# On the Covariance of ICP-based Scan-matching Techniques

arXiv: https://arxiv.org/abs/1410.7632 · HTML: https://mlsanity.com/paper/1410.7632/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2014.

## Built on by (most cited first, 5 of 5)

- [NeBula: Quest for Robotic Autonomy in Challenging Environments; TEAM CoSTAR at the DARPA Subterranean Challenge](https://mlsanity.com/paper/2103.11470/) (2021)
- [Learning-based Localizability Estimation for Robust LiDAR Localization](https://mlsanity.com/paper/2203.05698/) (2022)
- [Enhanced Laser-Scan Matching with Online Error Estimation for Highway and Tunnel Driving](https://mlsanity.com/paper/2207.14674/) (2022)
- [Deep Bayesian ICP Covariance Estimation](https://mlsanity.com/paper/2202.11607/) (2022)
- [Human-Interpretable Uncertainty Explanations for Point Cloud Registration](https://mlsanity.com/paper/2509.18786/) (2025)

## Abstract (arXiv)

This paper considers the problem of estimating the covariance of roto-translations computed by the Iterative Closest Point (ICP) algorithm. The problem is relevant for localization of mobile robots and vehicles equipped with depth-sensing cameras (e.g., Kinect) or Lidar (e.g., Velodyne). The closed-form formulas for covariance proposed in previous literature generally build upon the fact that the solution to ICP is obtained by minimizing a linear least-squares problem. In this paper, we show this approach needs caution because the rematching step of the algorithm is not explicitly accounted for, and applying it to the point-to-point version of ICP leads to completely erroneous covariances. We then provide a formal mathematical proof why the approach is valid in the point-to-plane version of ICP, which validates the intuition and experimental results of practitioners.