Gain and phase calibration of sensor arrays from ambient noise by cross-spectral measurements fitting

TL;DR

This paper presents a novel method for blind gain and phase calibration of sensor arrays using ambient noise measurements, employing low-rank matrix approximation and proximal algorithms to improve calibration accuracy.

Contribution

It introduces a non-convex least-squares formulation and two efficient algorithms for sensor calibration from ambient noise, avoiding complex setup procedures.

Findings

Calibration accuracy improves with spatial over-sampling.

Proposed algorithms effectively recover sensor gains and phases.

Numerical and experimental results validate the approach.

Abstract

We address the problem of blind gain and phase calibration of a sensor array from ambient noise. The key motivation is to ease the calibration process by avoiding a complex procedure setup. We show that computing the sample covariance matrix in a diffuse field is sufficient to recover the complex gains. To do so, we formulate a non-convex least-square problem based on sample and model covariances. We propose to obtain a solution by low-rank matrix approximation, and two efficient proximal algorithms are derived accordingly. The first one solves the problem modified with a convex relaxation to guarantee that the solution is a global minimizer, and the second one directly solves the initial non-convex problem. We investigate the efficiency of the proposed algorithms by both numerical and experimental results according to different sensing configurations. These show that efficient calibration highly depends on how the measurements are correlated. That is, estimation is achieved more accurately when the field is spatially over-sampled.