Asymptotically Optimal Blind Calibration of Acoustic Vector Sensor Uniform Linear Arrays

We study the blind calibration problem of uniform linear arrays of acoustic vector sensors for narrowband Gaussian signals, and propose an improved, asymptotically optimal blind calibration scheme. Following recent work by Ramamohan et al., we exploit the special (block-Toeplitz) structure of the underlying signals’ spatial covariance matrix. However, we offer a substantial improvement over their ordinary Least Squares (LS)-based approach: Using asymptotic approximations we obtain Optimally-Weighted LS estimates of the sensors’ gains and phases offsets. We show via simulations that our estimates exhibit near-optimal performance, with improvements reaching more than an order of magnitude in the mean squared estimation errors of the calibration parameters, as well as in directions of-arrival estimation.