  In this work, we consider the problem of joint calibration and
direction-of-arrival (DOA) estimation using sensor arrays. This joint
estimation problem is referred to as self calibration. Unlike many previous
iterative approaches, we propose geometry independent convex optimization
algorithms for jointly estimating the sensor gain and phase errors as well as
the source DOAs. We derive these algorithms based on both the conventional
element-space data model and the covariance data model. 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 bilinear
calibration model into a linear model, and subsequently by using standard
convex relaxation techniques to estimate the unknown parameters. Prior to the
algorithm discussion, 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.
