Gaussian Mixture Midway-Merge for Object SLAM with Pose Ambiguity

In this letter, we propose a novel method to merge a Gaussian mixture on matrix Lie groups and present its application for a simultaneous localization and mapping problem with sym- metric objects. The key idea is to predetermine the weighted mean called a midway point and merge Gaussian mixture components at the associated tangent space. Through this rule, the covariance ma- trix captures the original density more accurately, and the need for the back-projection is spared when compared to the conventional merge. We highlight the midway-merge by numerically evaluating dissimilaritymetricsofdensityfunctionsbeforeandafterthemerge on the rotational group. Furthermore, we experimentally discover that the rotational error of symmetric objects follows heavy-tailed behavior and formulate the Gaussian sum filter to model it by a Gaussian mixture noise. The effectiveness of our approach is validated through virtual and real-world datasets.