Calibration-free bearing estimation for arrays with randomly perturbed sensor locations

Calibration-free bearing estimation algorithms for linearly periodic arrays with the presence of sensor positioning errors are investigated. The Toeplitz approximation method (TAM) is used to cope with the two-dimensional (2-D) sensor positioning errors which are assumed to be independent identically distributed and Gaussian in each dimension. After a Toeplitz covariance matrix is reconstructed by the TAM, the eigenstructure-based bearing estimation algorithms, such as MUSIC, can be used as though the array were linear and equally spaced without using any calibration process. To improve the effectiveness of the TAM, a modification for TAM is described. Several examples are provided to illustrate the effectiveness of the proposed methods