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

TL;DR

This paper introduces Multiple Offsets Multilateration (MOM), a new mathematical framework for sensor network calibration that accurately computes receiver positions using unsynchronized reference nodes, applicable in various positioning scenarios.

Contribution

The paper presents MOM, a novel positioning formulation that handles multiple offsets and unsynchronized nodes, with theoretical analysis and robust solvers based on homotopy continuation.

Findings

MOM can determine receiver positions with minimal reference nodes.

The proposed solvers are efficient and robust to noise.

Experimental results validate MOM's effectiveness on synthetic and real data.

Abstract

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 of receivers and/or transmitters as well as time offsets if the devices are unsynchronized. In this paper, we expand the previous state-of-the-art on positioning formulations by introducing Multiple Offsets Multilateration (MOM), a new mathematical framework to compute the receivers positions with pseudoranges from unsynchronized reference transmitters at known positions. This could be applied in several scenarios, for example structure from sound and positioning with LEO satellites. We mathematically describe MOM, determining how many receivers and transmitters are needed for the network to be solvable, a study on the number of possible distinct solutions is presented and stable solvers based on homotopy continuation are derived. The solvers are shown to be efficient and robust to noise both for synthetic and real audio data.