ILA Viorela S., POLOK Lukáš, SMRŽ Pavel, ŠOLONY Marek and ZEMČÍK Pavel. Incremental Cholesky Factorization for Least Squares Problems in Robotics. In: Proceedings of The 2013 IFAC Intelligent Autonomous Vehicles Symposium. Gold Coast: IEEE Computer Society, 2013, pp. 18. ISBN 9783902823366. Available from: http://www.sciencedirect.com/science/article/pii/S1474667015349284 
Publication language:  english 

Original title:  Incremental Cholesky Factorization for Least Squares Problems in Robotics 

Title (cs):  Inkrementální Choleského faktorizace pro řešení problémů typu nejmenších čtverců pro robotické aplikace 

Pages:  18 

Proceedings:  Proceedings of The 2013 IFAC Intelligent Autonomous Vehicles Symposium 

Conference:  The 2013 IFAC Intelligent Autonomous Vehicles Symposium 

Place:  Gold Coast, AU 

Year:  2013 

URL:  http://www.sciencedirect.com/science/article/pii/S1474667015349284 

ISBN:  9783902823366 

DOI:  10.3182/201306263AU2035.00027 

Publisher:  IEEE Computer Society 

Files:  


Keywords 

Robotics, Least squares problems, SLAM, Incremental solvers 
Annotation 

The paper proposes a novel efficient incremental solution to least squares problems, with focus on the use in robotic applications, especially the simultaneous location an mapping problem. The results are very good, the proposed method significantly outperforms all the major state of the art implementations. 
Abstract 

Online applications in robotics, computer vision, and computer graphics rely on eciently solving the associated nolinear systems every step. Iteratively solving the nonlinear system every step becomes very expensive if the size of the problem grows. This can be mitigated by incrementally updating the linear system and changing the linearization point only if needed. This paper proposes an incremental solution that adapts to the size of the updates while keeping the error of the estimation low. The implementation also differs form the existing ones in the way it exploits the block structure of such problems and offers efficient solutions to manipulate block matrices within incremental nonlinear solvers. In this work, in particular, we focus our effort on testing the method on simultaneous localization and mapping (SLAM) applications, but the applicability of the technique remains general. The experimental results show that our implementation outperforms the state of the art SLAM implementations on all tested datasets. 
BibTeX: 

@INPROCEEDINGS{
author = {S. Viorela Ila and Luk{\'{a}}{\v{s}} Polok and
Pavel Smr{\v{z}} and Marek {\v{S}}olony and Pavel
Zem{\v{c}}{\'{i}}k},
title = {Incremental Cholesky Factorization for Least
Squares Problems in Robotics},
pages = {18},
booktitle = {Proceedings of The 2013 IFAC Intelligent Autonomous Vehicles
Symposium},
year = {2013},
location = {Gold Coast, AU},
publisher = {IEEE Computer Society},
ISBN = {9783902823366},
doi = {10.3182/201306263AU2035.00027},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=10347}
} 