172 research outputs found
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
Quaternion-Based Robust Attitude Estimation Using an Adaptive Unscented Kalman Filter
This paper presents the Quaternion-based Robust Adaptive Unscented Kalman Filter (QRAUKF) for attitude estimation. The proposed methodology modifies and extends the standard UKF equations to consistently accommodate the non-Euclidean algebra of unit quaternions and to add robustness to fast and slow variations in the measurement uncertainty. To deal with slow time-varying perturbations in the sensors, an adaptive strategy based on covariance matching that tunes the measurement covariance matrix online is used. Additionally, an outlier detector algorithm is adopted to identify abrupt changes in the UKF innovation, thus rejecting fast perturbations. Adaptation and outlier detection make the proposed algorithm robust to fast and slow perturbations such as external magnetic field interference and linear accelerations. Comparative experimental results that use an industrial manipulator robot as ground truth suggest that our method overcomes a trusted commercial solution and other widely used open source algorithms found in the literature
Lie Algebraic Unscented Kalman Filter for Pose Estimation
An unscented Kalman filter for matrix Lie groups is proposed where the time
propagation of the state is formulated on the Lie algebra. This is done with
the kinematic differential equation of the logarithm, where the inverse of the
right Jacobian is used. The sigma points can then be expressed as logarithms in
vector form, and time propagation of the sigma points and the computation of
the mean and the covariance can be done on the Lie algebra. The resulting
formulation is to a large extent based on logarithms in vector form, and is
therefore closer to the UKF for systems in . This gives an
elegant and well-structured formulation which provides additional insight into
the problem, and which is computationally efficient. The proposed method is in
particular formulated and investigated on the matrix Lie group . A
discussion on right and left Jacobians is included, and a novel closed form
solution for the inverse of the right Jacobian on is derived, which
gives a compact representation involving fewer matrix operations. The proposed
method is validated in simulations
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