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Registration and Merging Maps with Uncertainties

Larsson, Martin LU orcid ; Åström, Kalle LU orcid and Oskarsson, Magnus LU orcid (2018) 9th International Conference on Indoor Positioning and Indoor Navigation, IPIN 2018
Abstract

In this paper we address the problem of registering and merging two maps in two dimensions, given covariance estimates of the two maps. We show that if two maps are given in the same coordinate system, then the problem of merging them in a statistically optimal way can be formulated as a linear least squares problem, but if they are given in different coordinate systems as well the problem becomes highly non-linear and nonconvex. We show how we can relax the problem slightly in order to optimize over the registration (i.e. putting the two maps in the same coordinate system) and at the same time optimize over the merged map. The approach is based on finding all stationary points of the optimization problem and evaluating these to choose... (More)

In this paper we address the problem of registering and merging two maps in two dimensions, given covariance estimates of the two maps. We show that if two maps are given in the same coordinate system, then the problem of merging them in a statistically optimal way can be formulated as a linear least squares problem, but if they are given in different coordinate systems as well the problem becomes highly non-linear and nonconvex. We show how we can relax the problem slightly in order to optimize over the registration (i.e. putting the two maps in the same coordinate system) and at the same time optimize over the merged map. The approach is based on finding all stationary points of the optimization problem and evaluating these to choose the global optimum. We show on synthetic data that in many cases the proposed approach gives better results than naively registering and merging the maps. We also show results on real data, where we merge maps given by time-of-arrival measurements, and in these cases simpler linear methods perform just a good as the proposed method.

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Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
covariance, mapping, merging, rigid registration, SLAM, time-of-arrival
host publication
IPIN 2018 - 9th International Conference on Indoor Positioning and Indoor Navigation
article number
8533782
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
9th International Conference on Indoor Positioning and Indoor Navigation, IPIN 2018
conference location
Nantes, France
conference dates
2018-09-24 - 2018-09-27
external identifiers
  • scopus:85059058906
ISBN
9781538656358
DOI
10.1109/IPIN.2018.8533782
language
English
LU publication?
yes
id
ee2b25fe-7564-4d47-817c-a3853c677323
date added to LUP
2019-01-04 13:31:48
date last changed
2022-09-16 03:17:24
@inproceedings{ee2b25fe-7564-4d47-817c-a3853c677323,
  abstract     = {{<p>In this paper we address the problem of registering and merging two maps in two dimensions, given covariance estimates of the two maps. We show that if two maps are given in the same coordinate system, then the problem of merging them in a statistically optimal way can be formulated as a linear least squares problem, but if they are given in different coordinate systems as well the problem becomes highly non-linear and nonconvex. We show how we can relax the problem slightly in order to optimize over the registration (i.e. putting the two maps in the same coordinate system) and at the same time optimize over the merged map. The approach is based on finding all stationary points of the optimization problem and evaluating these to choose the global optimum. We show on synthetic data that in many cases the proposed approach gives better results than naively registering and merging the maps. We also show results on real data, where we merge maps given by time-of-arrival measurements, and in these cases simpler linear methods perform just a good as the proposed method.</p>}},
  author       = {{Larsson, Martin and Åström, Kalle and Oskarsson, Magnus}},
  booktitle    = {{IPIN 2018 - 9th International Conference on Indoor Positioning and Indoor Navigation}},
  isbn         = {{9781538656358}},
  keywords     = {{covariance; mapping; merging; rigid registration; SLAM; time-of-arrival}},
  language     = {{eng}},
  month        = {{11}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Registration and Merging Maps with Uncertainties}},
  url          = {{http://dx.doi.org/10.1109/IPIN.2018.8533782}},
  doi          = {{10.1109/IPIN.2018.8533782}},
  year         = {{2018}},
}