Online Multi-IMU Calibration Using Visual-Inertial Odometry

TL;DR

The paper tackles online calibration for multiple unsynchronized IMUs in visual-inertial odometry by formulating a centralized EKF that augments the MSCKF state with per-IMU intrinsic and extrinsic calibration parameters. The method updates all IMU streams without requiring synchronized prediction steps and leverages exteroceptive observations to render calibration states observable, enabling online refinement of biases and pose offsets $^{B}p_{I_i}$, $^{B}{q}_{I_i}$, $^{B}b_a$, and $^{B}b_ ext{ω}$. Validation includes Monte Carlo simulations and real-world experiments, demonstrating improved VIO accuracy with multiple IMUs and calibration online, while achieving calibration estimates comparable to offline optimizers like Kalibr. The approach is flexible to sensor count and quality, supports a wide range of update rates, and is released in an open-source repository to promote adoption and further evaluation.

Abstract

This work presents a centralized multi-IMU filter framework with online intrinsic and extrinsic calibration for unsynchronized inertial measurement units that is robust against changes in calibration parameters. The novel EKF-based method estimates the positional and rotational offsets of the system of sensors as well as their intrinsic biases without the use of rigid body geometric constraints. Additionally, the filter is flexible in the total number of sensors used while leveraging the commonly used MSCKF framework for camera measurements. The filter framework has been validated using Monte Carlo simulation as well as experimentally. In both simulations and experiments, using multiple IMU measurement streams within the proposed filter framework outperforms the use of a single IMU in a filter prediction step while also producing consistent and accurate estimates of initial calibration errors. Compared to current state-of-the-art optimizers, the filter produces similar intrinsic and extrinsic calibration parameters for each sensor. Finally, an open source repository has been provided at https://github.com/unmannedlab/ekf-cal containing both the online estimator and the simulation used for testing and evaluation.

Figures (10)

• Figure 1: Relationship graph between frames of reference showing translations and rotations between the primary {$I_0$} and supplemental {$I_1$...$I_N$} IMU frames
• Figure 2: Reduction of VIO position RMS errors with various IMU counts and acceleration error values without online calibration compared to a single VN-300. A 95% confidence interval is shown after taking 1000 samples with 100 second run times.
• Figure 3: Reduction of VIO position RMS errors with various IMU counts and acceleration error values with online calibration compared to a single VN-300 when there are initialization errors with standard deviations of $5^\circ$ and 20 mm for orientation and position, respectively. A 95% confidence interval is shown after taking 1000 samples with 100 second run times.
• Figure 4: IMU extrinsic position parameter filter convergence given a 20 mm standard deviation initial error using a VN-300 and VN-100. 1000 samples were taken with 100 second run times with the $3\sigma$ standard error shown in red.
• Figure 5: IMU intrinsic accelerometer bias convergence given a 0.1 $\frac{m}{s^2}$ standard deviation initial error using a VN-300 and VN-100. 1000 samples were taken with 100 second run times with the $3\sigma$ standard error shown in red.