Fast implementation of sparse iterative covariance-based estimation for array processing

Fast implementations of the SParse Iterative Covariance-based Estimation (SPICE) algorithm are presented for source localization in passive sonar applications. SPICE is a robust, user parameter-free, high-resolution, iterative and globally convergent estimation algorithm for array processing. SPICE offers superior resolution and lower sidelobe levels for source localization at the cost of a higher computational complexity compared to the conventional delay-and-sum beamforming method. It is shown in this paper that the computational complexity of the SPICE algorithm can be reduced by exploiting the Toeplitz structure of the array output covariance matrix using the Gohberg-Semencul factorization. The fast implementations for both the hydrophone uniform linear array (ULA) and the vector-sensor ULA scenarios are proposed and the computational gains are illustrated by numerical simulations.