Continuous Gaussian Process Pre-Optimization for Asynchronous Event-Inertial Odometry

TL;DR

This work tackles ego-motion estimation with fully asynchronous event and IMU data by introducing GPO, a local Temporal Gaussian Process–based preintegration framework. By performing a two-step pre-optimization, GPO builds a local TGP trajectory that enables linear preintegration and constant-time queries, supporting tight and efficient asynchronous fusion in event-inertial odometry. The authors demonstrate, through simulations and real-world datasets, that GPO achieves superior efficiency and competitive or improved accuracy compared with existing GP-based preintegration methods, significantly reducing computational load for online, asynchronous fusion. The proposed approach shows strong potential for robust, high-speed, HDR robotics applications where sensor streams operate at different frequencies and with missing synchronous samples.

Abstract

Event cameras, as bio-inspired sensors, are asynchronously triggered with high-temporal resolution compared to intensity cameras. Recent work has focused on fusing the event measurements with inertial measurements to enable ego-motion estimation in high-speed and HDR environments. However, existing methods predominantly rely on IMU preintegration designed mainly for synchronous sensors and discrete-time frameworks. In this paper, we propose a continuous-time preintegration method based on the Temporal Gaussian Process (TGP) called GPO. Concretely, we model the preintegration as a time-indexed motion trajectory and leverage an efficient two-step optimization to initialize the precision preintegration pseudo-measurements. Our method realizes a linear and constant time cost for initialization and query, respectively. To further validate the proposal, we leverage the GPO to design an asynchronous event-inertial odometry and compare with other asynchronous fusion schemes within the same odometry system. Experiments conducted on both public and own-collected datasets demonstrate that the proposed GPO offers significant advantages in terms of precision and efficiency, outperforming existing approaches in handling asynchronous sensor fusion.

Figures (5)

• Figure 1: System framework of the proposal. The GPO infers a local TGP-based trajectory during each pre-optimization (left part). The local trajectories, within the sliding-window of event-inertial odometry, will be queried by event feature trajectories to create asynchronous projection factors (right part).
• Figure 2: Simulation evaluations of the proposed GPO. (A) Accuracy comparison under various integration durations. We randomly sample 100 trials and compare their $\Delta \boldsymbol{C}$, $\Delta \boldsymbol{v}$, $\Delta \boldsymbol{r}$ with the ground truth for each integration period. (B) Procedural Jacobians evaluations. The Jacobian $\partial \Delta \boldsymbol{x}(\tau) / \partial \boldsymbol{b}(\tau)$ calculated using \ref{['eq:bias_jacobian_derivation']}, \ref{['eq:proceduralJacob']} is adopted to correct the integration results of known biases, and compared with the reintegration results. Ten interpolation times $\tau$ are randomly sampled within the integration duration, with 100 trials per evaluation. (C) Robustness evaluations. Raw IMU measurements are contaminated with Gaussian noise of varying magnitudes. (0.5 s, 100 Hz).
• Figure 3: Time cost comparison. Top: Preintegration time - LPM is fastest (blue dashed), GPO scales linearly (green solid), GPP has cubic complexity and becomes unstable with longer durations (red dotted, with shadow showing instability). Bottom: Query time - GPO achieves constant time for pseudo-measurements, Jacobians and covariance matrices (green solid), outperforming alternatives.
• Figure 4: Real-world experiment scenario.
• Figure 5: Estimated trajectory and landmarks for outdoor_05.