EKF-based Visual-Inertial Navigation on Matrix Lie group with Improved Consistency

Abstract

Visual-inertial navigation system (VINS) is one of enabling technologies for autonomous systems such as self-driving cars, unmanned aerial vehicles and space robots.<br/> While most VINS algorithms rely on point features due to their simplicity and abundance in the general environment, line features are alternative visual information in the low-texture environment compared to point features.<br/> In principle, the combination of point and line features would provide more geometric constraints about the structure of the environment than either one, which motivates us to design robust VINS algorithm with point and line features.<br/> <br/> A system observability plays an key role in analyzing the consistency of the state estimator.<br/> A state estimator is consistent, if the estimator errors are un-biased and have covariance equal to the one calculated by the filter.<br/> The nonlinear observability analysis for the VINS algorithms was carried out by finding the right null space of the observability matrix generated from the linearized system and measurement model.<br/> Many researches have been reported that the conventional VINS algorithms suffer from the inconsistent state estimates caused by obtaining spurious information along the unobservable direction, especially under the rotation about gravity direction.<br/> <br/> In this dissertation, we present a novel visual-inertial navigation algorithm using points and lines for low-cost and computationally constrained system in GPS-denied environment.<br/> To improve the consistency and robustness, we model the state space as a matrix Lie group, based on the recent theory of the invariant Extended Kalman filter (IEKF) and simultaneously exploit the points and lines as visual information for the VINS algorithm.<br/> The state-transition matrix and the observation models using points and lines on matrix Lie group are designed and described in details.<br/> In particular, as the main theoretical contributions, we prove that the proposed estimator has a consistent property for the rotation about gravity direction without any artificial remedies by corresponding observability analysis.<br/> This means that the proposed methods on matrix Lie group using points and lines naturally enforces the state vector to exist in the state space that maintains the unobservability characteristics.<br/> To validate the performance of the proposed methods, simulations with synthetic and real-world dataset are performed and the simulation results are matched with the observability analysis.