Gaussian Process Preintegration for Inertial-Aided State Estimation

In this letter, we present Gaussian Process Preintegration, a preintegration theory based on continuous representations of inertial measurements. A novel use of linear operators on Gaussian Process kernels is employed to generate the proposed Gaussian Preintegrated Measurements (GPMs). This formulation allows the analytical integration of inertial signals on any time interval. Consequently, GPMs are especially suited for asynchronous inertial-aided estimation frameworks. Unlike discrete preintegration approaches, the proposed method does not rely on any explicit motion-model and does not suffer from numerical integration noise. Additionally, we provide the analytical derivation of the Jacobians involved in the first-order expansion for postintegration bias and inter-sensor time-shift correction. We benchmarked the proposed method against existing preintegration methods on simulated data. Our experiments show that GPMs produce the most accurate results and their computation time allows close-to-real-time operations. We validated the suitability of GPMs for inertial-aided estimation by integrating them into a lidar-inertial localisation and mapping framework.