# On-Manifold Preintegration for Real-Time Visual-Inertial Odometry

arXiv: https://arxiv.org/abs/1512.02363 · HTML: https://mlsanity.com/paper/1512.02363/

## Key facts

- Cited by 95 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2015.

## Built on by (most cited first, 30 of 95)

- [Kimera: from SLAM to Spatial Perception with 3D Dynamic Scene Graphs](https://mlsanity.com/paper/2101.06894/) (2021)
- [Event-aided Direct Sparse Odometry](https://mlsanity.com/paper/2204.07640/) (2022)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [Kimera-Multi: Robust, Distributed, Dense Metric-Semantic SLAM for Multi-Robot Systems](https://mlsanity.com/paper/2106.14386/) (2021)
- [RoadMap: A Light-Weight Semantic Map for Visual Localization towards Autonomous Driving](https://mlsanity.com/paper/2106.02527/) (2021)
- [Exploring Event Camera-based Odometry for Planetary Robots](https://mlsanity.com/paper/2204.05880/) (2022)
- [EgoDistill: Egocentric Head Motion Distillation for Efficient Video Understanding](https://mlsanity.com/paper/2301.02217/) (2023)
- [CMax-SLAM: Event-based Rotational-Motion Bundle Adjustment and SLAM System using Contrast Maximization](https://mlsanity.com/paper/2403.08119/) (2024)
- [VILENS: Visual, Inertial, Lidar, and Leg Odometry for All-Terrain Legged Robots](https://mlsanity.com/paper/2107.07243/) (2021)
- [Deep Learning for Inertial Positioning: A Survey](https://mlsanity.com/paper/2303.03757/) (2023)
- [Event-based Simultaneous Localization and Mapping: A Comprehensive Survey](https://mlsanity.com/paper/2304.09793/) (2023)
- [From SLAM to Situational Awareness: Challenges and Survey](https://mlsanity.com/paper/2110.00273/) (2021)
- [RIO: Rotation-equivariance supervised learning of robust inertial odometry](https://mlsanity.com/paper/2111.11676/) (2021)
- [Benchmarking Egocentric Visual-Inertial SLAM at City Scale](https://mlsanity.com/paper/2509.26639/) (2025)
- [Avoiding Degeneracy for Monocular Visual SLAM with Point and Line Features](https://mlsanity.com/paper/2103.01501/) (2021)
- [Revisiting Rolling Shutter Bundle Adjustment: Toward Accurate and Fast Solution](https://mlsanity.com/paper/2209.08503/) (2022)
- [COVINS: Visual-Inertial SLAM for Centralized Collaboration](https://mlsanity.com/paper/2108.05756/) (2021)
- [LF-VISLAM: A SLAM Framework for Large Field-of-View Cameras with Negative Imaging Plane on Mobile Agents](https://mlsanity.com/paper/2209.05167/) (2022)
- [ImMesh: An Immediate LiDAR Localization and Meshing Framework](https://mlsanity.com/paper/2301.05206/) (2023)
- [Air-Ground Collaboration for Language-Specified Missions in Unknown Environments](https://mlsanity.com/paper/2505.09108/) (2025)
- [Continuous-Time vs. Discrete-Time Vision-based SLAM: A Comparative Study](https://mlsanity.com/paper/2202.08894/) (2022)
- [DVI-SLAM: A Dual Visual Inertial SLAM Network](https://mlsanity.com/paper/2309.13814/) (2023)
- [RD-VIO: Robust Visual-Inertial Odometry for Mobile Augmented Reality in Dynamic Environments](https://mlsanity.com/paper/2310.15072/) (2023)
- [IMU Data Processing For Inertial Aided Navigation: A Recurrent Neural Network Based Approach](https://mlsanity.com/paper/2103.14286/) (2021)
- [HybVIO: Pushing the Limits of Real-time Visual-inertial Odometry](https://mlsanity.com/paper/2106.11857/) (2021)
- [Probabilistic Spatial Distribution Prior Based Attentional Keypoints Matching Network](https://mlsanity.com/paper/2111.09006/) (2021)
- [Balancing the Budget: Feature Selection and Tracking for Multi-Camera Visual-Inertial Odometry](https://mlsanity.com/paper/2109.05975/) (2021)
- [Investigation of the Challenges of Underwater-Visual-Monocular-SLAM](https://mlsanity.com/paper/2306.08738/) (2023)
- [Robust Single Rotation Averaging Revisited](https://mlsanity.com/paper/2309.05388/) (2023)
- [Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learning](https://mlsanity.com/paper/2310.07902/) (2023)

## Abstract (arXiv)

Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time, this problem is further emphasized by the fact that inertial measurements come at high rate, hence leading to fast growth of the number of variables in the optimization. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes into single relative motion constraints. Our first contribution is a preintegration theory that properly addresses the manifold structure of the rotation group. We formally discuss the generative measurement model as well as the nature of the rotation noise and derive the expression for the maximum a posteriori state estimator. Our theoretical development enables the computation of all necessary Jacobians for the optimization and a-posteriori bias correction in analytic form. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated into a visual-inertial pipeline under the unifying framework of factor graphs. This enables the application of incremental-smoothing algorithms and the use of a structureless model for visual measurements, which avoids optimizing over the 3D points, further accelerating the computation. We perform an extensive evaluation of our monocular VIO pipeline on real and simulated datasets. The results confirm that our modelling effort leads to accurate state estimation in real-time, outperforming state-of-the-art approaches.