Abstract
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 uses that the time differences between four receivers characterize an ellipsoid. The second approach uses linear algebra techniques on the matrix of unsynchronized TDOA measurements. This approach is easily extended to more than four receivers and nine transmitters. In extensive experiments, the algorithms are shown to be robust to moderate Gaussian measurement noise and 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.
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Acknowledgements
The research leading to these results has received funding from the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) within the Research Training Group 1103 (Embedded Microsystems), the strategic research projects ELLIIT and eSSENCE, and Swedish Foundation for Strategic Research projects ENGROSS and VINST (grants no. RIT08-0075 and RIT08-0043).
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Burgess, S., Kuang, Y., Wendeberg, J., Åström, K., Schindelhauer, C. (2014). Minimal Solvers for Unsynchronized TDOA Sensor Network Calibration . In: Flocchini, P., Gao, J., Kranakis, E., Meyer auf der Heide, F. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2013. Lecture Notes in Computer Science(), vol 8243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45346-5_8
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