Joint Calibration and Synchronization of Two Arrays of Microphones and Loudspeakers Using Particle Swarm Optimization

Abstract

This work presents a methodology for the joint calibration and synchronization of two arrays of microphones and loudspeakers. The problem is modeled as estimation of the rigid motion of one array with respect to the other, as well as estimation of the synchronization mismatch between the two. The proposed method uses dedicated signals emitted by the loudspeakers of the two arrays to compute a set of time of arrival (TOA) estimates. Through a simple transformation, estimated TOAs are converted into a set of linearly independent time difference of arrival (TDOA) measurements, which are modeled by a system of nonlinear equations in the unknown parameters of interest. A maximum likelihood estimate is then given as the solution to a nonlinear weighted least squares (NWLS) problem, which is optimized applying a parallelizable variant of Particle Swarm Optimization (PSO). In this paper, we also derive the Cramér-Rao lower bound (CRLB), and benchmark it against the proposed method in a series of Monte Carlo (MC) simulations. Results show that the proposed method attains high-performance comparable to the CRLB.

Closed-Form Solution for Scaling a Wireless Acoustic Sensor Network

“…The undefined variables in (20) can be found upon substitution of the noisy measurements in (14) with their corresponding right-hand side equivalents in ( 2) and (11). Then, applying the approximation in (13) and simplifying, we get…”

“…Their method would estimate Direction of Arrival (DOA) measurements between emitter and sensor array nodes followed by applying Artificial Bee Colony (ABC) optimization to find the locations of the sensors. Recently, Kovalyov et al [13] proposed a method for joint localization and synchronization of two arrays of sensors and emitters by gathering TOA measurements between each sensor and emitter followed by applying particle swarm optimization (PSO) to find orientation, translation and synchronization parameters of one array with respect to the other. Active calibration methods generally attain high performance.…”

Closed‐form solution for scaling a wireless acoustic sensor network

“…Related work includes refs. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In [9], Haddad et al propose a robust time-of-arrival (TOA) estimation algorithm along with a least-square (LS) error minimisation technique for localising an acoustic sensor in a reverberant environment.…”

“…The objective is to both provide an efficient means to scale a WASN as new sensors join the network and a means to add individual sensors, which may not include a builtin emitter.Related work includes refs. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In [9], Haddad et al propose a robust time-of-arrival (TOA) estimation algorithm along with a least-square (LS) error minimisation technique for localising an acoustic sensor in a reverberant environment.…”

“…In the more popular active methods, individual WASN nodes include an emitter device that generates a dedicated signal whenever network calibration is performed. Related work includes [12][13][14][15][16][17]. The 'BeepBeep' system, proposed by Peng et al in [12], provides a method to estimate the range between two asynchronous devices.…”