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Minimal Solvers for Unsynchronized TDOA Sensor Network Calibration

Burgess, Simon LU ; Kuang, Yubin LU ; Wendeberg, Johannes ; Åström, Karl LU orcid and Schindelhauer, Christian (2014) 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS 2013) p.95-110
Abstract
Calibration of network nodes using only time differences of arrival (TDOA) measurements opens up for interesting applications in wireless ad-hoc sensor networks, e.g. finding the positions of cell phones by only ambient sounds or radio. We present two novel approaches for the problem of self-calibration of network nodes using only TDOA when both receivers and transmitters are unsynchronized. We consider the previously unsolved minimum problem of far field localization in three dimensions, which is to locate four receivers by the signals of nine unknown transmitters, for which we assume that they originate from far away. The first approach, the Ellipsoid TDOA method, is a geometric representation based on the fact that the time differences... (More)
Calibration of network nodes using only time differences of arrival (TDOA) measurements opens up for interesting applications in wireless ad-hoc sensor networks, e.g. finding the positions of cell phones by only ambient sounds or radio. We present two novel approaches for the problem of self-calibration of network nodes using only TDOA when both receivers and transmitters are unsynchronized. We consider the previously unsolved minimum problem of far field localization in three dimensions, which is to locate four receivers by the signals of nine unknown transmitters, for which we assume that they originate from far away. The first approach, the Ellipsoid TDOA method, is a geometric representation based on the fact that the time differences between four receivers characterize an ellipsoid. We calculate by linear least-squares regression the ellipsoid from the observed measurements of nine or more transmitters, by which the constellation of receivers is characterized. In the second approach we propose using linear algebra techniques on the matrix of unsynchronized TDOA measurements, enabling us to solve a set of linear equations for a parametrization of the unknowns. This approach is extended to more than four receivers and nine transmitters in a straightforward manner. In extensive experiments we evaluate and compare both approaches and analyze specific failure modes of the algorithms. Here, we demonstrate that the algorithms are robust to moderate Gaussian measurement noise and that the far field assumption is reasonable if the distance between transmitters and receivers is at least four times the distance between the receivers. In an indoor experiment using sound we reconstruct the microphone positions up to a mean error of 5 cm. (Less)
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
host publication
Lecture Notes in Computer Science
editor
Flocchini, P ; Gao, J ; Kranakis, E and Meyer auf der Heide, F
pages
13 pages
publisher
Springer
conference name
9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS 2013)
conference location
Sophia Antipolis, France
conference dates
2013-09-05 - 2013-09-06
external identifiers
  • scopus:84958248216
ISSN
1611-3349
0302-9743
ISBN
978-3-642-45346-5
DOI
10.1007/978-3-642-45346-5_8
language
English
LU publication?
yes
additional info
The proceedings of ALGOSENSORS 2013 will be published by Springer as a volume of the LNCS series. The workshop ALGOSENSORS 2013 was held as a part of the meeting ALGO 2013, September 2-6, 2013, Sophia Antipolis, France.
id
e77428d3-8201-4cbf-9562-89c8e978d558 (old id 4064631)
alternative location
http://link.springer.com/chapter/10.1007%2F978-3-642-45346-5_8
date added to LUP
2016-04-01 10:07:49
date last changed
2021-08-25 05:01:26
@inproceedings{e77428d3-8201-4cbf-9562-89c8e978d558,
  abstract     = {Calibration of network nodes using only time differences of arrival (TDOA) measurements opens up for interesting applications in wireless ad-hoc sensor networks, e.g. finding the positions of cell phones by only ambient sounds or radio. We present two novel approaches for the problem of self-calibration of network nodes using only TDOA when both receivers and transmitters are unsynchronized. We consider the previously unsolved minimum problem of far field localization in three dimensions, which is to locate four receivers by the signals of nine unknown transmitters, for which we assume that they originate from far away. The first approach, the Ellipsoid TDOA method, is a geometric representation based on the fact that the time differences between four receivers characterize an ellipsoid. We calculate by linear least-squares regression the ellipsoid from the observed measurements of nine or more transmitters, by which the constellation of receivers is characterized. In the second approach we propose using linear algebra techniques on the matrix of unsynchronized TDOA measurements, enabling us to solve a set of linear equations for a parametrization of the unknowns. This approach is extended to more than four receivers and nine transmitters in a straightforward manner. In extensive experiments we evaluate and compare both approaches and analyze specific failure modes of the algorithms. Here, we demonstrate that the algorithms are robust to moderate Gaussian measurement noise and that the far field assumption is reasonable if the distance between transmitters and receivers is at least four times the distance between the receivers. In an indoor experiment using sound we reconstruct the microphone positions up to a mean error of 5 cm.},
  author       = {Burgess, Simon and Kuang, Yubin and Wendeberg, Johannes and Åström, Karl and Schindelhauer, Christian},
  booktitle    = {Lecture Notes in Computer Science},
  editor       = {Flocchini, P and Gao, J and Kranakis, E and Meyer auf der Heide, F},
  isbn         = {978-3-642-45346-5},
  issn         = {1611-3349},
  language     = {eng},
  pages        = {95--110},
  publisher    = {Springer},
  title        = {Minimal Solvers for Unsynchronized TDOA Sensor Network Calibration},
  url          = {http://dx.doi.org/10.1007/978-3-642-45346-5_8},
  doi          = {10.1007/978-3-642-45346-5_8},
  year         = {2014},
}