The invariance of state estimation for robot navigation

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We are living in an era that are being changed by mobile robots such as unmanned aerial vehicles and self-driving cars. State estimation for navigation is one of the fundamental problems in mobile robot's applications. This work entirely focuses on two problems of state estimation for robot navigation, i.e., simultaneous localization and mapping (SLAM), and visual-inertial navigation systems (VINS). The SLAM problem asks whether it is possible for a robot to build a map of an unknown environment and simultaneously work out its own location within the map. The VINS problem aims at the estimates of a robot's pose and velocity by the on-board sensor fusion of a camera and an inertial measurement unit (IMU). After data association, both SLAM and VINS need a back-end solver to estimate the state of a robot and the environment, which mainly includes two methods: extended Kalman filter and optimization. The main contribution of this thesis is the invariance theory, which proposes the basic principles for state estimation, i.e., the actual estimates should be invariant under unobservable (deterministic or stochastic) transformations. The invariance theory does not only provide compact, elegant, profound explanations and insights of extended Kalman filter and optimization in SLAM and VINS, but also help to design new algorithms to improve the existing methods.
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