We introduce a factorization method to increase the calculation speed of incremental smoothing and mapping using Bayes tree (iSAM2), which is used in the back-end stage of simultaneous localization and mapping (SLAM), and to analyse the cause of the associated estimation error. iSAM2 is the method most commonly used to increase the accuracy of SLAM and shorten the calculation time required in real dense situations. In this paper, we describe the application of CUR matrix decomposition to iSAM2’s sparse linear system solver. CUR matrix decomposition is one of the low-rank matrix decomposition methods. It consists of matrices C and R, which are sets of columns and rows of the original matrix, and matrix U, which approximates the original matrix. Because of the characteristics of CUR matrix decomposition, it is possible to effectively approximate the sparse information matrix. Also, using principal component analysis, it is possible to identify the factors that increase or decrease the estimation error. We confirmed the feasibility of the proposed analysis method by applying it to real datasets and obtaining estimation errors similar to those obtained with iSAM2.

中文翻译：

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iSAM2使用CUR矩阵分解进行数据压缩和分析

我们介绍了一种分解方法，以提高用于同时定位和映射（SLAM）后端阶段的贝叶斯树（iSAM2）的增量平滑和映射的计算速度，并分析相关的估计误差的原因。iSAM2是最常用于提高SLAM精度并缩短实际密集情况下所需的计算时间的方法。在本文中，我们描述了CUR矩阵分解在iSAM2的稀疏线性系统求解器中的应用。CUR矩阵分解是低秩矩阵分解方法之一。它由矩阵C和R组成，矩阵C和R是原始矩阵的列和行的集合，而矩阵U则近似于原始矩阵。由于CUR矩阵分解的特性，可以有效地近似稀疏信息矩阵。而且，使用主成分分析，可以识别增加或减少估计误差的因素。通过将其应用于实际数据集并获得与iSAM2相似的估计误差，我们证实了所提出分析方法的可行性。