This paper presents a novel method for continuous integration over the 3D rotation group SO(3). The key idea is to model the system’s dynamics with Gaussian Processes (GPs) and learn the GP training data to match the system’s instantaneous angular velocity measurements. This is formulated as the minimisation of a simple cost function that leverages the application of linear operators over GP kernels. The proposed integration method over SO(3) is applied to the preintegration of inertial data provided by a 6-DoF-Inertial Measurement Unit (IMU). Unlike standard integration that requires the recomputation of the integrals every time the estimate changes, preintegration combines the IMU readings into pseudo-measurements that are independent from the pose estimate and allows for efficient multi-modal sensor-fusion. The pseudo-measurements generated by the proposed method are named Unified Gaussian Preintegrated Measurements (UGPMs). UGPMs rely on GP regression and linear operators to analytically integrate the acceleration data. Moreover, a mechanism for IMU bias and time-shift correction is introduced to allow for seamless multi-modal state estimation. Over quantitative experiments, we show that the UGPMs outperform the current state-of-the-art preintegration methods.
