IAA spectral estimation: Fast implementation using the Gohberg-Semencul factorization

We consider a fast implementation of the weighted least-squares based iterative adaptive approach (IAA) for spectral estimation of uniformly sampled sequences. IAA is a robust, user parameter-free and nonparametric adaptive algorithm that can work with a single data sequence or snapshot. Compared with the conventional periodogram, IAA can be used to significantly increase the resolution and suppress the sidelobe levels. However, due to its high computational complexity, IAA can only be used in applications with short data sequences. We present herein a novel fast implementation of IAA using a Gohberg-Semencul (G-S)-type factorization of the IAA covariance matrix. By exploiting the Toeplitz structure of the said matrix, we are able to reduce the computational cost by two orders of magnitudes even for sequences with moderate lengths.