NDLI: Efficient Cholesky Factor Recovery for Column Reordering in Simultaneous Localisation and Mapping

Content Provider	Springer Nature Link
Author	Touchette, S. Gueaieb, W. Lanteigne, E.
Copyright Year	2016
Abstract	Simultaneous Localisation And Mapping problems are inherently dynamic and the structure of the graph representing them changes significantly over time. To obtain the least square solution of such systems efficiently, it is desired to maintain a good column ordering such that fill-ins are reduced. This comes at a cost since general ordering changes require the complete re-computation of the Cholesky factor. While some methods have obtained good results with reordering at loop closing, the changes are not guaranteed to be limited to the scope of the loop, leading to suboptimal performance. In this article, it is shown that the Cholesky factorisation of an updated matrix can be efficiently recovered from the previous factorisation if the permutations are localised. This is experimentally demonstrated on 2D SLAM datasets. A method is then provided to identify when such recovery is advantageous over the complete re-computation of the Cholesky factor. Furthermore, a hybrid algorithm combining factorisation recovery and re-computation of the Cholesky factor is proposed for dynamically evolving problems and tested on SLAM datasets. Steps where reordering occurs can be executed up to 67 % faster with the proposed method.
Starting Page	859
Ending Page	875
Page Count	17
File Format	PDF
ISSN	09210296
Journal	Journal of Intelligent & Robotic Systems
Volume Number	84
Issue Number	1-4
e-ISSN	15730409
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-04-19
Publisher Place	Dordrecht
Access Restriction	Subscribed
Subject Keyword	Cholesky factorisation Factor modification Incremental reordering SLAM Smoothing and mapping Sparse matrices Control, Robotics, Mechatronics Electrical Engineering Artificial Intelligence (incl. Robotics) Mechanical Engineering
Content Type	Text
Resource Type	Article
Subject	Industrial and Manufacturing Engineering Artificial Intelligence Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Software

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