Robust air velocity estimation based on iterative implementation of Minimum Mean-Square Error (MMSE)

The problem of transonic air velocity estimation based on acoustic sensor array is addressed. According to the propagation property of acoustic waves transmitted in subsonic or supersonic air current, an observation model of linearly acoustic sensor array is established for a given measuring equipment. Then, a robust air velocity estimator, abbreviated as II-MMSE, is proposed based on the iterative implementation of Minimum Mean-Square Error (MMSE) criterion. As a sparse estimation method, II-MMSE takes account of the noise covariance information in the array observation data in a natural manner, thus it does not require the users to make any choice of hyperparameters. Additionally, the II-MMSE technique is computationally more efficient than the generally hyperparametric sparse estimation methods, and it yields good robustness to limited snapshots and array modeling errors. Simulations are implemented to show the efficacy of II-MMSE.