A unifying approach to minimal problems in collinear and planar TDOA sensor network self-calibration

This work presents a study of sensor network calibration from time-difference-of-arrival (TDOA) measurements for cases when the dimensions spanned by the receivers and the transmitters differ. This could for example be if receivers are restricted to a line or plane or if the transmitting objects are moving linearly in space. Such calibration arises in several applications such as calibration of (acoustic or ultra-sound) microphone arrays, and radio antenna networks. We propose a non-iterative algorithm based on recent stratified approaches: (i) rank constraints on modified measurement matrix, (ii) factorization techniques that determine transmitters and receivers up to unknown affine transformation and (iii) determining the affine stratification using remaining non-linear constraints. This results in a unified approach to solve almost all minimal problems. Such algorithms are important components for systems for self-localization. Experiments are shown both for simulated and real data with promising results.