Superresolution frequency estimation by alternating notch periodogram

A novel periodogram-based maximum-likelihood algorithm is proposed for a frequency estimation problem. It is called an alternating notch-periodogram algorithm (ANPA), since the original multidimensional maximum likelihood problem is decomposed into a sequence of much simpler one-dimensional problems of finding the peaks of notch periodograms. The ANPA achieves superresolution and a very low SNR threshold and can be computed and implemented in several efficient ways. First, with FFT and a concurrent Gram-Schmidt procedure using Schur's recursions, the notch periodogram can be computed without any costly eigendecomposition and matrix inversion. This approach can further lead to a mapping of the notch periodogram onto a VLSI architecture consisting mainly of a highly pipelined notch processor and two FFT processors. Second, without degrading the excellent performance of ANPA, the notch periodogram can be simplified and approximated to provide further computational reduction and implementational simplicity. >