# UNDERSTANDING TOA AND TDOA NETWORK CALIBRATION USING FAR FIELD APPROXIMATION AS INITIAL ESTIMATE

### Yubin Kuang, Erik Ask, Simon Burgess, Kalle Åström

#### Abstract

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.

#### References

- Birchfield, S. T. and Subramanya, A. (2005). Microphone array position calibration by basis-point classical multidimensional scaling. IEEE transactions on Speech and Audio Processing, 13(5).
- Biswas, R. and Thrun, S. (2004). A passive approach to sensor network localization. In IROS 2004.
- Chen, J. C., Hudson, R. E., and Yao, K. (2002). Maximum likelihood source localization and unknown sensor location estimation for wideband signals in the nearfield. IEEE transactions on Signal Processing, 50.
- Elnahrawy, E., Li, X., and Martin, R. (2004). The limits of localization using signal strength. In SECON-04.
- Niculescu, D. and Nath, B. (2001). Ad hoc positioning system (aps). In GLOBECOM-01.
- Pollefeys, M. and Nister, D. (2008). Direct computation of sound and microphone locations from timedifference-of-arrival data. In Proc. of International Conference on Acoustics, Speech and Signal Processing.
- Raykar, V. C., Kozintsev, I. V., and Lienhart, R. (2005). Position calibration of microphones and loudspeakers in distributed computing platforms. IEEE transactions on Speech and Audio Processing, 13(1).
- Sallai, J., Balogh, G., Maroti, M., and Ledeczi, A. (2004). Acoustic ranging in resource-constrained sensor networks. In eCOTS-04.
- Stewénius, H. (2005). Gröbner Basis Methods for Minimal Problems in Computer Vision. PhD thesis, Lund University.
- Thrun, S. (2005). Affine structure from sound. In Proceedings of Conference on Neural Information Processing Systems (NIPS), Cambridge, MA. MIT Press.

#### Paper Citation

#### in Harvard Style

Kuang Y., Ask E., Burgess S. and Åström K. (2012). **UNDERSTANDING TOA AND TDOA NETWORK CALIBRATION USING FAR FIELD APPROXIMATION AS INITIAL ESTIMATE** . In *Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,* ISBN 978-989-8425-99-7, pages 590-596. DOI: 10.5220/0003793305900596

#### in Bibtex Style

@conference{icpram12,

author={Yubin Kuang and Erik Ask and Simon Burgess and Kalle Åström},

title={UNDERSTANDING TOA AND TDOA NETWORK CALIBRATION USING FAR FIELD APPROXIMATION AS INITIAL ESTIMATE},

booktitle={Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,},

year={2012},

pages={590-596},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003793305900596},

isbn={978-989-8425-99-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,

TI - UNDERSTANDING TOA AND TDOA NETWORK CALIBRATION USING FAR FIELD APPROXIMATION AS INITIAL ESTIMATE

SN - 978-989-8425-99-7

AU - Kuang Y.

AU - Ask E.

AU - Burgess S.

AU - Åström K.

PY - 2012

SP - 590

EP - 596

DO - 10.5220/0003793305900596