Fast implementation of sparse iterative covariance-based estimation for source localization

Fast implementations of the sparse iterative covariance-based estimation (SPICE) algorithm are presented for source localization with a uniform linear array (ULA). 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 compared to the conventional delay-and-sum beamforming method; however, a traditional SPICE implementation has a higher computational complexity (which is exacerbated in higher dimensional data). It is shown that the computational complexity of the SPICE algorithm can be mitigated by exploiting the Toeplitz structure of the array output covariance matrix using Gohberg-Semencul factorization. The SPICE algorithm is also extended to the acoustic vector-sensor ULA scenario with a specific nonuniform white noise assumption, and the fast implementation is developed based on the block Toeplitz properties of the array output covariance matrix. Finally, numerical simulations illustrate the computational gains of the proposed methods.