In this paper, we focus on the problem of motion tracking in unknown environments using visual and inertial sensors. We term this estimation task visual–inertial odometry (VIO), in analogy to the well-known visual-odometry problem. We present a detailed study of extended Kalman filter (EKF)-based VIO algorithms, by comparing both their theoretical properties and empirical performance. We show that an EKF formulation where the state vector comprises a sliding window of poses (the multi-state-constraint Kalman filter (MSCKF)) attains better accuracy, consistency, and computational efficiency than the simultaneous localization and mapping (SLAM) formulation of the EKF, in which the state vector contains the current pose and the features seen by the camera. Moreover, we prove that both types of EKF approaches are inconsistent, due to the way in which Jacobians are computed. Specifically, we show that the observability properties of the EKF’s linearized system models do not match those of the underlying system, which causes the filters to underestimate the uncertainty in the state estimates. Based on our analysis, we propose a novel, real-time EKF-based VIO algorithm, which achieves consistent estimation by (i) ensuring the correct observability properties of its linearized system model, and (ii) performing online estimation of the camera-to-inertial measurement unit (IMU) calibration parameters. This algorithm, which we term MSCKF 2.0, is shown to achieve accuracy and consistency higher than even an iterative, sliding-window fixed-lag smoother, in both Monte Carlo simulations and real-world testing.

A periodic modulation of the local bandgap in the rotationally aligned MoS2/WSe2 bilayer creates a 2D electronic superlattice.

Two-dimensional materials and their heterostructures oer a new paradigm for studying physics, engineering, and materials on the nano-scale. In the course of this work I argue that layered heterostructures of two-dimensional crystals graphene, hexagonal boron nitride, and transition metal dichalcogenides provide new and interesting interlayer transport phenomena. Low-energy electron microscopy is employed to study the surface of atomically thin WSe 2 prepared by metal-organic chemical vapor deposition on epitaxial graphene substrates, and a method for unambiguously measuring the number of atomic layers is presented. Using very low-energy electrons to probe the surface of similar heterostructures, a relationship between extracted work function dierences from the layers and the nature of the electrical contact between them is revealed. An extension of this analysis is applied to surface studies of MoSe 2 prepared by molecular beam epitaxy on epitaxial graphene. A large work function dierence is measured between the MoSe 2 and graphene, and a model is provided which suggests that this observation results from an exceptional defect density in the MoSe 2 lm. I describe a theory for computing tunneling currents between two-dimensional crystals separated by a thin insulating barrier, and a few situations resulting in resonant tunneling and negative dierential resistance are illustrated by computed examples, as well as observed characteristics, for monolayer and bilayer graphene tunneling junctions and transistors. Acknowledgements First and foremost, I would like to thank my darling wife, who agreed to follow along with me on this journey toward a Ph.D., and remained by my side throughout. Never have I met a more lovely and dedicated person; diligent in her own undertakings, and yet compassionate and supportive in all her personal relationships. It is through her love, support, and exemplary work ethic over the years that I have been able to maintain course, and enjoy life while I do it. I am darn lucky to have met her, and I look forward to many more happy years together.