Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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. ,  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.  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.
['Silvère Bonnabel', 'Martin Barczyk', 'Francois Goulette']
I am writing a research paper on a idea On the covariance of ICP-based scan-matching techniques
[{"from": "human", "value": "I am writing a research paper on a idea On the covariance of ICP-based scan-matching techniques"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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. ,  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.  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."}]