Minimal Solvers for Unsynchronized TDOA Sensor Network Calibration

We present two novel approaches for the problem of selfcalibration 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.