Localizing Unsynchronized Sensors With Unknown Sources

• Published in: IEEE transactions on signal processing Vol. 71; pp. 641 - 654
• Main Authors: Badawy, Dalia El, Larsson, Viktor, Pollefeys, Marc, Dokmanic, Ivan
• Format: Journal Article
• Language: English
• Published: New York IEEE 2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: array signal processing; calibration; convex optimzation; Electrical Engineering, Electronic Engineering, Information Engineering; Elektroteknik och elektronik; Emission; Engineering and Technology; Euclidean geometry; Geometry; Localization; Location awareness; Microphones; Optimization; Receivers; Sensor arrays; Sensors; Signal Processing; Signalbehandling; Synchronization; Teknik; wireless sensor networks
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2023.3245284

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.