In this paper, the focus is on the gain and phase calibration of sparse sensor arrays to localize more sources than the number of physical sensors. The proposed technique is a blind calibration method as it does not require any calibrator sources. Joint estimation of the gain errors, phase errors, and source directions is a complicated non-convex optimization problem, which is transformed into a convex optimization problem by exploiting the underlying algebraic structure. It is shown that the developed solver is suitable for analog as well as one-bit measurements. Numerical experiments based on sparse rulers are provided to illustrate the developed theory.

In this paper, we present a calibration algorithm for acoustic vector sensors arranged in a uniform linear array configuration. To do so, we do not use a calibrator source, instead we leverage the Toeplitz blocks present in the data covariance matrix. We develop linear estimators for estimating sensor gains and phases. Further, we discuss the differences of the presented blind calibration approach for acoustic vector sensor arrays in comparison with the approach for acoustic pressure sensor arrays. In order to validate the proposed blind calibration algorithm, simulation results for direction-of-arrival (DOA) estimation with an uncalibrated and calibrated uniform linear array based on minimum variance distortion less response and multiple signal classification algorithms are presented. The calibration performance is analyzed using the Cramér-Rao lower bound of the DOA estimates.

In this paper, a specific reduced-channel Acoustic Vector Sensor (AVS) is proposed comprising one omni-directional microphone and only one particle velocity transducer, such that it can have an arbitrary orientation. Such a reduced transducer configuration is referred to as a Uniaxial AVS (U-AVS). The DOA performance of an array of U-AVSs is analyzed through its beampattern and compared to conventional configurations. It is shown that the U-AVS array beampattern results in an asymptotically biased estimate of the source location and it can be varied by choosing the orientation angles of the particle velocity transducers. Analytical expressions for the asymptotic bias of classical beamforming are proposed and verified both numerically as well as experimentally for Uniform Linear Arrays (ULAs). Furthermore, the Cramér-Rao Bound (CRB) and Mean Square Error (MSE) expressions are derived for a U-AVS array under a single source scenario and they are numerically evaluated for ULA. The implications of changing the orientations of the U-AVSs in the array on the MSE are discussed as well.

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.