A complete characterization and solution to the microphone position self-calibration problem

This paper presents a complete characterization and solution to microphone position self-calibration problem for time-of-arrival (TOA) measurements. This is the problem of determining the positions of receivers and transmitters given all receiver-transmitter distances. Such calibration problems arise in application such as calibration of radio antenna networks, audio or ultra-sound arrays and WiFi transmitter arrays. We show for what cases such calibration problems are well-defined and derive efficient and numerically stable algorithms for the minimal TOA based self-calibration problems. The proposed algorithms are non-iterative and require no assumptions on the sensor positions. Experiments on synthetic data show that the minimal solvers are numerically stable and perform well on noisy data. The solvers are also tested on two real datasets with good results.