Mounting Misalignment and Time Offset Self- Calibration Online Optimization Method for Vehicular Visual-Inertial-Wheel Odometer System

The visual-inertial-wheel odometry system significantly enhances the positioning accuracy of ground vehicles in global navigation satellite system (GNSS)-deprived environments. To fully exploit the fusion capabilities of vision, inertial measurement units (IMUs), and wheel odometers (referred to as odometry), precise calibration of their interrelated parameters is imperative. Conventional online calibration methods typically rely on a filtering framework, thereby limiting the potential improvement in online calibration accuracy. Therefore, we propose a self-calibrating online optimization approach based on the theory of preintegration for mounting misalignments and time offsets. Distinct from existing preintegration methods, a comprehensive IMU-odometer preintegration model is derived, considering the misalignments of position and attitude between the IMU and odometer, odometer scale factors, and IMU-odometer time offsets. Subsequently, to address camera-IMU time delays, visual factors with time offsets are designed. Then, the IMU-odometer preintegration and visual factors with time offsets are collectively incorporated into the graph-based optimization model, simultaneously optimizing spatial/temporal calibration parameters between sensors and the navigation state of the system. This overcomes the issue in existing online calibration methods that are influenced by the initial parameter values. Finally, both dataset and field test results indicate that our calibration method exhibits higher precision compared to other online calibration methods and offline tools. Our online calibration method achieves an error of approximately 0.013 m in the <inline-formula> <tex-math notation="LaTeX">$X/Y$ </tex-math></inline-formula> axis position, about 0.30° error in the <inline-formula> <tex-math notation="LaTeX">$Y/Z$ </tex-math></inline-formula> axis orientation, and a time delay error of approximately 0.44 ms between sensors. Furthermore, our approach serves as a versatile model easily applicable to optimization-based visual-inertial-wheel odometry frameworks.