## Abstract

We present a method for solving the previously unstudied

problem of localizing a set of receivers and directions

from transmitters placed far from the receivers,

measuring unsynchronized time of arrival data. The

same problem is present in node localization of microphone

and antenna arrays. The solution algorithm using

5 receivers and 9 transmitters is extended to the

overdetermined case in a straightforward manner. Degenerate

cases are shown to be when i) the measurement

matrix has rank 4 or less or ii) the directions from

the transmitters to the receivers lie on an intersection

between the unit sphere and another quadric surface.

In simulated experiments we explore how sensitive the

solution is with respect to different degrees of far field

approximations of the transmitters and with respect to

noise in the data. Using real data we get a reconstruction

of the receivers with a relative error of 14%.

problem of localizing a set of receivers and directions

from transmitters placed far from the receivers,

measuring unsynchronized time of arrival data. The

same problem is present in node localization of microphone

and antenna arrays. The solution algorithm using

5 receivers and 9 transmitters is extended to the

overdetermined case in a straightforward manner. Degenerate

cases are shown to be when i) the measurement

matrix has rank 4 or less or ii) the directions from

the transmitters to the receivers lie on an intersection

between the unit sphere and another quadric surface.

In simulated experiments we explore how sensitive the

solution is with respect to different degrees of far field

approximations of the transmitters and with respect to

noise in the data. Using real data we get a reconstruction

of the receivers with a relative error of 14%.

Original language | English |
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Title of host publication | 21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of |

Publisher | IEEE - Institute of Electrical and Electronics Engineers Inc. |

Pages | 2042-2046 |

Number of pages | 5 |

ISBN (Print) | 978-4-9906441-1-6 |

Publication status | Published - 2012 |

Event | 21st International Conference on Pattern Recognition (ICPR 2012) - Tsukuba, Japan Duration: 2012 Nov 11 → 2012 Nov 15 |

### Conference

Conference | 21st International Conference on Pattern Recognition (ICPR 2012) |
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Country/Territory | Japan |

City | Tsukuba |

Period | 2012/11/11 → 2012/11/15 |

### Bibliographical note

The proceedings of ICPR 2012 will in the future be available at IEEE Xplore. The page reference given above refer to the proceedings published on USB by IEEE, and distributed to the participants during the conference.## Subject classification (UKÄ)

- Mathematics

## Keywords

- Unsynchronized Time-of-Arrival
- sensor networks