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.
 This work investigates the relationship between system observability properties and estimator inconsistency for a Vision-aided Inertial Navigation System (VINS). In particular, first we introduce a new methodology for determining the unobservable directions of nonlinear systems by factorizing the observability matrix according to the observable and unobservable modes. Subsequently, we apply this method to the VINS nonlinear model and determine its unobservable directions analytically. We leverage our analysis to improve the accuracy and consistency of linearized estimators applied to VINS. Our key findings are evaluated through extensive simulations and experimental validation on real-world data, demonstrating the superior accuracy and consistency of the proposed VINS framework compared to standard approaches. The so-called direct visual SLAM methods have shown a great potential in estimating a semidense or fully dense reconstruction of the scene, in contrast to the sparse reconstructions of the traditional feature-based algorithms. In this paper, we propose for the first time a direct, tightly-coupled formulation for the combination of visual and inertial data. Our algorithm runs in real-time on a standard CPU. The processing is split in three threads. The first thread runs at frame rate and estimates the camera motion by a joint non-linear optimization from visual and inertial data given a semidense map. The second one creates a semidense map of high-gradient areas only for camera tracking purposes. Finally, the third thread estimates a fully dense reconstruction of the scene at a lower frame rate. We have evaluated our algorithm in several real sequences with ground truth trajectory data, showing a state-of-the-art performance.       Combining visual and inertial measurements has become popular in mobile robotics, since the two sensing modalities offer complementary characteristics that make them the ideal choice for accurate visual-inertial odometry or simultaneous localization and mapping SLAM. While historically the problem has been addressed with filtering, advancements in visual estimation suggest that nonlinear optimization offers superior accuracy, while still tractable in complexity thanks to the sparsity of the underlying problem. Taking inspiration from these findings, we formulate a rigorously probabilistic cost function that combines reprojection errors of landmarks and inertial terms. The problem is kept tractable and thus ensuring real-time operation by limiting the optimization to a bounded window of keyframes through marginalization. Keyframes may be spaced in time by arbitrary intervals, while still related by linearized inertial terms. We present evaluation results on complementary datasets recorded with our custom-built stereo visual-inertial hardware that accurately synchronizes accelerometer and gyroscope measurements with imagery. A comparison of both a stereo and monocular version of our algorithm with and without online extrinsics estimation is shown with respect to ground truth. Furthermore, we compare the performance to an implementation of a state-of-the-art stochastic cloning sliding-window filter. This competitive reference implementation performs tightly coupled filtering-based visual-inertial odometry. While our approach declaredly demands more computation, we show its superior performance in terms of accuracy.  In this paper, we study estimator inconsistency in vision-aided inertial navigation systems (VINS) from the standpoint of system's observability. We postulate that a leading cause of inconsistency is the gain of spurious information along unobservable directions, which results in smaller uncertainties, larger estimation errors, and divergence. We develop an observability constrained VINS (OC-VINS), which explicitly enforces the unobservable directions of the system, hence preventing spurious information gain and reducing inconsistency. This framework is applicable to several variants of the VINS problem such as visual simultaneous localization and mapping (V-SLAM), as well as visual-inertial odometry using the multi-state constraint Kalman filter (MSC-KF). Our analysis, along with the proposed method to reduce inconsistency, are extensively validated with simulation trials and real-world experimentation. Obtaining reliable state estimates at high altitude but GPS-denied environments, such as between high-rise buildings or in the middle of deep canyons, is known to be challenging, due to the lack of direct distance measurements. Monocular visual-inertial systems provide a possible way to recover the metric distance through proper integration of visual and inertial measurements. However, the nonlinear optimization problem for state estimation suffers from poor numerical conditioning or even degeneration, due to difficulties in obtaining observations of visual features with sufficient parallax, and the excessive period of inertial measurement integration. In this paper, we propose a spline-based high altitude estimator initialization method for monocular visual-inertial navigation system (VINS) with special attention to the numerical issues. Our formulation takes only inertial measurements that contain sufficient excitation, and drops uninformative measurements such as those obtained during hovering. In addition, our method explicitly reduces the number of parameters to be estimated in order to achieve earlier convergence. Based on the initialization results, a complete closed-loop system is constructed for high altitude navigation. Extensive experiments are conducted to validate our approach.    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.