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Positioning using wave signal measurements is used in several applications,such as GPS systems, structure from sound and Wifi based positioning.Mathematically, such problems require the computation of the positions ofreceivers and/or transmitters as well as time offsets if the devices areunsynchronized. In this paper, we expand the previous state-of-the-art onpositioning formulations by introducing Multiple Offsets Multilateration (MOM),a new mathematical framework to compute the receivers positions withpseudoranges from unsynchronized reference transmitters at known positions.This could be applied in several scenarios, for example structure from soundand positioning with LEO satellites. We mathematically describe MOM,determining how many receivers and transmitters are needed for the network tobe solvable, a study on the number of possible distinct solutions is presentedand stable solvers based on homotopy continuation are derived. The solvers areshown to be efficient and robust to noise both for synthetic and real audiodata.

Multiple Offsets Multilateration: a new paradigm for sensor network calibration with unsynchronized reference nodes