Today I read a paper titled “On the Covariance of ICP-based Scan-matching Techniques”
The abstract is:
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.