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Registration methods for point clouds have become a key component of many SLAM systems on autonomous vehicles. However, an accurate estimate of the uncertainty of such registration is a key requirement to a consistent fusion of this kind of measurements in a SLAM filter. This estimate, which is normally given as a covariance in the transformation computed between point cloud reference frames, has been modelled following different approaches, among which the most accurate is considered to be the Monte Carlo method. However, a Monte Carlo approximation is cumbersome to use inside a time-critical application such as online SLAM. Efforts have been made to estimate this covariance via machine learning using carefully designed features to abstract the raw point clouds [1]. However, the performance of this approach is sensitive to the features chosen. We argue that it is possible to learn the features along with the covariance by working with the raw data and thus we propose a new approach based on PointNet [2]. In this work, we train this network using the KL divergence between the learned uncertainty distribution and one computed by the Monte Carlo method as the loss. We test the performance of the general model presented applying it to our target use-case of SLAM with an autonomous underwater vehicle (AUV) restricted to the 2-dimensional registration of 3D bathymetric point clouds.

PointNetKL: Deep Inference for GICP Covariance Estimation in Bathymetric SLAM