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

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding


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.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • TOA, TDOA, anchor free, localization, sensor networks
Original languageEnglish
Title of host publicationICPRAM 2012 - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods, Volume 2
Number of pages7
ISBN (Print)978-9-898425-99-7
Publication statusPublished - 2012
Publication categoryResearch
Event1st International Conference on Pattern Recognition Applications and Methods (IPCRAM 2012) - Vilamoura, Algarve, Portugal
Duration: 2012 Feb 62012 Feb 8


Conference1st International Conference on Pattern Recognition Applications and Methods (IPCRAM 2012)
CityVilamoura, Algarve