Understanding TOA and TDOA Network Calibration using Far Field Approximation as Initial Estimate

Yubin Kuang, Erik Ask, Simon Burgess, Karl Åström

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Sammanfattning

This paper presents a study of the so called far field approximation to the problem of determining both the direction to a number of transmittors and the relative motion of a single antenna using relative distance measurements. The same problem is present in calibration of microphone and wifi-transmittor arrays. In the far field approximation we assume that the relative motion of the antenna is small in comparison to the distances to the base stations. The problem can be solved uniquely with at least three motions of the antenna and at least six real or virtual transmittors. The failure modes of the problem is determined to be (i) when the antenna motion is planar or (ii) when the transmittor directions lie on a cone. We also study to what extent the solution can be obtained in these degenerate configurations. The solution algorithm for the minimal case can be extended to the overdetermined case in a straightforward manner. We also implement and test algorithms for non-linear optimization of the residuals. In experiments we explore how sensitive the calibration is with respect to different degrees of far field approximations of the transmittors and with respect to noise in the data.
Originalspråkengelska
Titel på värdpublikationICPRAM 2012 - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods, Volume 2
FörlagSciTePress
Sidor590-596
Antal sidor7
ISBN (tryckt)978-9-898425-99-7
StatusPublished - 2012
Evenemang1st International Conference on Pattern Recognition Applications and Methods (IPCRAM 2012) - Vilamoura, Algarve, Portugal
Varaktighet: 2012 feb. 62012 feb. 8

Konferens

Konferens1st International Conference on Pattern Recognition Applications and Methods (IPCRAM 2012)
Land/TerritoriumPortugal
OrtVilamoura, Algarve
Period2012/02/062012/02/08

Ämnesklassifikation (UKÄ)

  • Matematik

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