# Joint On-Manifold Gravity and Accelerometer Intrinsics Estimation for Inertially Aligned Mapping

**Authors:** Ryan Nemiroff, Kenny Chen, Brett T. Lopez  
**arXiv:** [2303.03505](https://arxiv.org/abs/2303.03505)  
**Date:** 2023-03-06  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2303.03505v2/

## Key points

- Accurate alignment of a robot's trajectory or map to the inertial frame is crucial for reliable navigation and mapping
- Inertial measurement units (IMUs) can provide information about absolute roll and pitch with respect to gravity, but inaccuracies often arise from accelerometer biases and scale factor errors during initial calibration
- To improve accuracy, it is necessary to simultaneously estimate true gravity vector, accelerometer biases, and scale factor
- Authors propose a fixed-lag factor-graph-based estimator that optimizes over a larger time window and separates estimation of accelerometer intrinsics and gravity from other states
- Method introduces a novel velocity-agnostic measurement model for intrinsics and gravity, as well as a new method for optimizing the gravity vector on the unit sphere ($S^2$)
- Experimental results demonstrate accurate IMU state prediction, gravity-alignment, and correction of roll/pitch drift in diverse environments.

## Summary

The paper titled "Joint On-Manifold Gravity and Accelerometer Intrinsics Estimation for Inertially Aligned Mapping" addresses the challenge of accurately aligning a robot's trajectory or map to the inertial frame. This alignment is crucial for reliable robot navigation and mapping. While inertial measurement units (IMUs) can provide information about absolute roll and pitch with respect to gravity, inaccuracies often arise from accelerometer biases and scale factor errors during the IMU's initial calibration, particularly for low-grade IMUs. To improve the accuracy of aligning the robot's odometry frame with the inertial frame, it is necessary to simultaneously estimate the true gravity vector, accelerometer biases, and scale factor. To overcome these challenges, the authors propose a fixed-lag factor-graph-based estimator that addresses both issues. Their method not only estimates accelerometer scale factor but also mitigates limited observability by optimizing over a time window significantly larger than existing methods, while maintaining a lower computational burden. The proposed method separates the estimation of accelerometer intrinsics and gravity from other states using a novel velocity-agnostic measurement model for intrinsics and gravity. Additionally, they introduce a new method for optimizing the gravity vector on $S^2$ (the unit sphere). The effectiveness of their approach is demonstrated through experiments conducted on public and self-collected datasets in diverse environments. The experiments showcase accurate IMU state prediction, gravity-alignment, and correction of roll/pitch drift. Overall, this paper presents an innovative approach to address the challenges associated with aligning a robot's trajectory or map to the inertial frame. By estimating accelerometer intrinsics and gravity separately from other states and optimizing over a larger time window, their method improves measurement quality while reducing computational burden. The experimental results validate the effectiveness of their approach in diverse real-world scenarios.