RIs-Calib: An Open-Source Spatiotemporal Calibrator for Multiple 3D Radars and IMUs Based on Continuous-Time Estimation

TL;DR

RIs-Calib is presented: a spatiotemporal calibrator for multiple 3-D radars and IMUs based on continuous-time estimation, which enables accurate spatiotemporal calibration and does not require any additional artificial infrastructure or prior knowledge.

Abstract

Aided inertial navigation system (INS), typically consisting of an inertial measurement unit (IMU) and an exteroceptive sensor, has been widely accepted as a feasible solution for navigation. Compared with vision-aided and LiDAR-aided INS, radar-aided INS could achieve better performance in adverse weather conditions since the radar utilizes low-frequency measuring signals with less attenuation effect in atmospheric gases and rain. For such a radar-aided INS, accurate spatiotemporal transformation is a fundamental prerequisite to achieving optimal information fusion. In this work, we present RIs-Calib: a spatiotemporal calibrator for multiple 3D radars and IMUs based on continuous-time estimation, which enables accurate spatiotemporal calibration and does not require any additional artificial infrastructure or prior knowledge. Our approach starts with a rigorous and robust procedure for state initialization, followed by batch optimizations, where all parameters can be refined to global optimal states steadily. We validate and evaluate RIs-Calib on both simulated and real-world experiments, and the results demonstrate that RIs-Calib is capable of accurate and consistent calibration. We open-source our implementations at (https://github.com/Unsigned-Long/RIs-Calib) to benefit the research community.

Figures (11)

• Figure 1: Runtime visualization of spatiotemporal calibration in real-world experiments in RIs-Calib, where red boxes and bule entities in $A$ are IMUs and radars respectively, and discrete three-axis coordinate frames in $B$ present continuous-time B-splines maintained in estimator for spatiotemporal optimization.
• Figure 2: The pipeline of the proposed calibration method.
• Figure 3: The simulated scenario with uniformly distributed static targets and a sufficiently excited 8-shape trajectory represented by discrete three-axis coordinates.
• Figure 4: The system state and convergence performance in different stages: ($i$) INIT(1): Rotation B-spline Initialization (see Section \ref{['sect:rot_bspline_init']}); ($ii$) INIT(2): Extrinsics and Gravity Initialization (see Section \ref{['sect:extri_grav_init']}); ($iii$) INIT(2): Velocity B-spline Initialization (see Section \ref{['sect:vel_bspline_init']}); $(iv)$BO(j): the $j$-th batch optimization (see Section \ref{['sect:batch_opt']}). The white dashed line in each sub-figure indicates the zero line. For better readers' understanding, all spatiotemporal parameters are with respect to IMU-1, rather than with respect to the virtual central IMU maintained in the estimator.
• Figure 5: A visualization of the sparsity pattern of the normal equations built during one iteration of Levenberg-Marquardt. For better visibility, only 15 rotation and velocity control points are used to generate this plot. Parameter blocks are separated by black lines, in which the rotation (represented as unit quaternion in the estimator) and velocity control points are four and three dimensional respectively. Darker reds and blues represent larger positive and negative values, while whites are zeros.