Closed-form solutions for robust acoustic sensor localization

Abstract

This paper deals with the localization of acoustic sensors based on signals emitted by loudspeakers at known positions. In particular, a model for distortions in time-of-flight (TOF) estimates applicable to the sensor localization problem is presented along with closed-form solutions with low computational cost. The proposed techniques are able to approximate the sensor position even when the TOFs are corrupted by an unknown delay, there is a sampling frequency mismatch between the A/D and D/A converters associated with sensor and loudspeakers, and the speed of sound is unknown. Simulations and an experiment on real data demonstrate that the proposed methods are able to estimate sensor positions with less than 2 cm of error in the evaluated scenarios.

A Survey of Sound Source Localization Methods in Wireless Acoustic Sensor Networks

“…Consider a set of different microphones capturing the signal arriving from a sound source located at a spatial position x ∈ R 3 in an anechoic scenario, following the model of (20). The SRP is defined as the output power of a filter-and-sum beamformer steered to a given spatial location.…”

“…Some state-of-the-art solutions for acoustic sensor localization detail the challenges facing these algorithms and methods to tackle such problems in a unified context [20,21]. Furthermore, recent methodologies have been proposed for probe signal design aimed at improving TOF estimation [22], the joint localization of sensors and sources in an ad hoc array by using low-rank approximation methods [23], and an iterative peak matching algorithm for fast node autocalibration [24].…”

Acoustic Sensor Self-Localization: Models and Recent Results

“…The concise approach adopted here provides beginners with a glimpse of the main problems and solutions in the ASL field. Experienced researchers can also benefit from the unified approach covering recent ideas that are not standard in the area, as the ones described in [22][23][24]. In fact, many research opportunities may open up thanks to the unified way ASL problems and related solutions are described here.…”

“…In what follows, the TOF-based LS method known as T and the TDOF-based LS method known as D proposed in [22,23] are described.…”

“…Using the common assumption that the highest CCF/GCC peak (or, equivalently, the highest coefficient extracted by the MP method) is often related to the desired TOF, a reasonable strategy consists of using the highest coefficients obtained by the MP as a preliminary starting point for the set of estimated TOFs. This set cannot be directly used to infer the sensor location with LS techniques (like T or D ) because such techniques are very sensitive to TOFs/TDOFs errors [22], and one cannot assure beforehand that the initial set of TOFs is accurate (one may only expect that most of TOF/TDOF information is correct). At this point, the new robust region-based search mechanism-see Section 3.3-that solves the inverse problem of inferring the sensor location from the data by progressively partitioning some candidate regions (i.e., the winner ones) takes place.…”