Non-Parametric Extrinsic and Intrinsic Calibration of Visual-Inertial Sensor Systems

This paper presents a solution for the extrinsic and intrinsic calibration of visual-inertial sensor systems. Calibration is formulated as a joint state and parameter estimation problem of a continuous-time system with discrete-time measurements. A maximum-likelihood estimator is derived to estimate the transform between cameras and inertial sensors, temporal alignment, and inertial sensor intrinsic parameters, such as scale factors, axes misalignment, and sensor noise characteristics. The estimator is simple to implement, consistent, and asymptotically attains the Cramér-Rao lower bound. In contrast to the existing methods, it requires no tuning parameters. Detailed results from repeated calibration experiments with a camera-inertial measurement unit system are reported and compared with the results obtained from a modern, parametric method. We reach a precision of <1 mm in extrinsic translation, 1 mrad in orientation, and 10
$\mu \text{s}$
in time shift—within a calibration window of 20 s.