Localizing Unsynchronized Sensors with Unknown Sources

TL;DR

This paper introduces a novel method for localizing sensor arrays with unknown source positions and timing, directly estimating array geometry without prior timing information, and demonstrating superior accuracy and efficiency.

Contribution

The proposed approach uniquely recovers sensor array geometry directly from signals without estimating timing, using a new timing-insensitive loss function and semidefinite relaxation.

Findings

Achieves state-of-the-art accuracy in sensor localization

Works efficiently with few sources and receivers

Handles missing data and incorporates prior knowledge

Abstract

We propose a method for sensor array self-localization using a set of sources at unknown locations. The sources produce signals whose times of arrival are registered at the sensors. We look at the general case where neither the emission times of the sources nor the reference time frames of the receivers are known. Unlike previous work, our method directly recovers the array geometry, instead of first estimating the timing information. The key component is a new loss function which is insensitive to the unknown timings. We cast the problem as a minimization of a non-convex functional of the Euclidean distance matrix of microphones and sources subject to certain non-convex constraints. After convexification, we obtain a semidefinite relaxation which gives an approximate solution; subsequent refinement on the proposed loss via the Levenberg-Marquardt scheme gives the final locations. Our method achieves state-of-the-art performance in terms of reconstruction accuracy, speed, and the ability to work with a small number of sources and receivers. It can also handle missing measurements and exploit prior geometric and temporal knowledge, for example if either the receiver offsets or the emission times are known, or if the array contains compact subarrays with known geometry.