnetic measurements from the onboard MEMS sensors via the state observer, providing the MAV with accurate estimates of its full six degree-of-freedom states. Implementations on a quadrotor MAV and indoor flight test results demonstrate that the resulting state observer is effective in estimating the MAV’s states without relying on external navigation aids such as GPS. The properties of computational efficiency and simplicity in gain tuning make the proposed invariant observer-based navigation scheme appealing for actual MAV applications in indoor environments