Abstract

This dissertation investigates methodologies for consistent Kalman filtering with Lie-group based representations of the vehicle pose. Early results are centered around the relative navigation framework, which maintains filter observability and consistency by only tracking the state relative to the latest keyframe of an odometry system such as visual odometry or laser scan matching. A detailed derivation of a relative multiplicative extended Kalman filter, using a quaternion parameterization of the attitude state, is presented for application to multirotor vehicles. The remainder of the dissertation focuses on Kalman filtering using a Lie-group SE(3) pose representation, which improves filter consistency by correctly modeling the true non-Gaussian pose uncertainty distribution as a Gaussian distribution in the Lie algebra. An extensive tutorial introduction to matrix Lie groups is provided. This introduction attempts to fill in some of the gaps that exist in the background provided by the existing state estimation literature, and to also clarify connections between the pure mathematical concepts and the coordinate frame conventions used in engineering applications. Next, a discrete error-state Kalman-filtering framework using an SE(3) pose representation is developed. Benefits of this formulation, especially in the context of IMU-mechanized systems, include well-defined mechanisms for handling other filter states (such as IMU bias states) within the SE(3) propagation dynamics, and well-defined modeling of input noise. The error-state formulation is shown to have many similarities with other approaches in the literature, especially the invariant extended Kalman filter, while differences are also highlighted. Finally, the application of this error-state filtering framework to an IMU-mechanized system is developed. A primary contribution is an exact discretization of the propagation equations, assuming the angular velocity and acceleration measured by the IMU are constant over the propagation period. The corresponding error-state propagation Jacobians are also derived. Simulation results show significant advantages for filter accuracy and consistency over approximate discretization methods.

Degree

PhD

College and Department

Ira A. Fulton College of Engineering; Mechanical Engineering

Rights

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