Observability Analysis of IMU Intrinsic Parameters in Stereo Visual–Inertial Odometry

Jung, Jae Hyung; Heo, Sejong; Park, Chan Gook

doi:10.1109/tim.2020.2985174

Cited by 34 publications

(11 citation statements)

References 30 publications

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“…They further presented that the IMU intrinsic parameters are observable when all axes of the IMU are excited [30]. The same conclusion was drawn in [15] for a stereo camera-IMU system by using Lie derivatives. The camera intrinsic parameters (excluding distortion) are shown to be observable in [14] under general motion.…”

Section: A Observability Analysis and Self-calibrationsupporting

confidence: 62%

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Observability Analysis and Keyframe-Based Filtering for Visual Inertial Odometry with Full Self-Calibration

Huai¹,

Lin²,

Zhuang³

et al. 2022

Preprint

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Camera-IMU (Inertial Measurement Unit) sensor fusion has been extensively studied in recent decades. Numerous observability analysis and fusion schemes for motion estimation with self-calibration have been presented. However, it has been uncertain whether both camera and IMU intrinsic parameters are observable under general motion. To answer this question, we first prove that for a global shutter camera-IMU system, all intrinsic and extrinsic parameters are observable with an unknown landmark. Given this, time offset and readout time of a rolling shutter (RS) camera also prove to be observable. Next, to validate this analysis and to solve the drift issue of a structureless filter during standstills, we develop a Keyframebased Sliding Window Filter (KSWF) for odometry and selfcalibration, which works with a monocular RS camera or stereo RS cameras. Though the keyframe concept is widely used in vision-based sensor fusion, to our knowledge, KSWF is the first of its kind to support self-calibration. Our simulation and real data tests validated that it is possible to fully calibrate the camera-IMU system using observations of opportunistic landmarks under diverse motion. Real data tests confirmed previous allusions that keeping landmarks in the state vector can remedy the drift in standstill, and showed that the keyframe-based scheme is an alternative cure.

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Section: A Observability Analysis and Self-calibrationsupporting

confidence: 62%

“…This section identifies the condition when the time offset in outputs of an affine-input system is indistinguishable. For simple deduction, we rewrite the affine-input system (15) with scalar inputs u i , i = 1, 2, • • • , m,…”

Section: Appendix When Time Offset Is Unobservablementioning

confidence: 99%

Observability Analysis and Keyframe-Based Filtering for Visual Inertial Odometry with Full Self-Calibration

Huai¹,

Lin²,

Zhuang³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…( 14) and Eq. ( 15)], different choices of these intrinsic parameters can be made Nikolic et al 2016;Rehder and Siegwart 2017;Xiao et al 2019;Jung et al 2020). In the following, we present a range of commonly-used IMU…”

Section: Imu Intrinsic Model Variantsmentioning

confidence: 99%

“…Xiao et al (2019) improved the IMU pre-integration (Forster et al 2017) to incorporate the IMU intrinsic parameters in a keyframe based VINS algorithm for online self-calibration. Jung et al (2020) studied IMU intrinsic calibration within multi-state constrained Kalman filter (MSCKF) by using a stereo camera and an IMU sensor, where they also examined the inertial calibration results under planar and random motions.…”

Section: Imu Intrinsic Calibrationmentioning

confidence: 99%

“…analyzed the identifiability for IMU-camera temporal calibration given the measurements of a single IMU and a monocular camera and identified a degenerate motion that can cause the IMU-camera time offset to become unobservable. Jung et al (2020) studied the observability of stereo VINS with IMU intrinsics also based on Lie derivative to build the observability matrix and showed that the IMU intrinsics (including scale correction and axis misalignment for gyroscope and accelerometer, respectively) is observable given fully exited motions. Tsao and Jan (2019) built the observability matrix for VINS using linearized system model and showed that the camera intrinsics (only including focal length and principal points in their work) is observable.…”

Section: Observability and Degeneracymentioning

confidence: 99%

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Online Self-Calibration for Visual-Inertial Navigation Systems: Models, Analysis and Degeneracy

Yang¹,

Geneva²,

Zuo³

et al. 2022

Preprint

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In this paper, we study in-depth the problem of online self-calibration for robust and accurate visual-inertial state estimation. In particular, we first perform a complete observability analysis for visual-inertial navigation systems (VINS) with full calibration of sensing parameters, including IMU and camera intrinsics and IMU-camera spatial-temporal extrinsic calibration, along with readout time of rolling shutter (RS) cameras (if used). We investigate different inertial model variants containing IMU intrinsic parameters that encompass most commonly used models for low-cost inertial sensors. With these models, the state transition matrix and visual measurement Jacobians are analytically derived and the observability analysis of linearized VINS with full sensor calibration is performed. The analysis results prove that, as intuitively assumed in the literature, VINS with full sensor calibration has four unobservable directions, corresponding to the system's global yaw and translation, while all sensor calibration parameters are observable given fully-excited 6-axis motion. Moreover, we, for the first time, identify primitive degenerate motions for IMU and camera intrinsic calibration, which, when combined, may produce complex degenerate motions. This result holds true for the different inertial model variants investigated in this work and has significant impacts on practical applications of online self-calibration to many robotic platforms. Extensive Monte-Carlo simulations and real-world experiments are performed to validate both the observability analysis and identified degenerate motions, showing that online self-calibration improves system accuracy and robustness to calibration inaccuracies. We compare the proposed online self-calibration on commonly-used IMUs against the state-of-art offline calibration toolbox Kalibr, and show that the proposed system achieves better consistency and repeatability. As sensor calibration plays an important role in making real VINS work well in practice, based on our analysis and experimental evaluations, we also provide practical guidelines for how to perform online IMU-camera sensor self-calibration.

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A novel algorithm based on nonlinear optimization for parameters calibration of wheeled robot mobile chasses

Peng

Tan

et al. 2021

Applied Mathematical Modelling

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Observability Analysis of IMU Intrinsic Parameters in Stereo Visual–Inertial Odometry

Cited by 34 publications

References 30 publications

Observability Analysis and Keyframe-Based Filtering for Visual Inertial Odometry with Full Self-Calibration

Observability Analysis and Keyframe-Based Filtering for Visual Inertial Odometry with Full Self-Calibration

Online Self-Calibration for Visual-Inertial Navigation Systems: Models, Analysis and Degeneracy

A novel algorithm based on nonlinear optimization for parameters calibration of wheeled robot mobile chasses

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