Self-Calibration of Acoustic Scalar and Vector Sensor Arrays

In this work, we consider the self-calibration problem of joint calibration and direction-of-arrival (DOA) estimation using acoustic sensor arrays. Unlike many previous iterative approaches, we propose solvers that can be readily used for both linear and non-linear arrays for jointly estimating the sensor gain, phase errors, and the source DOAs. We derive these algorithms for both the conventional element-space and covariance data models. We focus on sparse and regular arrays formed using scalar sensors as well as vector sensors. The developed algorithms are obtained by transforming the underlying non-linear calibration model into a linear model, and subsequently by using convex relaxation techniques to estimate the unknown parameters. We also derive identifiability conditions for the existence of a unique solution to the self-calibration problem. To demonstrate the effectiveness of the developed techniques, numerical experiments, and comparisons to the state-of-the-art methods are provided. Finally, the results from an experiment that was performed in an anechoic chamber using an acoustic vector sensor array are presented to demonstrate the usefulness of the proposed self-calibration techniques.

Automated summary

In this work, the self-calibration problem of joint calibration and direction-of-arrival (DOA) estimation using acoustic sensor arrays is addressed. Novel solvers are proposed for both linear and non-linear arrays, capable of estimating the sensor gain, phase errors, and the source DOAs. The algorithms are derived for conventional element-space and covariance data models and are applicable to both sparse and regular arrays formed using scalar and vector sensors. Identifiability conditions for a unique solution are derived, and numerical experiments and comparisons are provided to demonstrate the effectiveness of the developed techniques. Experimental results using an acoustic vector sensor array in an anechoic chamber further showcase the usefulness of the proposed self-calibration techniques.