A High-Precision Integrated Calibration Method for Position and Attitude of Visual-Inertial System

Parameter	True value	Simulation result	Deviation
$α$ /（°）	-170.719	-170.742	0.023
$β$ /（°）	84.901	84.899	0.002
$γ$ /（°）	101.325	101.302	0.023
T_x /mm	14.607	13.654	0.953
T_y /mm	-144.036	-142.963	-1.073
T_z /mm	-183.533	-179.668	-3.865

Table 2. Sensor parameters of multi-camera IMU system
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Table 2. Sensor parameters of multi-camera IMU system
Device Main parameter Value
IMU Standard full range /（m·s^-2） 200
In-run bias stability /μg 15
Camera Focal length /mm 8
Resolution /（pixel×pixel） $1600 \times 1200$
Pixel size /（μm×μm） $4.5 \times 4.5$

Table 3. Calibration results of intrinsic parameters of multi-camera

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Table 3. Calibration results of intrinsic parameters of multi-camera

Intrinsic parameter	Camera 1	Camera 2	Camera 3
f /mm	7.8131	7.8031	7.8115
$u_{0}$ /pixel	796.1786	794.6990	793.3861
$v_{0}$ /pixel	592.8249	588.0393	602.7344
$k_{1}$	-0.0024	-0.0021	-0.0020
$k_{2}$	7.3610×10^-5	$4.6434 \times 10^{- 5}$	$3.7234 \times 10^{- 5}$
$k_{3}$	-6.6751×10^-7	$5.8504 \times 10^{- 8}$	$2.9718 \times 10^{- 7}$
$p_{1}$	1.2328×10^-4	$1.1121 \times 10^{- 4}$	$7.6300 \times 10^{- 5}$
$p_{2}$	-6.4214×10^-5	$6.4872 \times 10^{- 6}$	$2.9047 \times 10^{- 5}$

Table 4. Calibration results of extrinsic parameters of multi-camera IMU system

View table

Table 4. Calibration results of extrinsic parameters of multi-camera IMU system

Extrinsic parameter	IMU to camera 2	Camera 2 to camera 1	Camera 2 to camera 3
$α$ /（°）	-116.264	-18.319	-18.959
$β$ /（°）	83.839	-42.240	41.549
$γ$ /（°）	157.411	-11.919	7.684
T_x /mm	0.929	-83.565	84.975
T_y /mm	-138.920	47.372	43.953
T_z /mm	-193.072	-46.396	-48.929

Table 5. Standard deviations of extrinsic parameters calibration results
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Table 5. Standard deviations of extrinsic parameters calibration results
Extrinsic parameter $α / (°)$ $β / (°)$ $γ / (°)$ $T_{x} / m m$ $T_{y} / m m$ $T_{z} / m m$
Standard deviation 0.156 0.015 0.156 1.961 1.035 4.679

Table 6. Fitting error and fitting radius of static camera trajectory
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Table 6. Fitting error and fitting radius of static camera trajectory
Parameter Arc trajectory
Fitting error /mm 0.2122
Fitting radius /mm 179.61

Table 7. Fitting radii of camera trajectories and deviations between fitting trajectories and real trajectory
View table
Table 7. Fitting radii of camera trajectories and deviations between fitting trajectories and real trajectory
Parameter Proposed method Kailbr
Fitting radius /mm 176.42 175.65
Axis angle deviation /（ $°$ ） 0.3309 0.5545
Axis distance deviation /mm 3.47 4.28

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Keyao Ma, Yongjie Ren, Jiarui Lin, Zhiyuan Niu, Jigui Zhu. A High-Precision Integrated Calibration Method for Position and Attitude of Visual-Inertial System[J]. Laser & Optoelectronics Progress, 2023, 60(3): 0312021

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