Structure from motion algorithms have an inherent limitation that the reconstruction can only be determined up to the unknown scale factor. Modern mobile devices are equipped with an inertial measurement unit (IMU), which can be used for estimating the scale of the reconstruction. We propose a method that recovers the metric scale given inertial measurements and camera poses. In the process, we also perform a temporal and spatial alignment of the camera and the IMU. Therefore, our solution can be easily combined with any existing visual reconstruction software. The method can cope with noisy camera pose estimates, typically caused by motion blur or rolling shutter artifacts, via utilizing a Rauch-Tung-Striebel (RTS) smoother. Furthermore, the scale estimation is performed in the frequency domain, which provides more robustness to inaccurate sensor time stamps and noisy IMU samples than the previously used time domain representation. In contrast to previous methods, our approach has no parameters that need to be tuned for achieving a good performance. In the experiments, we show that the algorithm outperforms the state-of-the-art in both accuracy and convergence speed of the scale estimate. The accuracy of the scale is around @math from the ground truth depending on the recording. We also demonstrate that our method can improve the scale accuracy of the Project Tango's build-in motion tracking.
The closest previous works to ours are the papers by @cite_14 @cite_26 which address the same problem in a similar context. That is, they also apply off-the-shelf visual tracking software to recover the camera poses up to scale and thereafter fix the metric scale based on inertial measurements. However, in contrast to Ham's approach we do not assume that the relative orientation of the camera and IMU must be known a priori. Further, we propose scale estimation by matching accelarations from visual and inertial sensors in frequency domain instead of time domain. We compare our frequency-based approach both to Ham's original implementation and to our own implementation of Ham's time domain approach. The results show that our approach has better accuracy and faster convergence of the scale estimate.
@cite_14 @cite_26
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We propose a novel direct visual-inertial odometry method for stereo cameras. Camera pose, velocity and IMU biases are simultaneously estimated by minimizing a combined photometric and inertial energy functional. This allows us to exploit the complementary nature of vision and inertial data. At the same time, and in contrast to all existing visual-inertial methods, our approach is fully direct: geometry is estimated in the form of semi-dense depth maps instead of manually designed sparse keypoints. Depth information is obtained both from static stereo - relating the fixed-baseline images of the stereo camera - and temporal stereo - relating images from the same camera, taken at different points in time. We show that our method outperforms not only vision-only or loosely coupled approaches, but also can achieve more accurate results than state-of-the-art keypoint-based methods on different datasets, including rapid motion and significant illumination changes. In addition, our method provides high-fidelity semi-dense, metric reconstructions of the environment, and runs in real-time on a CPU. 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. We present VI-DSO, a novel approach for visual-inertial odometry, which jointly estimates camera poses and sparse scene geometry by minimizing photometric and IMU measurement errors in a combined energy functional. The visual part of the system performs a bundle-adjustment like optimization on a sparse set of points, but unlike key-point based systems it directly minimizes a photometric error. This makes it possible for the system to track not only corners, but any pixels with large enough intensity gradients. IMU information is accumulated between several frames using measurement preintegration, and is inserted into the optimization as an additional constraint between keyframes. We explicitly include scale and gravity direction into our model and jointly optimize them together with other variables such as poses. As the scale is often not immediately observable using IMU data this allows us to initialize our visual-inertial system with an arbitrary scale instead of having to delay the initialization until everything is observable. We perform partial marginalization of old variables so that updates can be computed in a reasonable time. In order to keep the system consistent we propose a novel strategy which we call "dynamic marginalization". This technique allows us to use partial marginalization even in cases where the initial scale estimate is far from the optimum. We evaluate our method on the challenging EuRoC dataset, showing that VI-DSO outperforms the state of the art. When fusing visual and inertial measurements for motion estimation, each measurement's sampling time must be precisely known. This requires knowledge of the time offset that inevitably exists between the two sensors' data streams. The first contribution of this work is an online approach for estimating this time offset, by treating it as an additional state variable to be estimated along with all other variables of interest inertial measurement unit IMU pose and velocity, biases, camera-to-IMU transformation, feature positions. We show that this approach can be employed in pose-tracking with mapped features, in simultaneous localization and mapping, and in visual-inertial odometry. The second main contribution of this paper is an analysis of the identifiability of the time offset between the visual and inertial sensors. We show that the offset is locally identifiable, except in a small number of degenerate motion cases, which we characterize in detail. These degenerate cases are either i cases known to cause loss of observability even when no time offset exists, or ii cases that are unlikely to occur in practice. Our simulation and experimental results validate these theoretical findings, and demonstrate that the proposed approach yields high-precision, consistent estimates, in scenarios involving either known or unknown features, with both constant and time-varying offsets.