A Unifying Approach to Minimal Problems in Collinear and Planar TDOA Sensor Network Self-Calibration

Abstract:
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 ultrasound) 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.