On the Comparison of Gauge Freedom Handling in Optimization-Based Visual-Inertial State Estimation

Zhang, Zichao; Gallego, Guillermo; Scaramuzza, Davide

doi:10.1109/lra.2018.2833152

Cited by 14 publications

(7 citation statements)

References 20 publications

(60 reference statements)

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“…Therefore, the NLLS problem (6) has certain ambiguities related to g(•), and parameters that are different by such transformations are equivalent. Note that in practice, a unique solution can be obtained by enforcing additional constraints [11].…”

Section: A Ambiguities and Equivalent Parametersmentioning

confidence: 99%

A Tutorial on Quantitative Trajectory Evaluation for Visual(-Inertial) Odometry

Zhang

Scaramuzza

2018

2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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513

226

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In this tutorial, we provide principled methods to quantitatively evaluate the quality of an estimated trajectory from visual(-inertial) odometry (VO/VIO), which is the foundation of benchmarking the accuracy of different algorithms. First, we show how to determine the transformation type to use in trajectory alignment based on the specific sensing modality (i.e., monocular, stereo and visual-inertial). Second, we describe commonly used error metrics (i.e., the absolute trajectory error and the relative error) and their strengths and weaknesses. To make the methodology presented for VO/VIO applicable to other setups, we also generalize our formulation to any given sensing modality. To facilitate the reproducibility of related research, we publicly release our implementation of the methods described in this tutorial.

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Section: A Ambiguities and Equivalent Parametersmentioning

confidence: 99%

A Tutorial on Quantitative Trajectory Evaluation for Visual(-Inertial) Odometry

Zhang

Scaramuzza

2018

2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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513

226

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“…This leads to a gauge freedom [89] of absolute position, velocity, and heading of the estimated solution. There are multiple approaches [99] to remedy gauge freedom and here, the simplest approach was taken. At the first keyframe for the lumbar IMU, a prior of zero position, zero velocity, and zero heading angle were set.…”

Section: Other Priorsmentioning

confidence: 99%

Body-Worn IMU Human Skeletal Pose Estimation Using a Factor Graph-Based Optimization Framework

McGrath

Stirling

2020

Sensors

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Traditionally, inertial measurement units- (IMU) based human joint angle estimation requires a priori knowledge about sensor alignment or specific calibration motions. Furthermore, magnetometer measurements can become unreliable indoors. Without magnetometers, however, IMUs lack a heading reference, which leads to unobservability issues. This paper proposes a magnetometer-free estimation method, which provides desirable observability qualities under joint kinematics that sufficiently excite the lower body degrees of freedom. The proposed lower body model expands on the current self-calibrating human-IMU estimation literature and demonstrates a novel knee hinge model, the inclusion of segment length anthropometry, segment cross-leg length discrepancy, and the relationship between the knee axis and femur/tibia segment. The maximum a posteriori problem is formulated as a factor graph and inference is performed via post-hoc, on-manifold global optimization. The method is evaluated (N = 12) for a prescribed human motion profile task. Accuracy of derived knee flexion/extension angle (4.34∘ root mean square error (RMSE)) without magnetometers is similar to current state-of-the-art with magnetometer use. The developed framework can be expanded for modeling additional joints and constraints.

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“…with respect to an offset rotation [19], [20]) and using the straightforward representations for position and velocity, we obtain a twelve-dimensional parameter space (of which we plot 2D slices). As it is observed, the landscape of the objective function is complex, but it has a clear minimum, reachable provided the solver is initialized in its basin of attraction.…”

Section: Maximum Likelihood Optimization Frameworkmentioning

confidence: 99%

Event-based, Direct Camera Tracking from a Photometric 3D Map using Nonlinear Optimization

Bryner

Gallego

Rebecq

et al. 2019

2019 International Conference on Robotics and Automation (ICRA)

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Event cameras are novel bio-inspired vision sensors that output pixel-level intensity changes, called "events", instead of traditional video images. These asynchronous sensors naturally respond to motion in the scene with very low latency (in the order of microseconds) and have a very high dynamic range. These features, along with a very low power consumption, make event cameras an ideal sensor for fast robot localization and wearable applications, such as AR/VR and gaming. Considering these applications, we present a method to track the 6-DOF pose of an event camera in a known environment, which we contemplate to be described by a photometric 3D map (i.e., intensity plus depth information) built via classic dense 3D reconstruction algorithms. Our approach uses the raw events, directly, without intermediate features, within a maximumlikelihood framework to estimate the camera motion that best explains the events via a generative model. We successfully evaluate the method using both simulated and real data, and show improved results over the state of the art. We release the datasets to the public to foster reproducibility and research in this topic.

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On the Comparison of Gauge Freedom Handling in Optimization-Based Visual-Inertial State Estimation

Cited by 14 publications

References 20 publications

A Tutorial on Quantitative Trajectory Evaluation for Visual(-Inertial) Odometry

A Tutorial on Quantitative Trajectory Evaluation for Visual(-Inertial) Odometry

Body-Worn IMU Human Skeletal Pose Estimation Using a Factor Graph-Based Optimization Framework

Event-based, Direct Camera Tracking from a Photometric 3D Map using Nonlinear Optimization

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