Gaussian Process Preintegration for Inertial-Aided State Estimation

Abstract

In this paper, 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 firstorder expansion for postintegration bias and inter-sensor timeshift 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.

Continuous Integration over SO(3) for IMU Preintegration

“…1 shows the block diagram of the proposed approach. This is similar to the pipeline proposed in [13] but with a "unified" treatment of the rotational integration.…”

“…Our previous work in [13] attempts to solve (1), (2), and (3) analytically using GPs as continuous models of the inertial measurements. Unfortunately, (1) does not have any known general analytical solution [4].…”

“…, Q) as per described in Section IV. This follows the formulation introduced in [13]. Therefore, ( 6) and ( 7) can be expressed as linear operations of the GP signals…”

“…However, relying on arbitrary motion models while a system's motion is not constrained leads to inaccuracies. Our previous work in [13] alleviates the dependence on a motion model by employing GPs for continuous data-driven probabilistic representation of the IMU measurements. This continuous representation of the inertial measurements also accommodates asynchronous sensors.…”

Gaussian Process Gradient Maps for Loop-Closure Detection in Unstructured Planetary Environments

“…Most of these works exploit the probabilistic nature and the inference capabilities to fill-up areas of missing data, to produce maps of a desirable resolution, to filter noise or for data fusion. Our work, in contrast, exploits the derivative (through linear operators) of the continuous elevation terrain to extract features of the Moreover, the use of GP regression and linear operators has already been leveraged for robotics state estimation in [29] to create continuous and accurate pre-integrated measurements from noisy inertial readings. In [30], GP regression is used to recover implicit surfaces with normal estimates for 3D surface reconstruction.…”