Self Calibration of Scalar and Vector Sensor Arrays

TL;DR

This paper introduces geometry independent convex optimization algorithms for joint calibration and DOA estimation in scalar and vector sensor arrays, improving accuracy and robustness over iterative methods.

Contribution

It proposes novel convex optimization algorithms for self calibration that are independent of array geometry, applicable to both scalar and vector sensors, and derives conditions for unique solutions.

Findings

Algorithms outperform state-of-the-art methods in simulations.

Effective calibration demonstrated in an anechoic chamber experiment.

Provides identifiability conditions for the calibration problem.

Abstract

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.